Investigations of p +Pb Collisions at Perturbative and Non-Perturbative QCD Scales
IInvestigations of p +Pb Collisions at Perturbative and Non-PerturbativeQCD Scales by Kurt Keys Hill
B.A. Physics, University of California Davis, 2011B.S. Mathematics, University of California Davis, 2011A thesis submitted to theFaculty of the Graduate School of theUniversity of Colorado in partial fulfillmentof the requirements for the degree ofDoctor of PhilosophyDepartment of Physics2020is thesis entitled:Investigations of p +Pb Collisions at Perturbative and Non-Perturbative QCD Scaleswritten by Kurt Keys Hillhas been approved for the Department of PhysicsProf. Jamie NagleDennis V. Perepelitsa DateThe final copy of this thesis has been examined by the signatories, and we find that both the content and theform meet acceptable presentation standards of scholarly work in the above mentioned discipline.iiHill, Kurt Keys (Ph.D., Physics)Investigations of p +Pb Collisions at Perturbative and Non-Perturbative QCD ScalesThesis directed by Prof. Jamie NagleHigh energy nuclear collisions manifest a variety of interesting phenomena over a broad range of energyscales. Many of these phenomena are related to the formation of a hot and dense state of deconfined quarks andgluons known as the quark gluon plasma (QGP). Chief among these are the observed near inviscid hydrodynamicexpansion of the QGP, as measured through azimuthal anisotropy coefficients of low- p T final state hadrons v n ,and the loss of energy of high- p T color charges as they traverse the QGP which is observed as a quenching ofstrongly-interacting final state objects like jets. Observations of these phenomena in Au+Au and Pb+Pb collisionsat RHIC and the LHC provide compelling evidence of QGP formation. Small collision systems, like p +Pb,also show evidence for the creation droplets of QGP through the observation of anisotropic flow; however,measurements of high- p T jet and particle spectra show no signs of the energy loss observed in large collisionsystems. Thus, small systems are an ideal venue to explore the relationship between high- and low- p T QGPphenomena. Furthermore, the low ambient energy of p +Pb compared to A+A collisions allow for the precisedetermination of perturbative process rates which can be used to understand the nuclear modification of nucleonparton densities.This dissertation explores 165 nb − of 8.16 TeV p +Pb data collected in 2016 with the ATLAS detectorat the LHC through the exposition of two measurements. The cross section and nuclear modification factorfor prompt, isolated photons are studied over a broad range of transverse energies and rapidities. These re-sults are compared to predictions from perturbative QCD calculations and a model of initial state energy loss.Additionally, the charged hadron azimuthal anisotropy coefficients, v and v , are measured via two-particlecorrelations as a function of particle p T and event centrality. Results are shown from minimum bias events andevents selected because of the presence of a high- p T jet. The elliptic flow coefficient is observed to be non-zerofor . < p T < GeV. These results are discussed in the context of hydrodynamic and energy loss models. edication
For Margarite. Thank you for accompanying me on this journey. I know I would not be here withoutyou.
Acknowledgements
First, I would like to acknowledge my advisors at CU for structuring an open and respectful environmentin which to learn, collaborate, and work. I am grateful that I landed in this group; this effort might have seemedinsurmountable had the lab not been such an enjoyable and stimulating place to be. To my advisor Jamie Nagle,thank you for your leadership, honesty, and compassion, and for teaching me to keep the greater context in sight.To my advisor Dennis Perepelitsa, thank you for the enthusiasm and curiosity you brought to the group. It wastruly difficult to not be excited when working with you. Thank you for mentoring and including me.I would like to highlight the support and guidance I received from the wonderful students and postdocs inthe group. To Qipeng Hu and Sanghoon Lim, it was such a pleasure collaborating with and learning from you.Thank you for your strong technical and intellectual support on the high p T flow result. I will always rememberour problem solving sessions fondly. To Darren McGlinchey and Ron Belmont, thank you for teaching andenduring me as I became more independent. Thank you for mentoring me on PHENIX. Thank you JavierOrjuela Koop and Theo Koblesky for bringing me up to speed. Thanks to Javier in particular for sharing hisgraphic design sensibilities and vast institutional knowledge of student life at CU. Thank you Blair Seidliz andJeff Ouellette for companionship while exploring the world of ATLASI would also like to thank my collaborators on ATLAS for keeping such an amazing piece of machineryrunning. Particularly, I thank my friends in ATLAS heavy ions that have been crucial support for the workpresented here: Peter Steinberg, Zvi Citron, Iwona Grabowska-Bold, Sasha Milov, Anne Sickles, Soumya Mo-hapatra, Aaron Angerami, Brian Cole, Martin Spousta, Martin Rybar, and Jiangyong Jia. Thank you WitoldKozanecki and Richard Hawkings for your help and guidance with the 2016 p +Pb luminosity length scale cali-bration.iI want to acknowledge some of my mentors and educators that introduced me to this path. To myundergrad advisors Manuel Calderón and Daniel Cebra, thank you for introducing me to heavy ions and physicsresearch in general. Thank you for taking me on and giving me a chance; I would not have considered gradschool without that exposure. Thank you Rosi Reed for bringing me up to speed when I knew nothing. Thankyou to my instructors Larry Green and Bruce Armbrust at LTCC for introducing me to math and physics duringa particularly formative time in my life. Thank you Bruce for stepping up to teach the physics sequence whenthey almost canceled the program.Finally I would like to offer my deepest gratitude to my family. Thank you for giving me the foundationof love and determination on which my education rests. To my parents, thank you for your open minds andhearts throughout my continued upbringing. You are the most generous people in my life, and I only hope Ican live up to your example. To Christine, I have always admired your moral character. Thank you for teachingme strength, leadership, and humor. It was always easier following in your footsteps. To Grammy, thank youfor your love and friendship. Thank you for teaching me to appreciate the value of craftsmanship. To Marcus,you have always inspired me with your determination and commitment. Thank you for always pushing to getout there. To Rick and Susan, thank you for your love and support. Thank you for distracting me from physicswith style and art and refining my ability to have a good time. To Karen, Holly, and Emma, it is such a pleasurehaving you in my life. Thank you for being there for me, especially during my time at Brookhaven.ii Contents
Chapter1
Introduction Ultra-Relativistic Heavy Ion Collisions The Experiment Centrality Determination (cid:104) N part (cid:105) and (cid:104) T AB (cid:105) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804.6.3 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Measurement of Direct Photon Production R p Pb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1165.5.1 pp Reference Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1165.6 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1185.6.1 Cross-Section Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195.6.2 R p Pb Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Results of the Measurement of Direct Photon Production R p Pb Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Measurement of Azimuthal Anisotropy Results of the Measurement of Azimuthal Anisotropy p +Pb and Pb+Pb Data . . . . . . . . . . . . . . . . . . . . . . . . . . 1858.3 Particle Pair Yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 Conclusions
Measurement of Direct Photon Spectra
A.1 MC Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193A.2 Cross section calculation data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196A.3 P- Efficiency data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198A.4 P- Purity data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203A.5 Total systematic uncertainty data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205A.6 P- S comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208A.6.1 Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208iA.6.2 Leakages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208A.7 Shower shape comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211A.8 Photon Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 B Measurement of Azimuthal Anisotropy
B.1 Multiplicity Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238B.2 Systematic uncertainties in v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243B.2.1 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243B.2.2 Signal extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243B.2.3 Jet selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245B.3 Systematic uncertainties in v vs. centrality . . . . . . . . . . . . . . . . . . . . . . . . . . . 248B.3.1 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248B.3.2 Signal extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248B.3.3 Jet selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248B.3.4 Signal extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248B.4 Template fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253B.5 Track φ flattening maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262ii Tables
Table Σ E Pb T data > 10 GeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.2 Summary of fits to Σ E Pb T data > 5 GeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.3 Summary of fits to Σ E Pb T data > 5 GeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.4 Summary of mean N part values for Glauber and Glauber-Gribov for each centrality class. . . . 814.5 Summary of mean T AB values for Glauber and Glauber-Gribov for each centrality class. . . . . 815.1 Photon triggers used in analysis, with the corresponding offline E γ T range where they are used,and sampled luminosities in both running periods. . . . . . . . . . . . . . . . . . . . . . . . 897.1 Triggers used in analysis, with the sampled luminosities in both running periods. . . . . . . . . 142A.1 Overview of P MC simulation samples used in this analysis. . . . . . . . . . . . . . . . . 194A.2 Overview of S MC simulation samples used in this analysis. . . . . . . . . . . . . . . . . 195A.3 Table of components in the N sigA calculation in center of mass rapidity range (1 . < η ∗ < . . Yields are each quoted after prescale correction . . . . . . . . . . . . . . . . . . . . . . 196A.4 Table of components in the N sigA calculation in center of mass rapidity range ( − . < η ∗ < . . Yields are each quoted after prescale correction . . . . . . . . . . . . . . . . . . . . . . 196iiiA.5 Table of components in the N sigA calculation in center of mass rapidity range ( − . < η ∗ < − . . Yields are each quoted after prescale correction . . . . . . . . . . . . . . . . . . . . . 197A.6 Table of efficiency values in period A in center of mass rapidity range (1 . < η ∗ < . . . . . 198A.7 Table of efficiency values in period B in center of mass rapidity range (1 . < η ∗ < . . . . . 198A.8 Table of efficiency values in from both running periods as the luminosity weighted average incenter of mass rapidity range (1 . < η ∗ < . . . . . . . . . . . . . . . . . . . . . . . . . 199A.9 Table of efficiency values in period A in center of mass rapidity range (0 . < η ∗ < − . . . . 199A.10 Table of efficiency values in period B in center of mass rapidity range (0 . < η ∗ < − . . . . 200A.11 Table of efficiency values in from both running periods as the luminosity weighted average incenter of mass rapidity range (0 . < η ∗ < − . . . . . . . . . . . . . . . . . . . . . . . . 200A.12 Table of efficiency values in period A in center of mass rapidity range ( − . < η ∗ < − . . . 201A.13 Table of efficiency values in period B in center of mass rapidity range ( − . < η ∗ < − . . . 201A.14 Table of efficiency values in from both running periods as the luminosity weighted average incenter of mass rapidity range ( − . < η ∗ < − . . . . . . . . . . . . . . . . . . . . . . . 202A.15 Table of inputs for the purity calculation for the forward-rapidity bin, showing raw sidebandyields N X , sideband leakage fractions from MC f X , and the final purity with asymmetricalerrors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203A.16 Table of inputs for the purity calculation for the mid-rapidity bin, showing raw sideband yields N X , sideband leakage fractions from MC f X , and the final purity with asymmetrical errors. . . 203A.17 Table of inputs for the purity calculation for the backward-rapidity bin, showing raw sidebandyields N X , sideband leakage fractions from MC f X , and the final purity with asymmetricalerrors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204A.18 Table of components of the total systematic uncertainty on the cross section shown as percentsfor each p T bin in center of mass rapidity range (0 . < η ∗ < − . . . . . . . . . . . . . . . 205A.19 Table of components of the total systematic uncertainty on the cross section shown as percentsfor each p T bin in center of mass rapidity range (0 . < η ∗ < − . . . . . . . . . . . . . . . 205ivA.20 Table of components of the total systematic uncertainty on the cross section shown as percentsfor each p T bin in center of mass rapidity range ( − . < η ∗ < − . . . . . . . . . . . . . . 206A.21 Table of components of the total systematic uncertainty on R p Pb shown as percents for each p T bin in center of mass rapidity range (0 . < η ∗ < − . . . . . . . . . . . . . . . . . . . . . 206A.22 Table of components of the total systematic uncertainty on R p Pb shown as percents for each p T bin in center of mass rapidity range (0 . < η ∗ < − . . . . . . . . . . . . . . . . . . . . . 206A.23 Table of components of the total systematic uncertainty on R p Pb shown as percents for each p T bin in center of mass rapidity range ( − . < η ∗ < − . . . . . . . . . . . . . . . . . . . . 207A.24 Table of components of the total systematic uncertainty for the forward-to-backward R p Pb ratioshown as percents for each p T bin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207v Figures
Figure α s as a function of momentum transfer Q [1]. . . . . . . . . 102.3 A summary of hadron mass calculations from LQCD (colored points), overlaid with measure-ments from world data (black lines) [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4 The cross section ratio, R, of σ ( e + e − → hadrons) to that of σ ( e + e − → µ + µ − ) as a func-tion of momentum scale from world data (points) compared to a naive quark and color scalingmodel [41]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5 A graphical representation of the Lund string fragmentation model. The left figure shows theFeynman diagram of the e + e − → q ¯ q process, and the right plot shows the space-time diagramof the fragmentation [44]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.6 A comparison between k t (left) and anti- k t (right) jet reconstruction algorithm performanceusing an event generated with few hard fragments and many random soft “ghost” particles [45]. 162.7 Diagram of a DIS process [48]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.8 Proton structure function, F , for various Q and x values as measured in DIS experiments [1]. 182.9 Proton PDFs from global fits to world data as a function of parton x for momentum scales GeV (a) and GeV (b) [1, 53]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.10 Proton nPDFs from global fits to world data as a function of parton x for momentum scale GeV. The results are presented as the ratio of PDFs in Pb nuclei to those from free protonsfor valence quarks, left, sea quarks, middle, and gluons, right [58]. . . . . . . . . . . . . . . . 21vi2.11 Temperature dependent pressure, energy, and entropy densities of quark matter from latticesimulations [63]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.12 A qualitative description of the QCD phase diagram for any given temperature and net baryondensity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.13 An illustration of centrality as measured with mid-rapidity charged particle multiplicity [7]. . . 262.14 An example of a Pb+Pb collision from the PHOBOS MC Glauber simulation [67]. The nucleonsare represented as circles, where their color marks which nucleus they originate from. The closedcircles are participating nucleons and the dashed circles are spectating nucleons. . . . . . . . . 262.15 N part distributions from p +Pb collisions from the PHOBOS MC Glauber simulation [67]. Theblack points are from the standard Glauber implementation, and the blue and red points arefrom the Glauber-Gribov extension with two different values of the fluctuation parameter Ω . . 272.16 Left:
The p T spectrum of charged hadrons from 200 GeVAu+Au collisions measured with a va-riety of RHIC experiments. The data is overlaid with theoretical calculations from both hy-drodynamics and pQCD [6]. Right:
The p T spectrum of identified charged hadrons from2.76 GeVPb+Pb collisions. The data is overlaid with theoretical calculations from the VISHNUhydrodynamic model [77]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.17 Distribution of 2-particle correlations in ∆ η and ∆ φ from 30-40% central Pb+Pb collisions at √ s NN = 5 . TeV [80]. Both particles are required to have p T = 2 − GeV. . . . . . . . . . 342.18 Elliptic flow v as a function of centrality from the event-plane method, 2- and 4-particle cor-relations, and Lee-Yang zeros methods √ s NN [81]. . . . . . . . . . . . . . . . . . . . . . . . 352.19 Coefficients v n from the EP method from 30-40% central Pb+Pb events plotted as a functionof p T with comparisons to theoretical simulations using viscus hydrodynamic expansion [82]. . 362.20 Coefficient v for identified hadrons measured at various centralities in Pb+Pb collisions with √ s NN = 2 . . The data are overlaid with curves from hydrodynamic simulations TeV [83]. . . 362.21 Coefficients v n from 30-40% central Pb+Pb events plotted as a function of p T [80]. . . . . . . 37vii2.22 Left: prompt and isolated photon R AA plotted as a function of the photon’s transverse en-ergy [88]. Right: Z boson R AA as a function of N part from Pb+Pb collisions at √ s NN =5 . TeV [28]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.23 Left: Charged particle R AA for various centralities of Pb+Pb collisions at √ s NN = 2 . TeVas a function of particle p T [89]. Right: inclusive jet R AA for various centralities of Pb+Pbcollisions at √ s NN = 5 . TeV as a function of jet p T [90]. . . . . . . . . . . . . . . . . . . 402.24 A representation of energy depositions in the CMS calorimeter system in a Pb+Pb di-jet event [91].. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.25 Di-jet yields from Pb+Pb collisions at √ s NN = 2 . TeV plotted as a function of their p T balance, x J , for several centrality classes [92]. . . . . . . . . . . . . . . . . . . . . . . . . . . 422.26 R AA (left), v (center), and v (right) from a theoretical jet quenching calculation showing goodagreement, at high p T , with the measured data [22]. . . . . . . . . . . . . . . . . . . . . . . 432.27 Two particle correlation functions in ∆ η and ∆ φ from minimum bias (left) and high multiplicity(right) selected events [14]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.28 Left: average eccentricities ε and ε for each system in the geometry scan from MC Glaubersimulations. Right: Flow coefficients v and v from each system plotted as a function of particle p T [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.29 Flow coefficients, v n , plotted as a function of particle p T for pp (left), p +Pb (center), and Pb+Pb(right). Measured data are shown as black markers and are overlaid with curves from the super-SONIC hydrodynamic simulation model [71]. . . . . . . . . . . . . . . . . . . . . . . . . . 452.30 Left:
Charged hadron nuclear modification factor R AA from Pb+Pb collisions compared to R p Pb as measured by the CMS collaboration. Right:
Azimuthal anisotropy coefficient v fromPb+Pb and p +Pb scaled to match at low p T [95]. . . . . . . . . . . . . . . . . . . . . . . . . 463.1 A diagram of the CERN accelerator complex, including the injection chain for the LHC [97]. . 483.2 A rendering of the LHC beam optics at IP2 during the 2018 Pb+Pb running period [98]. . . . 50viii3.3 An example from the online Vistar LHC monitoring showing the beam current, dipole magneticfield, and instantaneous luminosity as a function of time spanning a couple fills. . . . . . . . . 513.4 A rendering of the ATLAS detector with a cut away exposing the inner detector [99]. . . . . . 523.5 A rendering of the ATLAS inner detector barrel (top) and end-cap (bottom) sections [99]. . . . 543.6 A rendering of the ATLAS calorimeter systems [99]. . . . . . . . . . . . . . . . . . . . . . . 563.7 A diagram of a barrel EM calorimeter module [99]. . . . . . . . . . . . . . . . . . . . . . . . 573.8 The cumulative EM calorimeter material in radiation lengths as a function of absolute pseudo-rapidity [99]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.9 The cumulative hadronic calorimeter material in nuclear interaction lengths as a function ofabsolute pseudorapidity [99]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.10 A representation of one side of the Minimum Bias Trigger Scintillators [104]. . . . . . . . . . 613.11 A diagram of the ATLAS L1 trigger flow [99]. . . . . . . . . . . . . . . . . . . . . . . . . . 624.1 Correlation of the sum of the energy deposited in the p -going (y-axis) versus Pb-going (x-axis)forward calorimeters. The red histogram shows the average of the p -going energy for each Pb-going energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.2 Edge gaps measured from the forward edge of the calorimeter system ( η = 4 . ) on the p -going( Left ) and Pb-going (
Right ) sides of truth particles above 200 MeV. . . . . . . . . . . . . . . 674.3 Edge gaps measured from the forward edge of the calorimeter system ( η = 4 . ) on the p -going( Left ) and Pb-going (
Right ) sides of calorimeter clusters above 200 MeV. . . . . . . . . . . . 674.4 Histogram of the number of tracks associated with the second vertex in data (black) and HIJINGMC with no pileup (red). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.5 Distribution of vertex z − z in events with more than one vertex (black). . . . . . . . . . . . 684.6 Pb-going FCal Σ E Pb T distributions and event selection efficiency plotted as a function of FCal Σ E Pb T from P pp simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.7 Gaussian fits to FCal noise Σ E Pb T distributions from empty triggered events for each run. . . . 70ix4.8 Extracted means ( Left ) and widths (
Right ) from Gaussian fits to Σ E Pb T distributions from emptytriggers. The parameters are plotted for each run in chronological order (run index). . . . . . . 714.9 Extracted means from Gaussian fits to Σ E Pb T distributions from empty triggers after correction. 714.10 Mean Σ E Pb T from all bunch crossing positions (red) and from only the first position in thebunch train. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.11 Left:
Comparison between the Σ E Pb T distributions from each running period, both scaled tounit integral. Right:
The same comparison after applying a scale factor of 0.989 to each entryin the FCal C histogram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.12 Mean Σ E Pb T as a function of vertex z from period 1 ( Left ) and period 2 (
Right ). The plots arefit to a line, the parameters of which are used to correct for this effect in the data. . . . . . . . 734.13 Σ E Pb T distribution after all event selection and corrections and integrated over all runs. . . . . 734.14 Distribution of N part values from Glauber (with σ NN = (75 ± mb) and Glauber-Gribov(with σ NN = (75 ± mb and Ω = 0 . ) models at √ s NN p +Pb. . . . . . . . . . . 754.15 Gaussian fit to the Σ E Pb T noise distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . 764.16 Σ E Pb T distribution from simulated P events (black) fit with a gamma distribution con-volved with a Gaussian with width fixed by the noise fit (red). The lower panel gives the ratio ofdata to fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.17 Fit to Σ E Pb T distribution using the Glauber N part distribution and gamma distribution scalingmodel 1 ( Left ) and model 2 (
Right ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.18 Fit to Σ E Pb T distribution using the Glauber-Gribov N part distribution and gamma distributionscaling model 1 ( Left ) and model 2 (
Right ). . . . . . . . . . . . . . . . . . . . . . . . . . . 794.19 Fit to Σ E Pb T distribution using the Glauber N part distribution and gamma distribution scalingmodel 1 ( Left ) and model 2 (
Right ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.20 Fit to Σ E Pb T distribution using the Glauber-Gribov N part distribution and gamma distributionscaling model 1 ( Left ) and model 2 (
Right ). . . . . . . . . . . . . . . . . . . . . . . . . . . 794.21 Mean N part ( Left ) and T AB ( Right ) calculated from both Glauber and Glauber-Gribov modelsand plotted as a function of centrality class. . . . . . . . . . . . . . . . . . . . . . . . . . . . 80x4.22 Systematic variation of N part generated by setting efficiencies to 97% and 100%, and calculatedusing Glauber ( Left ) and Glauber-Gribov (
Right ) of each centrality class. . . . . . . . . . . . 834.23 Systematic variation of N part generated by varying Glauber parameters, and calculated usingGlauber ( Left ) and Glauber-Gribov (
Right ) of each centrality class. . . . . . . . . . . . . . . 834.24 Systematic variation of N part generated by varying the scaling model to model 1 compared tothe nominal model 2, and calculated using Glauber ( Left ) and Glauber-Gribov (
Right ) of eachcentrality class. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.25 Systematic variation of T AB generated by setting efficiencies to 97% and 100%, and calculatedusing Glauber ( Left ) and Glauber-Gribov (
Right ) of each centrality class. . . . . . . . . . . . 844.26 Systematic variation of T AB generated by varying Glauber parameters, and calculated usingGlauber ( Left ) and Glauber-Gribov (
Right ) of each centrality class. . . . . . . . . . . . . . . 854.27 Systematic variation of T AB generated by varying the scaling model to model 1 compared tothe nominal model 2, and calculated using Glauber ( Left ) and Glauber-Gribov (
Right ) of eachcentrality class. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.1 Trigger efficiency for each “stage” photon HLT loose trigger chains. . . . . . . . . . . . . . . . 915.2 Average ambient-energy-density as determined, event-by-event at particle level using the jet areamethod, and plotted as a function of truth photon E γ T in each pseudorapidity region for bothP and S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935.3 Ratio of resulting photon cross section measurements with and without jet-area subtraction ofthe UE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 945.4 Distribution of generator-level isolation values as a function of generator-level E γ T and Isolatedphoton cross-section at the generator-level in P events. . . . . . . . . . . . . . . . . . . 945.5 Reconstruction efficiency for truth isolated photons plotted as a function of E γ T in each centerof mass pseudorapidity slice for both running periods. . . . . . . . . . . . . . . . . . . . . . . 965.6 A pictorial representation of the shower shape variables used for photon identification. . . . . . 97xi5.7 Shower shape parameter, R η , in each pseudorapidity slice from representative E γ T bin ( GeV Pb+ p period, Bottom: Pb+ p period ratio . . . . . . . . . . . . . . . . . 1025.15 Mean relative energy difference of reconstructed to truth E γ T for tight identified and isolatedphotons plotted as a function of truth E γ T in each pseudorapidity slice. . . . . . . . . . . . . . 1035.16 Reconstructed photon energy resolution for tight identified and isolated photons plotted as afunction of truth E γ T in each pseudorapidity slice. . . . . . . . . . . . . . . . . . . . . . . . . 1035.17 Top: The total per-event-yields of reconstructed electrons (black) and misidentified photons(red). Bottom: The photon misidentification rate defined as the ratio of the two spectra. . . . . 1045.18 Top: Measured photon cross section from this analysis (black) and misidentified photon crosssection from electrons from Z decays in MC (red). Bottom: The electron contamination definedas the ratio of the two spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105xii5.19 The ratio of extracted electron energy from an example 13 TeV run using OF C ( µ = 0) to thatusing OF C ( µ = 20) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1065.20 Di-electron invariant mass distribution in data compared to MC for uncorrected (left) and cor-rected(right) electron energy scale data at mid rapidity. . . . . . . . . . . . . . . . . . . . . . 1075.21 Di-electron invariant mass distribution in data compared to MC for uncorrected (left) and cor-rected (right) electron energy scale data at forward rapidity. Note the different range in y-axisfor the ratios in the bottom panels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.22 Sideband A, B, C, and D yields (Top) and ratios to A (Bottom) from both data taking periodscombined. Photon purity is calculated from these ratios together with leakage fractions. Thehistograms are fit to polynomial functional forms, though the fits are not used in the cross sectioncalculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1095.23 Sideband leakage fractions from truth isolated photons in Monte Carlo simulations plotted as afunction of E γ T in each pseudorapidity slice from the p +Pb (Top) and Pb+ p (bottom) runningperiods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105.24 Purities for tight identified and isolated photons calculated via the sideband method with leak-ages from both P and S data overlay. Top: purities; bottom: ratios. . . . . . . . . . 1115.25 Purities for tight identified and isolated photons calculated via the direct method using toy MCsfor the statistical error, and those calculated using the smoothed sideband method. . . . . . . . 1125.26 Photon E γ T response matrix for tight and isolated truth matched photons from MC data overlayin each pseudorapidity region. The bin from 17-20 GeV acts as an underflow bin. . . . . . . . 1135.27 The fraction of photon counts that remain in the same E γ T bin after reconstruction as measuredin MC data overlay in each pseudorapidity region . . . . . . . . . . . . . . . . . . . . . . . . 1135.28 Bin migration corrections plotted as a function of E γ T in each pseudorapidity region for bothrunning periods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1145.29 Bin migration corrections plotted as a function of E γ T in each pseudorapidity region. The cor-rections are fit with a logistic function which is used for the applied corrections. . . . . . . . . . 114xiii5.30 (Top) A comparison of the photon E T spectrum in data (blue) and MC (red), showing that thedata spectrum is slightly steeper than that of MC. (Bottom) The ratio of the two including anexponential fit which is used as a factor to reweight the MC to match the data. . . . . . . . . . 1155.31 Bin migration corrections, determined after MC to data spectrum reweighting, plotted as afunction of E γ T in each pseudorapidity region. The corrections show a negligible difference tothe nominal values in Fig. 5.29. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155.32 Left : Comparison of prompt, isolated photon spectrum measured by ATLAS in √ s = 8 TeV pp data (identical to the points in Fig. 3 in Ref. [116]), to that in P A14 NNPDF23LO at thesame energy. Right : P/data ratio in each measured η selection (systematic uncertaintieson data not shown). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1175.33 Comparison of prompt, isolated photon spectrum in P A14 NNPDF23LO simulation at . TeV (with ∆ y = − . boost) and TeV for each pseudorapidity slice. . . . . . . . . . 1175.34 Left : Ratio of prompt, isolated photon spectrum in P A14 NNPDF23LO simulation be-tween . TeV (with ∆ y = − . boost) and TeV for each pseudorapidity slice. Right : Ex-trapolated √ s = 8 . TeV pp reference spectrum with center of mass boost by ∆ y = − . .The spectra are shown for each pseudorapidity slice. . . . . . . . . . . . . . . . . . . . . . . 1185.35 Summary of the relative sizes of major sources of systematic uncertainty in the cross-sectionmeasurement, as well as the combined uncertainty (excluding luminosity), shown as a functionof photon transverse energy E γ T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195.36 R bkg estimated using the BDFE method plotted as a function of E γ T . . . . . . . . . . . . . . . 1215.37 The effect of systematic variations in R bkg when calculating the purity. . . . . . . . . . . . . . 1215.38 The effect of systematic variations in the definition of the non-tight sideband when calculatingthe purity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1225.39 The relative deviation in the purity when varying the non-tight definition. . . . . . . . . . . . 1225.40 The effect of systematic variations in the definition of the non-iso sideband when calculating thepurity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123xiv5.41 The relative deviation in the purity when varying R bkg (magenta), the non-isolation definition(cyan), non-tight definition (orange), and their quadratic sum (yellow band). The plots areshown in the usual pseudorapidity bins and both. . . . . . . . . . . . . . . . . . . . . . . . . 1235.42 The relative deviation in the bin migration correction from the systematic variations in the energyresolution and scale in MC as well as the scale factor uncertainty. . . . . . . . . . . . . . . . . 1255.43 Effect on total cross section by changing particle level isolation cut to match the detector level. . 1255.44 The default fraction of hard photons in the P MC sample for each rapidity bin, plotted asa function of photon transverse energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1265.45 Ratios of the resulting cross sections with the direct fraction re-weighting to those from thenominal fraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1275.46 Summary of total systematic uncertainties on previously measured TeVphoton spectrum [116],each panel showing a different | η | selection. (A global luminosity uncertainty of 1.9% is notincluded.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1275.47 Left: Comparison of the J-calculated cross-section for boosted 8.16 TeV pp and non-boosted 8 TeV pp collisions, in the kinematic E γ T and η lab bins used in the analysis. Right: Extracted extrapolation from J compared to the nominal values from P. . . . . . 1285.48 Ratio between the constructed pp reference using correction factors from P and that usingcorrection factors from J, plotted as a percent of the P values as well as the factorscalculated with J +CT10 to J +MSTW2008. . . . . . . . . . . . . . . . . . . . 1295.49 A breakdown of all systematic uncertainties on the R p Pb measurement. . . . . . . . . . . . . . 1295.50 Summary of the relative size of major sources of systematic uncertainty in the forward-to-backwardratio of the nuclear modification factor R p Pb . . . . . . . . . . . . . . . . . . . . . . . . . . . 1306.1 Photon cross sections as a function of transverse energy E γ T . . . . . . . . . . . . . . . . . . . . 1326.2 A breakdown of all systematic uncertainties in the cross-section prediction from J withthe EPPS16 nPDF set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133xv6.3 Nuclear modification factor R p Pb for isolated, prompt photons as a function of photon trans-verse energy E γ T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1346.4 Ratio of the nuclear modification factor R p Pb between forward and backward pseudorapidityfor isolated, prompt photons as a function of photon transverse energy E γ T . . . . . . . . . . . . 1367.1 MB trigger efficiency as a function of multiplicity in 2016 p +Pb collisions . . . . . . . . . . . 1397.2 L1_TEX trigger efficiency as a function of multiplicity in 2016 p +Pb data. . . . . . . . . . . . 1407.3 The η − φ distributions and φ projections of tracks such that the values represent the relativedeviation from the mean in φ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1417.4 Multiplicity ( left ) and track p T ( right ) distributions from the two sets of events considered:minbias with high multiplicity triggers in green, and those with 100 GeV jets in magenta. . . . 1427.5 dN ch /dη vs η , uncorrected for detector inefficiencies, for central ( left ) and peripheral events( right ) from the two sets of events considered: minbias with high multiplicity triggers in green,and those with 100 GeV jets in magenta. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1427.6 Two dimensional reconstruction efficiency of MinBias tracks as a function of track p T and η obtained from MC based prompt charged pions. . . . . . . . . . . . . . . . . . . . . . . . . 1447.7 Example of same event two-particle correlation (left), mixed event two-particle correlation (mid-dle) and per-particle-yield after correction for the acceptance effect. . . . . . . . . . . . . . . 1477.8 Example of fully corrected per-A-pair yields of two-particle correlations for MBT (left column)and jet (right column) events and peripheral (top row) and central (bottom row) selections. . . 1487.9 Template fitting output for MBT events using both multiplicity and Σ E PbT to select high andlow event activities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1547.10 Template fitting output for jet events using both multiplicity and Σ E PbT to select high and lowevent activities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1557.11 The distribution of track ∆ η with respect to both the leading and sub-leading jets. . . . . . . . 1577.12 Template fitting output for jet events using both with and without the B-particle jet rejection. . 158xvi7.13 A graphical representation of the transverse and towards azimuthal regions relative to a high p T object, shown as a yellow triangle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1597.14 v versus p T for MBT (left), 75 GeV jet (center), and 100 GeV jet (right) events with and withouttrigger and tracking efficiency corrections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1617.15 v versus p T for MBT (left), 75 GeV jet (center), and 100 GeV jet (right) events with and withoutsagitta tracking correction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1617.16 Combined performance uncertainty, plotted as the absolute difference in v between the variedand nominal selections, for MBT (left), 75 GeV jet (center), and 100 GeV jet (right) events. . . 1627.17 v versus p T for both MBT (left), 75 GeV jet (center), and 100 GeV jet (right) events with thenominal values using the mixed event correction, and variation without the correction. The solidblue points in the sub-panels are the differences after smoothing. . . . . . . . . . . . . . . . . 1637.18 v versus p T for both MBT (left), 75 GeV jet (center), and 100 GeV jet (right) events with thenominal and two varied P reference selections. The solid blue and red points in the sub-panelsare the differences after smoothing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1637.19 Combined signal extraction uncertainty, plotted as the absolute difference in v between thevaried and nominal selections, for MBT (left), 75 GeV jet (center), and 100 GeV jet (right) events.1647.20 v versus p T for 75 GeV (left) and 100 GeV (right) jet events from data compared to those foundusing the MC data overlay sample. The red line is a fit to all points above 3 GeV, and acts as anestimate for the amount of the v signal can be attributed to the jet-UE bias. . . . . . . . . . . 1657.21 v versus p T for 75 GeV (left) and 100 GeV (right) jet events with offline jet p T thresholdsvariations of +5 GeV. The solid blue points in the sub-panels are the differences after smoothing. 1667.22 v versus p T for 75 GeV (left) and 100 GeV (right) jet events with the nominal and varied ∆ η jet p T selection. The solid blue points in the sub-panels are the differences after smoothing. . . . . 1667.23 The number of charged tracks with ∆ R < . from the jet axis jets in different p T windowsfrom 100 GeVjet events. The left plot show the results from events from 0-5% central events andthe right is for 70-90% central events. The solid blue points in the sub-panels are the differencesafter smoothing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167xvii7.24 v versus p T for 75 GeV (left) and 100 GeV (right) jet events with the nominal and variedassociated particle rejection jet multiplicity selection. The solid blue points in the sub-panels arethe differences after smoothing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1677.25 v versus p T for 75 GeV (left) and 100 GeV (right) events comparing the nominal results tothose generated from tracks with an η < . in the lab frame. The solid blue points in thesub-panels are the differences after smoothing. . . . . . . . . . . . . . . . . . . . . . . . . . . 1687.26 Combined jet selection uncertainty for MBT (left), 75 GeV jet (center), and 100 GeV jet (right)events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1687.27 v versus | ∆ η | in low (orange), mid (blue), and high (red) p T ranges for MBT (left), 75 GeV jet(center), and 100 GeV jet (right) events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1697.28 The η distribution of associated (B) tracks used to generate correlation functions from 100 GeVjet events for several different values of track-track gap requirements. For each variation, themean of | η | is reported quantifying the change in the distributions. . . . . . . . . . . . . . . . 1707.29 v versus | ∆ η | in low (orange), mid (blue), and high (red) p T ranges for 75 GeV jet (left), and100 GeV jet (right) events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1717.30 The η distribution of associated (B) tracks used to generate correlation functions from 100 GeVjet events for several different values of jet-track gap requirements. For each variation, the meanof | η | is reported quantifying the change in the distributions. . . . . . . . . . . . . . . . . . . 1717.31 Comparison of v results from data from period 1 and 2 separately. The right plot is after theassociated particles are restricted to have η Lab < . , and the left is without restriction. Thered dashed lines are the result of a constant fit for which the χ /N DF is quoted on the figure. . 1727.32 v versus p T for both 75 GeV (left) and 100 GeV (right) jet events with the nominal values andthose with flattening corrections applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1737.33 v versus p T for 75 GeV (left) and 100 GeV (right) jet events with the nominal ”all” jet rejectionand those in which only the leading and sub-leading (in p T ) jets are used in the B particle rejection.1737.34 v versus p T 100 GeV jet events with the simple two jet rejection compared to those generatedwith the two opposite jet rejection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174xviii7.35 v versus p T for MBT and MBT+HMT events. The right figure gives the MBT+HMT aftertrigger prescale correction, and the left is uncorrected. . . . . . . . . . . . . . . . . . . . . . . 1757.36 The relative uncertainty in v from all sources versus p T for MBT (left), 75 GeV jet (center), and100 GeV jet (right) events. The combined uncertainty is shown as the black curve. . . . . . . . 1757.37 The relative uncertainty in v from all sources versus p T for MBT (left), 75 GeV jet (center), and100 GeV jet (right) events. The combined uncertainty is shown as the black curve. . . . . . . . 1757.38 The relative uncertainty in UE-UE (top) and HS-UE (bottom) pair fractions in 0-5% centralevents from all sources versus p T for MBT (left), 75 GeV jet (center), and 100 GeV jet (right)events. The combined uncertainty is shown as the black curve. . . . . . . . . . . . . . . . . . 1768.1 Distribution of v (left) and v (right) plotted as a function of the A-particle p T . . . . . . . . . 1778.2 Measured v factorization check plotted as a function of the A-particle p T . . . . . . . . . . . . 1788.3 Distribution of v plotted as a function of centrality. . . . . . . . . . . . . . . . . . . . . . . 1808.4 Coefficients v and v (left panel) and R p Pb (right panel) plotted as a function of particle p T for p +Pb collisions compared to those from a jet quenching calculation. . . . . . . . . . . . . . 1818.5 Coefficients v and v from the MBT event sample compared to calculations relevant to thelow- p T regime from hydrodynamics and to the high- p T regime from an ‘eremitic’ framework. . 1828.6 Predictions of azimuthal anisotropy from P using the same two-particle formalism usedfor the data results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1848.7 Scaled p +Pb v values plotted as a function of the A-particle p T overlaid with v from 20–30%central Pb+Pb data at √ s NN = 5.02 TeV [80]. . . . . . . . . . . . . . . . . . . . . . . . . . . 1858.8 Particle pair yield composition fractions for MBT events (top), events with jet p T > GeV(bottom left), and events with jet p T > GeV (bottom right) plotted as a function of theA-particle p T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1878.9 Underlying event–underlying event (UE–UE) (open circles) and hard scatter–underlying event(HS–UE) (open squares) particle-pair yield composition fractions plotted as a function of theA-particle p T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188xix8.10 Underlying event–underlying event (UE–UE) (open circles) and hard scatter–underlying event(HS–UE) (open squares) particle-pair yield composition fractions plotted as a function of eventcentrality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189A.1 Reconstruction efficiency comparison for period A (top) and period B (bottom). . . . . . . . . 208A.2 Tight ID efficiency comparison for period A (top) and period B (bottom). . . . . . . . . . . . 209A.3 Isolation efficiency comparison for period A (top) and period B (bottom). . . . . . . . . . . . . 209A.4 Sideband B leakage fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210A.5 Sideband C leakage fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210A.6 Sideband D leakage fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210A.7 Shower shape parameter, R η , in each pseudorapidity slice from E T bins GeV < E T < GeV (above) and GeV < E T < GeV (below). Reconstructed data plotted as blackpoints overlaid with MC before (blue histogram) and after (red histogram) fudging. . . . . . . 212A.8 Shower shape parameter, R φ , in each pseudorapidity slice from E T bins GeV < E T < GeV (above) and GeV < E T < GeV (below). Reconstructed data plotted as blackpoints overlaid with MC before (blue histogram) and after (red histogram) fudging. . . . . . . 213A.9 Shower shape parameter, R had , in each pseudorapidity slice from E T bins GeV < E T < GeV (above) and GeV < E T < GeV (below). Reconstructed data plotted as blackpoints overlaid with MC before (blue histogram) and after (red histogram) fudging. . . . . . . 214A.10 Shower shape parameter, R had , in each pseudorapidity slice from E T bins GeV < E T < GeV (above) and GeV < E T < GeV (below). Reconstructed data plotted as blackpoints overlaid with MC before (blue histogram) and after (red histogram) fudging. . . . . . . 215A.11 Shower shape parameter, W η , in each pseudorapidity slice from E T bins GeV < E T < GeV (above) and GeV < E T < GeV (below). Reconstructed data plotted as blackpoints overlaid with MC before (blue histogram) and after (red histogram) fudging. . . . . . . 216xxA.12 Shower shape parameter, W η , in each pseudorapidity slice from E T bins GeV < E T < GeV (above) and GeV < E T < GeV (below). Reconstructed data plotted as blackpoints overlaid with MC before (blue histogram) and after (red histogram) fudging. . . . . . . 217A.13 Shower shape parameter, W totes , in each pseudorapidity slice from E T bins GeV < E T < GeV (above) and GeV < E T < GeV (below). Reconstructed data plotted as blackpoints overlaid with MC before (blue histogram) and after (red histogram) fudging. . . . . . . 218A.14 Shower shape parameter, ∆ E , in each pseudorapidity slice from E T bins GeV < E T < GeV (above) and GeV < E T < GeV (below). Reconstructed data plotted as blackpoints overlaid with MC before (blue histogram) and after (red histogram) fudging. . . . . . . 219A.15 Shower shape parameter, E ratio , in each pseudorapidity slice from E T bins GeV < E T < GeV (above) and GeV < E T < GeV (below). Reconstructed data plotted as blackpoints overlaid with MC before (blue histogram) and after (red histogram) fudging. . . . . . . 220A.16 Shower shape parameter, fracs1, in each pseudorapidity slice from E T bins GeV < E T < GeV (above) and GeV < E T < GeV (below). Reconstructed data plotted as blackpoints overlaid with MC before (blue histogram) and after (red histogram) fudging. . . . . . . 221B.1 Run-by-run multiplicity distributions for each trigger used to construct the minimum bias se-lection. Vertical lines are drawn to indicate the thresholds partitioning the N trk range. In eachregion, only the trigger offering the largest number of events is used. . . . . . . . . . . . . . . 239B.2 Run-by-run multiplicity distributions for each trigger used to construct the minimum bias se-lection. Vertical lines are drawn to indicate the thresholds partitioning the N trk range. In eachregion, only the trigger offering the largest number of events is used. . . . . . . . . . . . . . . 240B.3 Total run-by-run multiplicity distributions composing the minimum bias selection. Verticallines are drawn to indicate the thresholds partitioning the N trk range. In each region, only thetrigger offering the largest number of events is used. . . . . . . . . . . . . . . . . . . . . . . 241xxiB.4 Total run-by-run multiplicity distributions composing the minimum bias selection. Verticallines are drawn to indicate the thresholds partitioning the N trk range. In each region, only thetrigger offering the largest number of events is used. . . . . . . . . . . . . . . . . . . . . . . 242B.5 v versus p T for MB (left), 75 GeV jet (center), and 100 GeV jet (right) events with and withouttrigger and tracking efficiency corrections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243B.6 Combined performance uncertainty, plotted as the absolute difference in v between the variedand nominal selections, for MB (left), 75 GeV jet (center), and 100 GeV jet (right) events. . . . 243B.7 v versus p T for both MB (left), 75 GeV jet (center), and 100 GeV jet (right) events with thenominal values using the mixed event correction, and variation without the correction. . . . . . 244B.8 v versus p T for both MB (left), 75 GeV jet (center), and 100 GeV jet (right) events with thenominal and two varied P reference selections. . . . . . . . . . . . . . . . . . . . . . . . . . . 245B.9 Combined signal extraction uncertainty, plotted as the absolute difference in v between thevaried and nominal selections, for MB (left), 75 GeV jet (center), and 100 GeV jet (right) events. 245B.10 v versus p T for 75 GeV (left) and 100 GeV (right) jet events with offline jet p T thresholdsvariations of +5 GeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246B.11 v versus p T for 75 GeV (left) and 100 GeV (right) jet events with the nominal and varied ∆ η jet p T selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247B.12 v versus p T for 75 GeV (left) and 100 GeV (right) jet events with the nominal and variedassociated particle rejection jet multiplicity selection. . . . . . . . . . . . . . . . . . . . . . . 247B.13 Combined jet selection uncertainty for MB (left), 75 GeV jet (center), and 100 GeV jet (right)events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248B.14 Combined performance uncertainty in v as a function of centrality, plotted as the absolutedifference between the varied and nominal selections, for MB (left), 75 GeV jet (center), and100 GeV jet (right) events. The uncertainties are determined separately for . < p A T < GeV(top row), < p A T < GeV (middle row), and < p A T < GeV (bottom row). . . . . . . . 249xxiiB.15 Combined signal extraction uncertainty in v as a function of centrality, plotted as the absolutedifference between the varied and nominal selections, for MB (left), 75 GeV jet (center), and100 GeV jet (right) events. The uncertainties are determined separately for . < p A T < GeV(top row), < p A T < GeV (middle row), and < p A T < GeV (bottom row). . . . . . . . 250B.16 Combined jet selection uncertainty in v as a function of centrality, plotted as the absolutedifference between the varied and nominal selections, for 75 GeV (left) and 100 GeV jet (right)events. The uncertainties are determined separately for . < p A T < GeV (top row),
Quantum Chromodynamics (QCD). The properties of QCD depend on the energyscale of the interaction. At high energies, its coupling strength is weak, and perturbative calculation methods arehighly successful. At low energies, however, the coupling is strong and non-perturbative. The confining scale ofquarks and gluons corresponds naturally to the transition between these regimes. The complexity of the QCDinteraction gives rise to a wealth of rich emergent phenomena that are not obvious from the fundamental degreesof freedom of the theory.Nuclear collision experiments at CERN in Europe and Brookhaven National Laboratory in the USA pro-vide an opportunity to study QCD matter across a broad range of energy scales. The discovery that the QGPflows as a collective fluid in large collision systems, such as Au+Au and Pb+Pb, has led to the development ofeffective models describing the dynamics of the deconfined but strongly coupled regime [4–6]. These describethe entire collision evolution from initial spatial energy depositions to final state hadron distributions throughthe nearly inviscid hydrodynamic expansion of the QGP. In this well established framework, anisotropic flow, asmeasured by the azimuthal modulation of particle momenta, are a gradient response of the fluid to the spatialgeometry anisotropies of the interacting nucleons. In data, this nuclear geometry can be inferred through cen-trality , measured via the overall event activity, and a model of the geometry, such as the Monte Carlo Glauber [7]model. The success of these hydrodynamic descriptions at all centralities has led to this model becoming thestandard paradigm. However, the average transverse momentum ( (cid:104) p T (cid:105) ) of the expanding QGP is of order a fewhundred MeV, and therefore, this picture is only applicable to the bulk of the particles produced with low p T .That said, measurements of particle azimuthal anisotropy show significant non-zero results extending well intothe high p T regime.High p T particles originate from rare, high-energy scatterings during the earliest times in the collision.These perturbative processes free quarks and gluons from the initial colliding nucleons that, given sufficient en-ergy, fragment into collimated clusters of particles called jets . Since these scatterings occur early in the collisionevolution, jets can act as probes of the bulk QGP matter as they must traverse the expanding medium. Mea-surements of the rates of these processes show that the QGP is largely opaque to jets; i.e., jets lose energy as theypass through the medium through a process called jet quenching [8–10]. Furthermore, the level of jet energyloss is observed to be smaller for less central (more peripheral ) events in which the transverse size of the QGPis smaller. Given a path length dependent effect, it is plausible that the high p T azimuthal anisotropy is due tothe jet traversing different paths through the QGP. Both the signal at low and high p T would then be due to thesame geometric pattern of the interacting nucleons; however, the mechanism to transfer this pattern to the finalstate particle momentum distribution would be different in each case.Small collision systems, where one or both of the colliding bodies consist of at most a few nucleons, demon-strate flow signatures similar to those in large systems [11–17]. These observations were unexpected because itwas thought that partons in such small regions would not interact enough to behave collectively. Nevertheless,the ability of hydrodynamic models to accurately describe the data has led to the conclusion that a QGP, with itscharacteristic evolution as a response to the initial interacting nucleon geometry, is being created in these systems.However, the jet quenching phenomena seen in large systems is notably absent [18–21]. This raises the questionof whether it is possible for collective QGP droplets to form in such a way that they don’t modify the jet energyspectrum. Or perhaps there is some jet modification, but the current measurements are not sensitive enough todetect it. Thus, small systems provide a testing ground to study QGP phenomena in relation to the size of theQGP droplet. There is an opportunity to test theories that relate the flowing medium to energy loss mechanismsin a situation in which one exists without the other [22–24].The modification to measured perturbative process rates from the interaction with the QGP is known asa final state effect, since the mechanism modifies the parton after the high energy scattering. However, there alsoare initial state effects that modify process rates in nuclear collisions. These modifications are usually interpretedas changes to the parton densities of nucleons when they are bound in nuclei. Thus, in large collision systems,strongly interacting final states, like jets, will contain both effects creating a potential ambiguity. Final stateparticles that don’t interact via QCD, like electroweak bosons, are unmodified by the presence of the QGP [25–28]. Thus, studying electroweak (EW) processes in these collisions can provide a “standard candle” from whichto measure QGP phenomena and map out the parton densities in the initial colliding nucleons. Furthermore,asymmetric systems like p +Pb allow the study of these processes in a “clean” nuclear environment with limitedambient particle production.This thesis details two novel measurements in √ s NN = 8 . TeV p +Pb collisions from the Large HadronCollider (LHC) and using the ATLAS detector published as Refs. [29, 30]: a measurement of the productioncross section of direct, high p T photons, and a measurement of the azimuthal anisotropy of charged particles overa broad range of p T . Chapter 2 gives an overview of the physics of ultra relativistic nuclear collisions to providecontext for these measurements. Chapter 3 presents the experimental apparatus and data used in the analyses. Ananalysis to calibrate event-by-event geometric properties of the colliding bodies is given in Chapter 4. Chapters 5and 6 detail a measurement of the production cross section of high energy photons. The results are compared totheoretical predictions from perturbative calculations, with and without nuclear parton distribution modification,and an expectation from a model predicting energy loss of the scattering partons before the high energy scatter.Chapters 7 and 8 present a measurement of flow signals in these collisions as they depend on the transversemomentum of the particles produced and the underlying process which creates them. Finally, conclusions aregiven in Chapter 9. hapter 2Ultra-Relativistic Heavy Ion Collisions During the ultra-relativistic collisions of heavy ions, nuclei act as sources of many microscopic scatteringcenters that interact via the strong, weak, and electromagnetic interactions as the nuclei move through each other.Initial kinetic energy from the impacting particles is converted into, sometimes, thousands of final state particlesthat expand in all directions. These collision fragments can be captured in detectors and used to infer conclusionsabout the whole evolution of the collision.It is helpful to consider a given collision in a probabilistic sense as a single sample from the set of allpossible outcomes. To paraphrase the totalitarian principle (its modern incarnation attributed to Gell-Mann),any outcome that is not strictly forbidden by natural conservation laws is compulsory; i.e., it must happen withsome non-zero probability. Particle colliders like the Large Hadron Collider (LHC) and the Relativistic HeavyIon Collider (RHIC) are capable of generating millions of collisions per second, enabling experiments like ATLASto record enormous sets of data and capture all but the rarest of outcomes.This thesis is concerned, primarily, with phenomena associated with the strong interaction, so-called dueto its dominance at a certain length scale with respect to the other three fundamental interactions. In thischapter, some time is spent reviewing QCD within the context of the Standard Model of Particle Physics. Thenan overview of QCD matter is presented, including discussions of hadrons and deconfined media. Finally, thegeometry and evolution of nuclear collisions are explored in the context of experimental results. High energy physics seeks to understand the fundamental building blocks and dynamics of matter in theuniverse. The current best understanding is encapsulated in the so-called Standard Model of Particle Physics(SM). Standard Model of Elementary Particles three generations of matter(fermions) I II III interactions / force carriers(bosons) masschargespin Q UARK S u ≃ ⅔ ½ up d ≃ −⅓ ½ down c ≃ ⅔ ½ charm s ≃ 96 MeV/c² −⅓ ½ strange t ≃ ⅔ ½ top b ≃ −⅓ ½ bottom L EP T O N S e ≃ − electron ν e <1.0 eV/c²0½ electronneutrino μ ≃ − muon ν μ <0.17 MeV/c²0½ muonneutrino τ ≃ − tau ν τ <18.2 MeV/c²0½ tauneutrino G AU G E B O S O N S VE C T O R B O S O N S g gluon γ photon Z ≃ Z boson W ≃ W boson S CA L AR B O S O N S H ≃ higgs Figure 2.1: A chart of the particles making up the Standard Model [31].The dynamics of matter are governed by four fundamental interactions: gravity, electromagnetism, andthe strong and weak forces. Gravity is a factor of about weaker than the other three [32], and is not includedin the SM. Interactions occur between bodies that carry a property that is specific to each type of interaction. Thisproperty is called electric charge, color charge, or weak isospin for electromagnetic, strong, or weak interactionsrespectively. All matter is composed of twelve fermions (spin 1/2 particles), shown in the first three columns ofFig. 2.1. These are divided into quarks which hold color, and leptons that do not. Quarks and the upper rowof leptons carry electric charge; the bottom row of leptons, the neutrinos, are neutral. All of the fermions carryweak isospin. Each row in the chart corresponds to the three generations of mass hierarchy, the left being lightestand the right being heaviest. Finally, each of the fermions has a corresponding anti-particle with exactly thesame properties, but opposite electric charge. The SM is represented mathematically as a quantum field theory with SU(3) × SU(2) L × U(1) gaugesymmetry. The SU(3) component gives rise to QCD along with eight gauge bosons, known collectively as gluons,corresponding to the eight generators of the symmetry. The remaining SU(2) L × U(1) symmetry defines theelectroweak theory and the three weak bosons, W ± and Z , and the photon of electromagnetism. The gaugebosons act to mediate the interactions between the fermions, via particle exchange, and are thus known as forcecarriers. All of the gauge bosons are required to be massless in order to preserve local gauge symmetry; however,the weak bosons acquire mass through interaction with an additional scalar field via the Higgs mechanism. Thegauge symmetries of the SM are continuous, and therefore, Noether’s theorem states there are conservation lawsfor each symmetry. In this case, the corresponding charges are conserved under those interactions. QCD is a quantum field theory with SU(3) gauge symmetry that describes the dynamics of quarks andgluons in the SM. The generators, T C , of the SU(3) Lie group are the eight elements with Lie algebra, [ T A , T B ] = if ABC T C (2.1)defined by the totally anti-symmetric structure constants of SU(3) , f ABC . The elements, T C , are representedby the × Gell-Mann matrices. A local gauge transformation from the group can then be constructed viaexponential mapping of the generators to yield the unitary transformation U ( x ) = e iα C ( x ) T C , (2.2)where the functions α C ( x ) parameterize the group operation. The fundamental representation of the group isthree dimensional corresponding to color charges red, green, and blue. Quark fields, ψ ( x ) , take the form of Except for, perhaps, the neutrinos, whose masses are still uncertain. It is interesting to note that the existence of anti-particles (first proposed by Dirac in his development of relativistic quantummechanics) and the fermionic nature of matter particles are not a consequences of quantum mechanics per se . These two properties followsimply from the algebraic structure of the Poincaré group comprising the symmetries of space-time under relativity. See Refs. [33, 34]. color vectors in this space and transform under gauge rotation as ψ ( x ) → U ab ( x ) ψ b ( x ) = e iα A ( x ) T Aab ψ b ( x ) . (2.3)The color vector indices will be suppressed moving forward.Ordinary space-time derivatives acting on transformed vectors will receive an extra term, thus breakingthe symmetry. This is solved by introducing a covariant derivative D µ = ∂ µ − ig s T C A Cµ , (2.4)where g s is the QCD coupling constant, and A Cµ , is a new set of dynamical gauge fields, one for each generator.These are the gluon fields, whose transformation rules can be determined by requiring the gauge invariance of ¯ ψD µ ψ .Geometrically, imposing SU(3) gauge symmetry defines a principal SU(3) -bundle, P on the space-timemanifold. To generalize the derivative, a Lie algebra valued 1-form, A (a connection) is defined on P thatconnects the tangent spaces (fibers) of different points in space-time. Then ig s T C A Cµ is the pullback of A from P to space-time. The curvature on P is the field strength, a Lie algebra valued 2-form that, when pulled back,can be determined as [ D µ , D ν ] = − ig s T A F Aµν (2.5) = ⇒ F Aµν = ∂ µ A Aν − ∂ ν A Aµ − g s f ABC A Bµ A Cν . (2.6)The third term on the RHS implies a coupling between the gluon fields themselves. This is a direct consequenceof the non-Abelian nature of the symmetry group.Finally, the fully covariant QCD Lagrangian density is given by L = (cid:88) q ¯ ψ q ( iγ µ D µ − m ) ψ q − F Aµν F A µν , (2.7)where the sum runs over all quark flavors. From this, the dynamics of QCD systems can be derived via theprinciple of least action. Interactions in renormalizable quantum field theories (such as those in the SM) depend on the energy scaleof the interaction. If one imagines a particle (probe) scattering off a target, this scale acts as the resolving powerof the probe. A higher momentum (energy) probe resolves shorter distance (time) scales. Quantum uncertaintyimplies the breaking of energy/momentum conservation to a certain degree, allowing fluctuations that take theform of short-lived particles. These fluctuations change the effective values the parameters of the theory (e.g.coupling constants and particle masses) in a scale dependent way. To use the more formal language of Feynmandiagrams, loop corrections to vertices and propagators involve off-shell integrals that diverge. A strategy forhandling these divergences is to augment the theory parameters in a way as to cancel the divergence at the givenscale. This renormalization procedure introduces a scale dependence to the parameters.The renormalization group equation encodes the relationship between a coupling constant, g , and theenergy scale, µ , β ( g ) = ∂g∂ log µ , (2.8)where the beta function, β , can be found by studying the divergences perturbatively in successive loop corrections.In QCD the equation reads β ( α s ) = ∂α s ∂ log Q = − ( b α s + b α s + b α s + · · · ) , (2.9)where b n is the n -loop beta function, α s = g s / π , and Q is the momentum transfer of the interaction. Thiscan be solved analytically for the first correction, b = (33 − n f ) / (12 π ) , where n f = 3 is the number of lightquarks ( u , d , and s ). With an appropriate choice of Λ QCD , the solution can be expressed as α s ( Q ) = 1 b log( Q / Λ QCD ) . (2.10)Eqn. 2.10 implies that the QCD coupling strength actually decreases with the momentum scale, Q , approachingzero for vary large Q , or equivalently, very short distance scales. Thus, QCD is said to be asymptotically free. Thisdiscovery earned the authors, Gross, Wilczek, and Politzer, the 2004 Nobel Prize in physics [35]. The momentumscale, Λ QCD , determines a threshold between strong and weak coupling regimes. Fig. 2.2 gives a summary of α s measurements.0Figure 2.2: A summary of measurements of α s as a function of momentum transfer Q [1]. Asymptotic freedom describes the QCD coupling at short distance scales, where the theory can be handledwith perturbative methods (pQCD). However, the Eqn. 2.10 has a divergence in the coupling as Q → Λ QCD .This behavior indicates a breakdown in the perturbative assumptions, thus implying the need for new method-ology at large distance scales.Experimentally, the fundamental particles participating in QCD have only been observed in color singletbound states, a phenomenon known as color confinement. Quarks cannot be isolated in vacuum and are inferredindirectly from hadron spectra and deep inelastic scattering data (see Sec. 2.3.1). The typical hadron mass thendefines a natural resolving scale of QCD charges (i.e. Λ QCD ).A non-perturbative approach to QCD exists in which space-time is discretized into a lattice. In this Lat-tice QCD (LQCD), quarks fields are located at lattice points and are connected by gluon fields. The infinitedimensional integrals from the path integral formulation become finite dimensional and can be computed di-rectly. The lattice spacing sets a high frequency cutoff that regulates the integrals, and the discrete nature ofthe problem lends itself to computational methods. Final results are typically extrapolated to continuous space.1Being non-perturbative, LQCD calculations can be valid in the strong coupling regime but are limited in thatsystem dynamics cannot be modeled. Thus, properties related to hadron structure, like hadron masses, formfactors, and the equilibrium QCD equation of state, can be calculated from first principles, but time dependantphenomena like hydrodynamic transport coefficients cannot.Considering the simplest problem of a heavy quark–anti-quark bound state, in which the motion of thequarks is negligible, the effective QCD potential has been shown to match the Cornell-type potential [36, 37], V ( r ) = − α s r + σr . (2.11)The first term, dominant at short distances, is a perturbative Coulomb-like contribution, and the second, string-like potential with tension σ , is dominant at long distances [38]. This string-like behavior is interpreted as acolor flux tube in which transverse gluons are suppressed, due to their self interactions, leaving a collimated colorfield. This is then responsible for the confining behavior; as the quarks are pulled apart, the potential energygrows to a point in which the string “breaks”, i.e. a new quark–anti-quark pair is created, leaving two hadronsin the final state.This picture of color flux tubes is well established in LQCD for heavy quarks, but is not rigorous forlight quark bound states. In fact, color confinement in general has no analytic proof. It is seen as an emergentphenomenon produced via dynamical chiral symmetry breaking [39]. Nevertheless, it is helpful to keep thispicture in mind. As described in the previous Section 2.2.3, low-energy QCD matter consists of quarks bound in colorsinglet hadrons. The constituent quarks and guons are known collectively as partons. The observed states takethe form of mesons, bound quark–anti-quark, and baryons, bound three-quark states. Before the Quark Model,the net number of baryons minus anti-baryons was observed to be conserved in scattering experiments and wasproposed as an explanation for why the proton was stable. This led to a proposed quantum number, B , called This differs from an actual string system in that in this case, σ is distance independent. B = 1 / and anti-quarks B = − / . Thus, mesons, which can decay purely leptonically, are composed of a quark and anti-quark( B = 0 ).Hadronic states are, then, the outcome of a quark chemistry obeying a set of quantum number conser-vation rules: color, baryon number, and spin. Though the fundamental theory describing the structure of theseparticles is known, the energy scale is non-perturbative and the dynamics are not fully understood. However,LQCD methods are able to calculate hadron masses with good accuracy. Fig. 2.3 shows a plot of hadron massesfrom world data overlaid with calculations from LQCD.Figure 2.3: A summary of hadron mass calculations from LQCD (colored points), overlaid with measurementsfrom world data (black lines) [1]. It is notable that baryon number conservation is broken in perturbative QCD via Adler–Bell–Jackiw anomalies in higher than treelevel diagrams. However, it is believed that the quantity B − L , where L is lepton number, is exactly conserved [40]. Measurements of hadrons from e + e − annihilation experiments provide a particularly clear test of theQuark Model and QCD. If one assumes the existence of charged quarks, then the process of e + e − → q ¯ q ,mediated by a photon, is expected. However, given confinement, there must be a subsequent step in whichthe quarks become hadrons, which is non-perturbative. Nevertheless, if all hadronic final states are integrated,properties of the fundamental process can be inferred. In particular, one can compare the inclusive crosssection for having a hadronic final state [41], σ ( e + e − → hadrons) , to that of having muons in the final state, σ ( e + e − → µ + µ − ) . One might naively expect the following counting relation σ ( e + e − → hadrons) = 3 (cid:88) q e q σ ( e + e − → µ + µ − ) , (2.12)where e q is the fraction of the unit charge for the quark and the factor of three is for the three colors in QCD.The ratio reduces to R = σ ( e + e − → hadrons) σ ( e + e − → µ + µ − ) (2.13) = 3 (cid:88) q e q . (2.14)Thus, R = 2, 10/3, or 11/3 for 3, 4, or 5 quark flavors respectively. Fig. 2.4 shows R as a function of the scatteringmomentum scale from world data compared to the naive model. The steps in the predictions correspond tothe scale at which there is enough total energy to create heavier quark pairs. The vertical arrows correspondto hadronic resonances going off scale. The agreement validates the three quark colors and the Quark Modelin general. The modest disagreement can be attributed to the fact that higher order processes involving gluonvertices were ignored.The scattered partons in these reactions become hadrons through a process called fragmentation. At suf-ficiently high energy, the color charges can become dozens of hadrons emanating from the collision in a roughlyconical pattern called a jet . This non-perturbative hadronization process is parameterized by fragmentation func-tions, probability densities in terms of a momentum scale and the fraction of the initial parton’s momentum goingto each hadron [1]. These fragmentation functions can be used to compute structure functions that contribute The ability to separate the quark scattering properties from the hadronization by a difference of scales is called factorization. σ ( e + e − → hadrons) to that of σ ( e + e − → µ + µ − ) as a function ofmomentum scale from world data (points) compared to a naive quark and color scaling model [41].directly to individual hadron production cross sections. Though e + e − reactions were used for this example, thisprocess of fragmentation is universal and applies to parton scattering in hadronic collisions as well.The phenomenological Lund string model [42], represented in Fig. 2.5, considers fragmentation as aniterative breaking of the color strings mentioned in Sec. 2.2.3. In this picture, a fragmenting quark–anti-quarkpair is placed on a light cone, spreading in opposite ( x ) directions with gluon string connections. The quarksprogress until the potential energy in the string grows to the point that it “breaks” by creating a new quark–anti-quark pair (hadron) at a space-time point called a vertex. Each vertex is spacelike separated and the hadron carriesaway some fraction of the total energy. The probability to tunnel out a hadron of mass m is given by the LundSymmetric Fragmentation Function f ( x ) of the form f ( x ) = N x (1 − x ) a e − bm x . (2.15)The process continues until there is not enough energy to further break the string. Vertices will lie on a hyperbolain the space-time diagram on average. The model represents gluons as excitations on the string. Hadrons areconsidered as quark pairs without enough energy to break the string connecting them; the quarks switch directionsback and forward in a confined “ yo-yo mode”. The Lund model is employed in a number of Monte Carlo (MC)event generators, and has enjoyed great success representing jet fragmentation to hadrons. These generators (themost popular being the P event generator [43]) have become an indispensable tool for experimental efforts.5Figure 2.5: A graphical representation of the Lund string fragmentation model. The left figure shows the Feynmandiagram of the e + e − → q ¯ q process, and the right plot shows the space-time diagram of the fragmentation [44].In principle, summing the four-momenta of all the hadrons in a jet will yield the kinematics of the initialparton. However, in practice, it is impossible to know the origin of any given hadron in an event, particularlyin hadronic collisions where there are potentially many partons interacting simultaneously. Therefore, clusteringalgorithms were developed to collect nearby hadrons into jet objects. Presently, the most popular method is theso-called anti- k t clustering algorithm [45].The anti- k t algorithm is part of class of sequential clustering algorithms differentiated by a distance metricbetween particles i and j (or detector objects like reconstructed tracks or calorimeter towers), d ij , and betweenparticles i and the beam, d iB . The process is to find the smallest distances, and if it is d ij , combine the particles;if it is d iB , label it a jet and remove it from the list. Continue the process until the list of particles is empty. Thedistances take the form: d ij = min( k pT i , k pT j ) ∆ ij R (2.16) d iB = k pT i , (2.17)where ∆ ij = ( y i − y j ) + ( φ i − φ j ) and k T i , y i , and φ i are the particle’s transverse momentum, rapidity,and azimuthal angle respectively. The parameter R sets a scale for the rough size of the clusters. If p = 1 , thealgorithm is called k t , if p = 0 , it is called Cambridge/Aachen, and if p = − , it is called anti- k t .6Each version has the common geometric distance factor, and thus, clustered jets tend to be composed ofconstituents close in angle. However, the k t algorithm is highly susceptible to low momentum, soft , fragmentsthat are not necessarily part of a coherent jet, particularly problematic in “messy” hadronic collisions. In theanti- k t case, soft particles are likely to be clustered with nearby high momentum, hard , particles which formthe core of a conical jet shape. The overall jet shape is defined, primarily, by the hardest particle, in contrast tothe k t jet case. Fig. 2.6 shows a comparison between k t and anti- k t algorithms on a single event with few hardfragments and many random soft “ghost” particles (for details see Ref. [45]). The shape of the jets in the k t caseare affected by the ghost particles, whereas the anti- k t jets are more circular.Figure 2.6: A comparison between k t (left) and anti- k t (right) jet reconstruction algorithm performance usingan event generated with few hard fragments and many random soft “ghost” particles [45]. In the previous Section 2.3.1, hadrons were defined by their quark content. However, on short timescales,quantum fluctuations make the story much more complicated. The quarks in a hadron radiate gluons that getreabsorbed or connect to the other quarks, and these gluons split to quark anti-quark pairs, etc. Thus, given ahigh enough resolving power, one not only sees the quarks that contribute to the quantum number rules for agiven hadron (valence quarks) but also other quarks in the SM that are fluctuating in and out of existence withinthe hadron (sea quarks).7Consider lepton-proton scattering in which the interaction is mediated by a virtual electroweak boson asshown in Fig. 2.7. As discussed above, the structure of an object depends on the scale of the probe. At lowenergies, the long wavelength of the interaction can only resolve the proton as a whole; the internal interactionsof the constituents are smoothed over at long time scales, and the body behaves coherently. Calculations in thisregime take the form of Mott scattering [46].On the other hand, consider the case at very high energies, or deep inelastic scattering (DIS), in whichthe proton breaks apart [47]. To the lepton, the proton is highly Lorentz contracted and its constituents are timedilated. The internal dynamics of the proton are happening at much longer timescales than the interaction, andthus, the boson is imaging a freeze frame of the state of the proton in which the partons have a fixed fraction ofthe longitudinal momentum, x . At a high-scattering-momentum scale, Q , the short distance of the interactionmeans the interference with any other interaction between the lepton and proton can be ignored, and the non-perturbative hadronization of the struck parton happens much later and can be factored out of the process.Thus, the proton can be considered a source of approximately incoherent partons, and the scattering between thepartons can be considered elastic. The fundamental pieces of information are probability distributions for eachpossible parton at any given x . Furthermore, assuming factorization holds, these Parton Distribution Functions(PDFs) are universal descriptions of the hadron, i.e., they do not depend on the probe.Figure 2.7: Diagram of a DIS process [48].8The scattering cross section for this process, considering photon exchange only, can be expressed in termsof proton structure functions, F and F L , as dσ dxdQ = 4 πα xQ (cid:2) (1 + (1 − y ) ) F ( x, Q ) − y F L ( x, Q ) (cid:3) , (2.18)where y is the fraction of the lepton’s initial energy lost in the interaction [1]. For elastic scattering on freepoint-like partons, the structure functions obey so-called Bjorken scaling , in which they are independent of Q ,and F L = F − xF = 0 . (2.19)The structure function can be expressed in terms of the PDFs, f q ( x ) , for quark q simply as F ( x ) = x (cid:88) q e q f q ( x ) . (2.20)Figure 2.8: Proton structure function, F , for various Q and x values as measured in DIS experiments [1].9Structure functions of the proton, F , are plotted for various Q and x values in Fig. 2.8. One can seethe scale independence for a range around x ≈ − . However the scaling is broken for lower x . This breakingcan be attributed to corrections from higher orders in pQCD that were not considered above. The parton cansplit before interacting by emitting a gluon that carries away some momentum. There is an ambiguity betweenwhat corrections should be included as part of the hadron structure, f q , and what should be part of the pQCDscattering coefficients. The standard approach is to realize that the emissions should be collinear with the partonto some extent. Thus an arbitrary collinear factorization scale is imposed on the transverse momentum of theemissions, below which, it is categorized with the hadron. The integrals over these processes are divergent butcan be renormalized into running PDFs, as with the running of the QCD coupling. The DGLAP evolutionequations govern the evolution of the PDFs with the scale parameter [49–52]. As with the renormalization scale,the collinear factorization scale is typically chosen to be the scattering parameter Q [1].Figure 2.9: Proton PDFs from global fits to world data as a function of parton x for momentum scales GeV (a)and GeV (b) [1, 53].Fig. 2.9 shows proton PDFs for two different momentum scales. The valence quarks are peaked at signif-icant fractions of the total momentum as one might expect. At lower values of x , the probability of finding a seaquark is greater than that of the valence quarks. However, in this region the gluon density is much greater, and0even looks divergent at low x and high Q . It is believed that at low enough x , the gluon density saturates as therate of gluon recombination reaches that of splitting.Gluon saturation is associated with a scale, Q s ( Q ) , which can be interpreted as the maximum color chargeper transverse area of the nucleon at interaction scale Q [54]. For sufficient collision energies, Q s (cid:29) Λ QCD ,and thus the gluon fields my be treated in the weak coupling regime. However, the high densities amplify theinteractions such that they cannot be treated perturbatively. The problem is framed in a renormalization grouppicture where high x partons are viewed as static sources of lower x gluons, and the interactions are resumed inorders of the parton rapidity. The outcome is an effective classical Yang-Mills theory that describe the overlappingcolor fields as a Color Glass Condensate (CGC) [54]. In this theory, coherent low x gluons condense and formeffective partons with transverse size on the order of /Q s . This framework has been used with the IP-Sat modelto describe the low x region of DIS data to good accuracy [55].So far, the discussion has been limited to free protons. However, the internal structure of nucleons boundin nuclei can also be probed in DIS. The PDFs of a nucleus, f Aq , with A total nucleons and Z protons can bewritten as a linear combination of the individual proton and neutron PDFs, f p/Aq and f n/Aq , as f Aq ( x, Q ) = ZA f p/Aq ( x, Q ) + A − ZA f n/Aq ( x, Q ) . (2.21)It was observed, first by the European Muon Collaboration (EMC), that the PDFs for protons bound to largenuclei differed from those for free protons, f pq [56]. This finding was unexpected because of the vast differencein scales between the nuclear and nucleon binding energies. The observation was that there was a reductionin the scattering rate for x ≈ . , and an enhancement for x ≈ . . Further studies to lower x showed areduction for x < . [57]. These findings prompted the development of nuclear PDFs (nPDF) to be used inthe calculations of scattering cross sections in nuclear collisions. These nPDFs are determined from global fits toworld data. Fig. 2.10 gives an example of nucleon nPDFs represented as ratios R P bX ( x, Q ) = f p/P bX ( x, Q ) f pX ( x, Q ) , (2.22)for valence quarks, X = V , sea quarks, X = S , and gluons, X = G . One can see the reduction for x ≈ . ,enhancement for x ≈ . , and depletion for x < . , now known as the EMC-effect, anti-shadowing, and1shadowing regions, respectively. One also sees a sharp increase in the valence quark case at the highest values of x due to the Fermi motion of the nucleons within the nucleus.Figure 2.10: Proton nPDFs from global fits to world data as a function of parton x for momentum scale GeV.The results are presented as the ratio of PDFs in Pb nuclei to those from free protons for valence quarks, left, seaquarks, middle, and gluons, right [58]. Given that hadrons are composite objects with well defined binding energies, it is natural to assume thatthere could be a form of matter with high enough energy density such that hadrons could not exist. In this state,quarks and gluons would be deconfined and free to move about independently. This is analogous to increasingthe temperature of ice to make water or to ionize gas into a plasma. Asymptotic freedom implies the existenceof a weakly interacting gas of quarks and gluons at extremely high temperatures ( T (cid:29) Λ QCD ). However, in thestrongly coupled regime, it is not obvious what to expect.The first work suggesting a limit to the temperature of hadronic matter is that of Hagedorn in his statisticalbootstrap model [59] which, interestingly, came before the establishment of the Quark Model and QCD as thetheory of the strong interaction. In this case, he was trying to understand the origin of the exponential spectrumof hadronic masses by applying simple equilibrium statistical mechanics. The model postulated that hadronicstates are self similar; each state is composed of lighter states ad infinitum . A limiting temperature naturallyarises due to the increasing availability of higher mass states with increasing energy, thus limiting the averagekinetic energy of per particle. By constraining this model with the measured hadron spectrum, a temperatureof T c ≈ MeV was extracted. With the acceptance of the Quark Model, it was proposed that this critical2temperature is instead the result of a second order phase transition from hadronic matter to matter composed ofdeconfined quarks and gluons called quark-gluon plasma (QGP) [60, 61].In the decades since these initial predictions, deconfinement has been explored in LQCD simulationsin which the QCD equation of state can be determined. Calculations in this framework are limited to low netbaryon densities due to due to the so-called “sign problem” in lattice quantum field theories [62]. However, resultsindicate a smooth crossover between quark and hadron matter at T ≈ MeV in remarkable agreement with theHagedorn temperature. Fig. 2.11 shows temperature dependent pressure, energy, and entropy densities of quarkmatter from lattice simulations [63]. At high temperature, the values slowly approach the non-interacting particlelimit as expected from asymptotic freedom. Around T = 150 MeV, the values vary rapidly with temperature asthe phase space grows from the added color degrees of freedom.Figure 2.11: Temperature dependent pressure, energy, and entropy densities of quark matter from lattice simu-lations [63].The phases of QCD matter are typically depicted on a scale of temperature and net baryon density (orbaryon chemical potential) as shown in Fig.2.12. The nuclei of atoms exist at zero temperature and baryon densityof one. For small baryon densities, the transition from hadrons to QGP is around T = 150 MeV, where LQCDsimulations indicate a smooth cross over between QGP and hadronic phases. Alternatively, at low temperatureand high baryon density are neutron stars, and as the density grows, long range color Cooper pairs are believed toform creating a superconductor type material [64]. It is presently unknown whether a first order phase transition3and associated critical point occurs at moderate temperature and baryon density, but experimental search effortsare underway at RHIC, FAIR and NICA.Figure 2.12: A qualitative description of the QCD phase diagram for any given temperature and net baryondensity.The experimental evidence for the creation of the QGP in heavy ion collisions at RHIC and the LHC areplentiful. Aspects of which will be discussed in detail in Sec. 2.4. At RHIC and the LHC, respectively, Au and Pb nuclei are accelerated to velocities close to the speed oflight and then allowed to collide. The nuclei are Lorentz contracted into disks in the center-of-mass (lab) frameby factors of 100 and 2500. The overlapping disks form a geometry dependent on the impact parameter and thestochastic distribution of the nucleons within each nucleus; nucleons in the overlap region are said to participate and the rest spectate . The spectator nucleons shear off and continue at beam rapidity which is roughly 5.3 and8.5 for the two cases. The participating nucleons act as sources of longitudinal quarks and gluons that form acontinuum of interacting color fields as the two nuclei move through each other. Most interactions are soft, withlittle exchanged momentum (i.e. Q (cid:46) GeV ), and most of the energy ends up at large absolute rapidities nearthe beam line. However, a significant amount of energy is distributed in the final state amongst low momentumhadrons at mid-rapidity ( | y | < ). For example [63], in head on Pb+Pb collisions with total energy per nucleon4pair of √ s NN = 2 . TeV, the total transverse energy in | y | < . can be around . TeV. The energy densitycan be estimated as (cid:15) = 1 A t dE T dy , (2.23)where A is the area of the overlap and t is the time since the initial contact [65]. In this case, about fm / c afterthe collision gives (cid:15) ≈ GeV / fm , or about 20 times that normal nuclear matter.As will be shown in Sec. 2.4.3, the QGP that carries this immense energy density acts as a strongly coupledliquid, not a weakly interacting gas as would be expected at much higher energies. This liquid has been observedto flow in response to the initial geometry of the colliding nuclei, a process described with good accuracy byrelativistic hydrodynamic simulations [4–6]. Additionally, the medium has shown a high level of opacity to highenergy color charges created from scatterings in the earliest times of the collisions [8–10]. This phenomenon ofjet quenching will be discussed in more detail in Sec. 2.4.4. Finally, a growing body of evidence points to thecreation of a QGP in small collision systems like p +Pb and even pp [11–17]. This will be discussed in Sec. 2.4.5 In nuclear collisions (A+A), one often wants to study the rates of processes in comparison to those in pp collisions. In this way, effects from the nucleons being part of larger nuclei can be separated from effectsof individual nucleon-nucleon scattering. However, there will be a trivial scaling just because A+A collisionshave more binary nucleon interactions and, thus, more opportunities to include any given process. Therefore, tomake these comparisons, one would want to know the total number of pp -like collisions, N coll , or consideringthat some quantities might instead scale with the total initial matter density, one would want to know the totalnumber of participating nucleons, N part . The scaling factor for hard processes is the nuclear thickness function , T AB , defined as T AB = (cid:90) d (cid:126)b (cid:90) d (cid:126)xρ A ( (cid:126)x ) ρ B ( (cid:126)x − (cid:126)b ) , (2.24)for nuclei A and B with transverse nucleon density profiles ρ A ( (cid:126)x ) and ρ B ( (cid:126)x ) respectively. This acts as an effectivenucleon-nucleon luminosity and, given the nucleon-nucleon inelastic cross section, σ NN , can be related to N coll T AB = N coll σ NN . (2.25)The problem is that there is no way of knowing these quantities directly since the nuclei collide with random,femtometer scale, impact parameter and have fluctuating distributions event-to-event.The strategy is to measure centrality as percentiles of some detector quantity as a proxy of overall eventactivity such as multiplicity or total transverse energy, and then map this distribution onto the distribution ofpossible N part or N coll . Thus, these quantities can be inferred on average from the event activity. An illustrationof centrality as measured with mid-rapidity charged particle multiplicity is shown in Fig. 2.13. So-called central collisions have a large N part , small impact parameter, b , and produce a large number of charged particles; peripheral collisions have a small N part , large b , and produce a small number of charged particles. The process of determiningcentrality will be discussed in detail in Ch. 4. Here we present an overview of determining the distributions of N part and N coll with a Monte Carlo (MC) Glauber model [7].The Glauber model works in the short wavelength limit where nucleons can be considered semi-classicalobjects that have straight line trajectories, undisturbed by interactions. Nucleon positions are chosen randomlyevent-by-event according a realistic 3-d distribution. For spherical nuclei, like Pb and Au, the distribution is onlyradially dependent and takes the form of a Fermi distribution ρ ( r ) = ρ 11 + e r − Ra . (2.26)The radius, R , and skin depth, a , are chosen to match measured charge distributions from low energy electronscattering experiments [66]. To model inter-nucleon repulsion, a minimum separation (typically d min > . fm)is imposed by re-throwing any given nucleon if it overlaps with another. The parameters are scaled through aniterative procedure to account for this distortion on the nucleon distribution function [66].Given the nucleon positions, the general assumptions allow for an entirely 2-d collision process in thetransverse plane. Impact parameters, b , with-respect-to the calculated nuclei centers are chosen randomly suchthat dN/db ∝ b in a range significantly larger than the average diameter of the nucleus. Nucleons are given aball diameter, D = (cid:112) σ NN /π , dependent on the measured pp cross section, σ NN for the given collision energy.6Figure 2.13: An illustration of centrality as measured with mid-rapidity charged particle multiplicity [7].Figure 2.14: An example of a Pb+Pb collision from the PHOBOS MC Glauber simulation [67]. The nucleonsare represented as circles, where their color marks which nucleus they originate from. The closed circles areparticipating nucleons and the dashed circles are spectating nucleons.7Individual nucleons are tagged as wounded (or participating) if they overlap with any nucleons from the othernucleus. The nuclei collide if there is at least one nucleon-nucleon interaction. Fig. 2.14 shows an examplePb+Pb collision from the PHOBOS MC Glauber simulation [67].Figure 2.15: N part distributions from p +Pb collisions from the PHOBOS MC Glauber simulation [67]. Theblack points are from the standard Glauber implementation, and the blue and red points are from the Glauber-Gribov extension with two different values of the fluctuation parameter Ω .The Glauber-Gribov extension of the above simulation incorporates nucleon size fluctuations. In this case, σ NN is distributed as (1 /λ ) P ( σ/λ ) where P = ρ σσ + σ e − ( σ − σ σ ) . (2.27)Here, σ and Ω are the mean and width of σ NN . Fig.2.15 shows N part distributions from p +Pb collisions forsimulations using both standard Glauber and the Glauber-Gribov extension for proton size fluctuations (only theprojectile proton size is allowed to fluctuate in this case). The added fluctuations act to broaden the distribution,giving access to larger values of N part in the tail corresponding to larger sizes of the proton.These Glauber models are important, not only to determine centrality as a whole, but because they canprovide geometrical information about the initial energy densities that are used as initial conditions for trans-port models like hydrodynamics. The spatial distribution of participating nucleons can be decomposed into8eccentricity moments as ε n = (cid:112) (cid:104) r cos( nφ ) (cid:105) + (cid:104) r sin( nφ ) (cid:105) (cid:104) r (cid:105) , (2.28)where the brackets indicated averages over nucleons and events [68]. As will be discussed in more detail in thenext Section, non-zero eccentricities give rise to momentum anisotropies in the final state hadron spectra viahydrodynamic expansion. In the previous section, the Glauber model was described as a method to determine the number and spatialgeometry of the participating nucleons in heavy ion collisions. How the energy deposited by these overlappingnucleons evolves into the hadrons seen in detectors is the topic of this Section. The standard paradigm for thismulti stage process proceeds in order: 1) initial energy depositions, 2) pre-hydrodynamics, 3) hydrodynamicevolution, 4) hadronization, 5) hadronic scattering, and finally, free streaming of hadrons to the detector. Thereare quite a few packages on the market that simulate this process, and as a whole, they have been highly successfulin describing the experimental results. This is not meant to be an exhaustive review of the topic, but a briefoverview of the techniques typically used. For a detailed treatment of the subject, see Refs. [5, 69].Hydrodynamics is an effective field theory of dynamical matter appropriate at large distance and timescales relative to the microscopic constituents and their dynamics but small with respect to the entire system.The dynamics of the theory are determined by tracking conserved currents described by the energy-momentumtensor, T µν , a symmetric space-time tensor constructed from the effective energy density and velocity fields, (cid:15) and u µ , the metric tensor, g µν , and all gradients that respect the symmetries. If the system is close to equilibrium,the gradients will be small. Thus, T µν is often represented as a gradient expansion T µν = T µν (0) + T µν (1) + T µν (2) + · · · , (2.29)where T µν (0) contains no gradients, T µν (1) has single gradient terms, etc. In Minkowski space, conservation rules areimposed by requiring ∂ µ T µν = 0 , (2.30)9which serve as the equations of motion. Similar rules can be made to include conserved charges, like Baryonnumber, but these are excluded from the present conversation. The zeroth order approximation gives rise to idealhydrodynamics such that T µν (0) = ( (cid:15) + P ) u µ u ν + P g µν = (cid:15)u µ u ν + P ∆ µν , (2.31)where the two P factors have been grouped into the projection tensor, ∆ µν . The coefficient P is identified asthe pressure which must be related to (cid:15) through an equation of state which is typically calculated at equilibriumin LQCD simulations.In practical scenarios, like high energy nuclear collisions, systems are not in equilibrium and there aresignificant gradients. Including higher orders introduces dissipative terms that are typically grouped into scalar, Π , and traceless, π µν , components representing bulk and shear stress respectively. The energy-momentum tensortakes form T µν = T µν (0) + π µν + Π∆ µν . (2.32)To first order, this becomes T µν = T µν (0) + ησ µν + ζ∂ ρ u ρ ∆ µν , (2.33)where σ µν = ∆ µρ ∂ ρ u ν + ∆ νρ ∂ ρ u µ − 23 ∆ µν ∂ ρ u ρ . (2.34)The transport coefficients, η and ζ , are the shear and bulk viscosities which depend on the internal dynamics ofthe microscopic theory, and can, therefore, provide a connection from hydrodynamic simulations to fundamentalproperties of QCD. Given an initial T µν , these equations can then be used to evolve fluid cells in simulation. The initial condi-tions are generated by first determining an energy density, typically by parameterizing the overlap of participatingnucleons in a Glauber model. For example, one can add a simple Gaussian at the location of each nucleon [70], If second order corrections are included, there emerge 15 separate coefficients, and third order corrections bring this number to68 [5]. . - . fm / c), the system is packaged into T µν and passed offto the hydrodynamic simulation. This pre-hydrodynamic stage has the effect of smoothing out the initially largeenergy gradients and bringing the system into the range of applicability of hydrodynamics. There is a significantuncertainty in these early stage models and many seem rather ad hoc . Notice the broad range of techniques indescribed above, from the zero-coupling free streaming case, to the weak coupling IP-Glasma, and finally to thestrong coupling superSONIC. In large collision systems, the hydrodynamic phase is so dominant that results arerelatively insensitive to the particular model or start time. However, for small systems, it can have a significantimpact. Therefore, small collision systems could serve as a testing ground for pre-hydrodynamic models.Once T µν has been passed to the hydrodynamics code, the system is evolved until individual fluid cellsreach the critical temperature, at which point hadronization takes over. A contiguous transition hyper-surface, σ ,is constructed by connecting cells below the critical temperature. Then the phase change to hadrons is handledby the Cooper-Frye prescription [76] such that energy and momentum is conserved; i.e. T µν is made to becontinuous across the boundary. If the fluid cells on the transition hyper-surface are assumed to be in local1equilibrium, the momentum distribution of hadron resonance i is E dN i d p = (cid:90) f i ( x µ , p µ ) p µ dσ µ , (2.35)where f i ( x, p ) are distribution functions in phase space. The hadrons then undergo a gas scattering phase untilbecoming so diffuse that they free-stream to the detectors. All observables in particle collisions are derived from measurements of final state particles that end up indetectors. As discussed in briefly in Sec 2.3.2, QCD processes are separated by differences in scale. Particleswith large p T originate from perturbative processes that show different behavior of production rates for low p T particles. In nuclear collisions, low p T particles predominantly come from the hadronization of the bulk QGPmedium and are thus emitted at later times, whereas high p T particles are created in hard scatterings in the initialoverlap of the colliding discs. Observables relating mostly to the soft, bulk interactions are discussed here, andthose relating to hard processes are detailed in the next Section 2.4.4.The p T spectrum of particles can then be divided into low p T ( p T (cid:46) GeV) and high p T ( p T (cid:38) GeV)regions. The left panel of Fig. 2.16 shows the p T spectrum of charged particles from central Au+Au collisions atRHIC. The low p T behavior is roughly exponential and in good agreement with hydrodynamic simulations. Athigh p T , the spectrum changes to a power law shape that can be described by pQCD. The collective hydrodynamicexpansion of the QGP affects the shape of the particle p T spectrum. The fluid undergoes rapid radial expansionin the transverse plane, giving particles a large velocity boost. The right panel of Fig. 2.16 shows the p T spectrumfor identified hadrons overlaid with results from hydrodynamic simulations. The spectrum for heavier hadronsare pushed out to higher p T as one would expect if the particles gained a common velocity boost, providingevidence for the presence of strong radial flow.Hydrodynamic expansion converts initial energy density gradients from overlapping nucleus geometryanisotropies into hadron momentum distributions. Thus, an imprint of the initial transverse distribution of thenucleons is left on the distribution of final state hadrons. This is in striking contrast to what one would expectif there was no collectivity; if each nucleon-nucleon interaction were independent, the total distribution of the2Figure 2.16: Left: The p T spectrum of charged hadrons from 200 GeVAu+Au collisions measured with a variety ofRHIC experiments. The data is overlaid with theoretical calculations from both hydrodynamics and pQCD [6]. Right: The p T spectrum of identified charged hadrons from 2.76 GeVPb+Pb collisions. The data is overlaid withtheoretical calculations from the VISHNU hydrodynamic model [77].produced particles would be azimuthally symmetric. These azimuthal anisotropies, are measured relative to theso-called reaction plane, Ψ r , the plane spanned by the impact parameter and the beam axis. The distribution ofparticle azimuthal angles can then be measured relative to Ψ r and decomposed in a Fourier series E d Nd p = 12 π d Np T dp T dy (1 + ∞ (cid:88) n =1 v n cos [ n ( φ − Ψ r )]) , (2.36)where the coefficients v n quantify the magnitude of the anisotropy. The coefficients v and v quantify ellipticand triangular flow respectively.The reaction plane must be estimated event-by-event. This can be done using the anisotropy of the particlesthemselves by calculating the event plane as Ψ n = (cid:16) tan − Σ i sin( nφ i )Σ i cos( nφ i ) (cid:17) /n , (2.37)where the sums run over the particles, and n is the harmonic number. In this way, each harmonic estimates adifferent event plane. In practice, the event plane is determined in a different region of pseudorapidity than where3the flow is measured in order to remove auto-correlations. Up to a correction from the event plane resolution,the flow coefficients can be determined simply as v n = (cid:104) cos[ n ( φ − Ψ n )] (cid:105) , (2.38)where the angle brackets represents an average over all particles and over all events.Complementary methods to determine v n have been invented using so-called multi-particle cumulants .Instead of estimating the reaction plane, these methods correlate particles in various combinations. For exam-ple [78], v n can be calculated using 2- and 4-particle correlations as v n { } ≡ (cid:112) (cid:104) cos[ n ( φ − φ )] (cid:105) (2.39)and v n { } ≡ (cid:0) (cid:104) cos[ n ( φ − φ )] (cid:105) − (cid:104) cos[ n ( φ + φ − φ − φ )] (cid:105) (cid:1) / . (2.40)The different multi-particle estimators of v n are sensitive to fluctuations in different ways, and can therefore beused to learn more about the underlying v n distributions [79]. Using the previous example, v n { } = (cid:113) (cid:104) v n (cid:105) + σ v n (2.41)and v n { } ≈ (cid:113) (cid:104) v n (cid:105) − σ v n , (2.42)where the approximation is exact in the limit of Gaussian fluctuations.Figure 2.17 shows a distribution of 2-particle ∆ η - ∆ φ correlations in mid-central Pb+Pb collisions. Thereare two ridge structures at ∆ φ = 0 and ∆ φ = π which extent across the whole acceptance in ∆ η . These ridgesindicate a strong elliptical modulation to the momentum distribution of particles in the transverse plane. Thefact that the structure is almost independent of the particle separation in η suggests that this is a global eventphenomenon that fits with the collective expansion picture of the hydrodynamic model. The strong elliptic flowis a response to the highly elliptical shape of the nuclear overlap in mid-central collisions. Additionally, there isa peak near ∆ η = ∆ φ = 0 from short range correlations created by particle decays and jets. If flow correlations4Figure 2.17: Distribution of 2-particle correlations in ∆ η and ∆ φ from 30-40% central Pb+Pb collisions at √ s NN = 5 . TeV [80]. Both particles are required to have p T = 2 − GeV.are defined to be those corresponding with the event geometry, then these jet-type correlations can be considered non-flow . Because a large component of non-flow comes from “small number” particle correlations like decays,multi-particle correlation methods using larger numbers of particles tend to be less sensitive to non-flow. Inlarge collision systems, flow signals are strong enough to dominate non-flow; however, as will be discussed inmore detail in Sec.2.4.5, care must be taken to separate non-flow from flow signals when studying small collisionsystems.Fig. 2.18 shows the elliptic flow, v , from various methods plotted as a function of event centrality inPb+Pb collisions. The v is smallest in the most central collisions where the impact parameter is small and theoverlap region is more circular. The distribution peaks between 30% and 50% central where the overlap geometryis most elliptical. The v { } is everywhere greater than that of the event-plane method (EP), and the v { } isalways less than that of the EP. This makes sense given the way the fluctuations influence v { } and v { } ; theseparation between the two methods is larger in the most central and most peripheral cases, where the geometricanisotropy is driven by the event-to-event distributions of nucleons and less by the impact parameter. On the5Figure 2.18: Elliptic flow v as a function of centrality from the event-plane method, 2- and 4-particle correla-tions, and Lee-Yang zeros methods √ s NN [81].other hand, v { } should be more insensitive to non-flow correlations than v { } , so perhaps there is somecontamination.Simulations using viscus hydrodynamic expansion are able to reproduce the distributions of v n to a highdegree of precision at low p T . Fig.2.19 shows v n as a function of particle p T using the EP method [82]. The v islarger than the other harmonics as expected from the large ellipticity of the overlapping nuclei in this centrality.Additionally, the viscosity dampens higher harmonics to a greater degree; this produces lower values for higherorder v n given the same initial spatial eccentricities. The points for each harmonic increase with p T over theplotted range as one might naively expect from anisotropic expansion; i.e., fluid cells with higher velocity feltgreater expansion forces from gradients and, thus, have a greater anisotropy. The theoretical curves match thedata points almost perfectly. Anisotropic flow can also be studied with identified hadrons. Fig. 2.20 shows v for identified hadrons; the heavier hadron v distributions are pushed out in p T in good agreement withhydrodynamic simulations, again providing evidence for a collective velocity field driving the expansion.6Figure 2.19: Coefficients v n from the EP method from 30-40% central Pb+Pb events plotted as a function of p T with comparisons to theoretical simulations using viscus hydrodynamic expansion [82].Figure 2.20: Coefficient v for identified hadrons measured at various centralities in Pb+Pb collisions with √ s NN = 2 . . The data are overlaid with curves from hydrodynamic simulations TeV [83].If the flow coefficients are plotted in a broader p T range, as in Fig. 2.21, one sees a much more complicatedstructure. As before, v n rises with p T until about 3 GeV, then decreases for higher p T . At p T ≈ GeV there7Figure 2.21: Coefficients v n from 30-40% central Pb+Pb events plotted as a function of p T [80].is a change in slope indicating, perhaps, a change in the origin of the correlation. Hydrodynamic expansionpredicts the low p T rise of v n , but predicts only monotonically increasing behavior with p T . As discussed above,about 3 GeV is where the slope in the particle p T spectrum changes indicating a change from bulk to hardscattering particle production. Thus it fits that this is where the hydro-like behavior of the v n stops. After 3 GeV,there are particles from jets and other hard scattering processes entering these correlations in increasingly higherproportions. Thus, one might assume there is a mixture of particles from QGP hadronization and from jetfragmentation at any given p T ; the lower p T region is dominated by particles from the bulk, and the high p T region is dominated by jet particles (almost by definition at say p T ≈ GeV). The possible origin of flow likecorrelations at high p T will be discussed in the next Section 2.4.4. In contrast to bulk particle production, hard scattering events are rare. These processes can be used todetermine information about nPDFs and may be considered probes to study the QGP. Particle p T distributionscan be compared to expectations from pp collisions scaled by T AB . Define the nuclear modification factor, R AB ,to measure process X in A+B collisions R AB ( p T ) = N evnt dN X AB /dp T (cid:104) T AB (cid:105) dσ Xpp /dp T , (2.43)8where N evnt N X AB is the per-event-yield of observations of X in A+B collisions, and σ Xpp is the cross section of X in pp collisions. Thus, R AB quantifies the comparison of process rates between A+B and pp collisions, where R AB = 1 indicates that the nuclear collision can be considered an incoherent superposition of N coll different pp collisions. Deviation from unity can be due to a number of possibilities:• First, the process could not scale with T AB . Consider particle production at mid-rapidity for collisionsof a fixed energy where x ≈ p T / ( √ s /2). At low x , where gluon densities are high, nucleons can beconsidered opaque disks of dense color fields. Thus, one would expect soft particle production toscale with simply with the overall number of overlapping nucleons ( N part ). On the other hand, hardprocesses occur between high x partons that are relatively diffuse within the nucleons. Therefore, theseprocesses should scale with the number of opportunities for the high x partons to find each other in acombinatorial sense ( N coll ). Models of particle production assuming a two component soft and hardlinear scaling with N part and N coll are generally very successful [84–86].• Second, the process could have a modified initial state production rate, as expected to some degree fromnuclear PDF modification and the proton–neutron ( isospin ) asymmetry.• Finally, the object’s kinematics could be modified due to interaction with the QGP; i.e., particles loseor gain energy on average, and, because the spectrum is steeply falling this causes an apparent increaseor decrease in the final state production rate respectively.Figure 2.22 shows the R AA for direct photons and Z bosons in Pb+Pb collisions. In this context, directphotons are defined as those created initially in hard scattering between partons and not from the decay of hadronslike π . Because these are not colored objects, they do not interact strongly with the QGP and, therefore, providea clean test of T AB scaling and nPDF effects. Both figures show an R AA around unity within uncertaintiesindicating no modification over a broad range of centrality. The left plot provides a prediction from a next-to-leading order pQCD calculation (J [87]) including nPDF modifications. The predicted modification issmall compared to the uncertainties in the data. At sufficient beam energy, it is believed the gluon fields condense and saturate, and the nucleons can be considered disks of CGC. R AA plotted as a function of the photon’s transverse energy [88].Right: Z boson R AA as a function of N part from Pb+Pb collisions at √ s NN = 5 . TeV [28].The left panel of Fig. 2.23 shows the R AA of charged hadrons in Pb+Pb collisions. The p T ranges from0.5 to almost 200 GeV and shows a significant suppression of the Pb+Pb spectra that is stronger in more centralcollisions. There is a rising behavior at low p T that peaks around 2 GeV, continuing to a decreasing trend untilabout 7 GeV, where it starts rising again until the statistics run out. It is worth pointing out that the extrema inthese distributions correspond to the points where the behavior in the flow coefficients also changes, shown inFig. 2.21 changed. As before, the low p T region is dominated by particles from the bulk; the rising behavior maybe due to the radial flow of the medium pushing particles to higher p T on average, while the overall suppressionis due to the different scaling behavior. At high p T , T AA scaling should hold and nPDF modification could notcause such a strong effect, thus, the suppression is an effect of the energy loss of particles traversing the QGP.This phenomenon is known as jet quenching .Microscopically, jets emerge from scattered asymptotically free partons; this happens at the earliest timesin the collisions. The high p T parton then must move through the developing QGP fire-ball while fragmenting.The parton and its fragments are colored and interact strongly with the plasma, radiating gluons and losing energyas they move through. Single hadron spectra give a piece of the picture, but the physics of in-medium energy0Figure 2.23: Left: Charged particle R AA for various centralities of Pb+Pb collisions at √ s NN = 2 . TeV as afunction of particle p T [89]. Right: inclusive jet R AA for various centralities of Pb+Pb collisions at √ s NN =5 . TeV as a function of jet p T [90].loss is convoluted with the fragmentation process. Thus, jet quenching can be studied more directly with fullyreconstructed jets. The right panel of Fig. 2.23 shows the inclusive jet R AA . As with the single hadrons there isa clear ordering with centrality, and suppression is less for higher p T jets. It is remarkable that even jets with p T near 1 TeV exhibit such large modification.At tree level in pQCD diagrams, quark and gluon final states are most often balanced by other quarks andgluons. Thus, jets tend to come in pairs balancing each other in p T and azimuth in a di-jet configuration. Thisprovides another way to study jet quenching by correlating reconstructed jets in any given event. These di-jetsystems are created anywhere in the nuclear overlap region and with isotropic orientation. One would assumethe amount of energy loss is a function of the distance traveled in the medium. Therefore, the level of quenchingfrom either is random event-to-event but correlated between the jets; i.e., if the jets were created near the surfaceof the medium, one jet is likely to experience more quenching than the other. Fig. 2.24 shows a representationof the calorimeter energy depositions in a single Pb+Pb di-jet event. The jets are balanced in azimuth, but thereis a large asymmetry in their p T .Figure 2.25 shows the di-jet p T balance, x J = p jet2 T /p jet1 T , where jets 1 and 2 are the leading and sub-leading jets respectively. The most probable value in the pp case is near unity showing that most di-jet systemsare balanced. There is a roughly linear decrease in the yield as one moves to lower values of x J . This is due to1Figure 2.24: A representation of energy depositions in the CMS calorimeter system in a Pb+Pb di-jet event [91].higher order multi-jet processes that produce a significant imbalance for the two leading jets. The case for centralPb+Pb collisions is very different where the most probable value is x J ≈ . . In more peripheral collisions, thePb+Pb values seem to smoothly converge to the pp values, showing that the effect is controlled by the transversesize of the QGP.Returning now to the non-zero flow coefficients observed at high p T in Pb+Pb collisions (Fig.2.21). Above10 GeV is in the hard scattering regime, and as is seen in Fig. 2.23, hadrons are significantly affected by quenching.It has been predicted that the quenching phenomena is what is causing the flow signal [93, 94]. In this case the jetenergy loss has a path-length dependence, and the shape of the QGP is elliptical at early times; thus the jet losesmore energy traversing the major axis than if it was traversing the minor axis. This geometry yields a modulationin the jet energy loss that gives rise to the “flow” signal. Consistently modeling the R AA and v n in a singleframework has been a long standing challenge to the field (known as the “ R AA + v puzzle”). However, progresshas been made, particularly by Ref. [22]. Figure 2.26 shows data of R AA , v , and v compared to theory curvesable to match the data quite well above about 10 GeV.2Figure 2.25: Di-jet yields from Pb+Pb collisions at √ s NN = 2 . TeV plotted as a function of their p T balance, x J , for several centrality classes [92]. Small collision systems are those in which at least one of the colliding nuclei comprises only a few nucleonsor even just one. Asymmetrical systems like d +Au and p +Pb were originally proposed to study nuclear effects notrelated to the formation for the QGP, and today, still provide the best hadron-hadron collision data for nPDFglobal analyses. However, relatively recently it was discovered that these small systems exhibit signs of collective3Figure 2.26: R AA (left), v (center), and v (right) from a theoretical jet quenching calculation showing goodagreement, at high p T , with the measured data [22].expansion similar to large systems [17]. In the years since, small systems have become a testing ground for QGPrelated phenomena.Figure 2.27: Two particle correlation functions in ∆ η and ∆ φ from minimum bias (left) and high multiplicity(right) selected events [14].Fig. 2.27 shows two-particle correlation functions from inclusive minimum bias (left) and high multi-plicity (right) pp collisions. The left plot is what one would expect, there is a strong peak at ∆ η = ∆ φ = 0 from short range jet and resonance correlations, and there is a broad away-side ridge from momentum balancingparticles (e.g. di-jet pairs). The high multiplicity plot on the right is similar except for the surprising additionof a noticeable near-side ridge extending the full range in ∆ η . This near-side ridge calls into question earlier4assumptions that these small systems are too small to create the QGP. Note the difference between the rightpanel of Fig. 2.27 and Fig. 2.17 for the Pb+Pb case; the flow signal-to-background is much stronger in Pb+Pbthan pp . Methods have since been developed to subtract contributions from non-flow correlations that wouldcontaminate the extracted v n . This will be discussed in detail in Ch.7.Figure 2.28: Left: average eccentricities ε and ε for each system in the geometry scan from MC Glaubersimulations. Right: Flow coefficients v and v from each system plotted as a function of particle p T [17].Since it’s initial discovery, flow signals have been systematically studied in many small systems at RHICand the LHC. Perhaps the most striking of these comes from the so-called small systems geometry scan at RHICto test whether the flow signal is correlated with the initial eccentricities, as with large systems. In this case,small nuclei with different spatial geometries, p , d , and He , were collided on Au target nuclei. The left panel ofFig. 2.28 shows the average ellipticity, ε , and triangularity, ε , for the three species from Glauber simulations. Asone might expect p +Au has significantly smaller ε than d +Au and He+Au, and He+Au has significantly larger ε than the other two. The right panel of Fig. 2.28 shows the resulting v and v from the scans. The ordering5is precisely what is expected given collective fluid expansion translating the spatial anisotropies into momentumanisotropies. Ref. [17] also shows hydrodynamic models are in good agreement with the data. Furthermore,Fig. 2.29 shows that a single hydrodynamic model can describe the measured flow signal from pp , p +Pb, andPb+Pb without tuning model parameters between the systems, providing confidence that the flow signal observedin these small systems is of the same origin as that of large systems.Figure 2.29: Flow coefficients, v n , plotted as a function of particle p T for pp (left), p +Pb (center), and Pb+Pb(right). Measured data are shown as black markers and are overlaid with curves from the superSONIC hydrody-namic simulation model [71].Fig. 2.30 shows a comparison to the charged hadron nuclear modification factor between inclusive Pb+Pband p +Pb systems. The p +Pb results show no sign of the suppression observed in Pb+Pb. If the flow results,discussed above, really do imply the creation of a QGP droplet, one might expect it to be accompanied by energyloss. One possibility is that these small systems create too small a droplet to affect the high p T parton; i.e. thereis some path-length dependence, but the path length is too short. Using the same reasoning as was used for thePb+Pb case, the fact that small systems like p +Pb do not exhibit jet quenching signals means there should be nomechanism to create a flow pattern at high p T .The right panel of Fig. 2.30 shows the flow coefficient v for these same systems, where the p +Pb values arescaled to match the Pb+Pb values at low p T . The shapes of the distributions are remarkably similar up until the p +Pb values run out of statistics at p T ≈ − GeV. The data are overlaid with a result from a jet quenchingcalculation showing good agreement with the Pb+Pb data for p T (cid:38) GeV. The fact that the p +Pb points agreein this range (though with significant uncertainty) raises the question of whether the same high p T flow signal6Figure 2.30: Left: Charged hadron nuclear modification factor R AA from Pb+Pb collisions compared to R p Pb as measured by the CMS collaboration. Right: Azimuthal anisotropy coefficient v from Pb+Pb and p +Pb scaledto match at low p T [95].exists in a system in which there is no observed jet quenching. The results in Ch. 7 will extend the p T range ofthis measurement and provide insight to the long standing R AA + v puzzle. hapter 3The Experiment It is hard to overstate how important particle accelerators have been in the development of humanity’scurrent understanding of the universe. Every new accelerator has led to discoveries that inform us of the mostbasic properties of matter and how it came to be in the cosmological record. This dissertation is based on datataken at the state-of-art and highest energy accelerator facility in the world, the LHC at CERN. The experimentalapparatus consists of the LHC accelerator chain that accelerates and collides hadrons, and the ATLAS detectorthat measures the particles emanating from the collision point. In this Chapter, an overview is given of the LHCand its injector chain, the ATLAS detector, with details provided for the most relevant aspects, and the datasetused for the analyses. The LHC [96] is the largest particle collider in the world. It is a 26.7 km circular synchrotron that inhabitsthe tunnel that was built for the, now decommissioned, Large Electron-Positron collider (LEP). The tunnel liesabout 100 m below the French and Swiss countryside and has eight straight sections, and eight arc sections.Due to the limited space in the LEP tunnel, the two rings that store the two counter-rotating beams share thesame twin-bore superconducting magnet system. The twin-bore design is more compact but less flexible dueto magnetic coupling between the rings. There are four detector experiments located on the ring at the fourinteraction points (IP) where the beams are crossed and switch magnet bores. The two general purpose and highrate detectors are ATLAS at IP1 and CMS at IP5. The purpose built heavy ion physics experiment, ALICE, livesat IP2, and LHCb, the experiment focusing on physics relating to the bottom quark, is located at IP8.8The beams are steered in the eight arc sections by 1232 8.33 T dipole magnets and focused with 392quadrupole magnets. To create such immense fields, the magnets are cabled with NbTi and held in the super-conducting regime at 1.9 K with superfluid helium. The eight straight sections are used for utility insertions.Four of these sections are used for the IPs, where IP2 and IP8 also store the beam injector systems. There are twosections used for beam cleaning and collimation: one section houses the beam dumping system, and one sectioncontains the two radio frequency (RF) systems - one for each beam. The RF cavities accelerate the beam byapplying an alternating gradient potential that attracts the beam particles as they enter, and repulses the particlesas they exit. Thus, the particles are clustered longitudinally in bunches with dimension defined by the frequencyand the speed of the bunches (the speed of light, c ). In the case of the LHC, the bunch length must be similarto that of the injector of 1.7 ns · c . Therefore, the 400.8 MHz RF system (creating 2.5 ns · c bunches) in the LHCcan accommodate the injected beam with minimal losses. The bunches are spaced by a minimum of 25 ns whichallows for 3564 bunch places on the rings.Figure 3.1: A diagram of the CERN accelerator complex, including the injection chain for the LHC [97].9The full injection chain connects some of the oldest and newest accelerator systems at CERN. A diagramcan be viewed in Fig. 3.1. The protons and Pb atoms are ionized and accelerated in Linacs up to 50 MeV forprotons and 4.2 MeV/n for Pb. The protons then enter the Booster at 1.4 GeV, the Proton Synchrotron (PS)at 25 GeV, the Super PS (SPS) at 450 GeV, before being injected into the LHC at 7 TeV. For Pb ions, they gofrom the Linac to the Low Energy Ion Ring (LEIR) at 72 MeV/n, the PS at 6 GeV/n, the SPS at 177 GeV/n,before entering the LHC at 2.76 TeV/n. Each beam of the LHC is filled in 12 steps from the SPS, and eachSPS fill takes 3 to 4 steps from the PS in a process that can take close to an hour. The filled bunch positions forma pattern such that bunch crossings occur at the IPs.The principal performance metric of a collider is luminosity ( L ). This is the beam-beam parameter thatwhen combined with a process cross section, gives the rate of said process as dN p dt = Lσ p . (3.1)For Gaussian beam profiles colliding head on, the instantaneous luminosity can be expressed as L = f n n πσ x σ y , (3.2)where n and n are the number of particles in the colliding bunches 1 and 2, f is the frequency at which theycollide, and σ x and σ y are the beam widths in x and y . The transverse trajectory of the particles in a synchrotronis approximated for each coordinate x and y as x ( s ) , y ( s ) = A x,y (cid:112) β x,y cos( ψ x,y ) , (3.3)where ψ and the amplitude function β are implicit functions of the longitudinal distance parameter s [1]. In thiscase, the β functions modulate the envelope of the beam in the transverse planes. Thus, for higher luminosity,the beam is squeezed so that its transverse size reaches a minimum at the IP; the β function at this minimum isdefined to be β ∗ or beta-star . The beams are sent through a special pair of quadrupole triplet focusing magnetsat each IP to lower the β ∗ to as small as possible. At IP1 and IP5 beam sizes are squeezed to about a factor of12.5 smaller. Fig. 3.2 shows a rendering of the beam optics in the ALICE detector at IP2 during the 2018 Pb+Pb The difference in the maximum energy between the protons and ions is due to the different mass-to-charge ratio. Magnetic fieldsbend charged particles with the same momentum-to-charge ratio in the same arcs. Thus, the maximum momentum for the Pb ions is Z/A = 82 / times the momentum of the proton in the same system. τ = N Lσk , (3.4)where N is the initial beam intensity, L is the initial luminosity, σ is the total scattering cross section for theparticles comprising the beam, and k is the number of IPs. At the LHC for pp running, given the design specifiedluminosity of L = 10 cm − s − , this gives the time to reach /e of the initial luminosity as about 29 hours [96].Adding in other corrections shortens the life time to about 15 hours. The scattering cross section is larger andinter-beam forces are stronger for heavy ion beams, and therefore, lifetimes tend to be shorter. Because of thisdecay behavior, most of the luminosity recorded at the experiments is from the earlier period in a given fill.Fig. 3.3 shows a representation of beam luminosity and intensity over time. One can see the stepwise increasesin intensity as the beam are filled from the SPS. Then the magnetic field ramps up as the bunches are brought tofull energy. The decay slope kinks at the point the beams are brought into collision. Finally the beam is dumpedabout 10 hours later, and the magnets are ramped down.Figure 3.3: An example from the online Vistar LHC monitoring showing the beam current, dipole magneticfield, and instantaneous luminosity as a function of time spanning a couple fills.2 The ATLAS experiment [99] is a large acceptance general purpose detector designed for high luminosityrunning at the LHC. The detector comprises many different specialized sub-systems in a cylindrical format with25 m diameter and 44 m length. The inner detector houses layers of silicon pixel and strip tracking detectorsspanning | η | < . and is surrounded by a thin superconducting solenoid creating a 2 T magnetic field. Outsideof the solenoid is the high-granularity Pb-liquid-argon (LAr) electromagnetic calorimeter covering the range | η | < . . The hadronic calorimeter is composed multiple technologies spanning | η | < . . Surrounding thecalorimeter is the three layer muon spectrometer amid a toroid magnet system. The trigger has a hardware Level-1(L1) system capable of a rejection of about × and a software High Level Trigger (HLT) providing furtherrejection based on the full detector information. A rendering of the detector is shown in Fig. 3.4.Figure 3.4: A rendering of the ATLAS detector with a cut away exposing the inner detector [99].ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) inthe centre of the detector and the z -axis along the beam pipe. The x -axis points from the IP to the centre ofthe LHC ring, and the y -axis points upward. Cylindrical coordinates ( r, φ ) are used in the transverse plane,3 φ being the azimuthal angle around the z -axis. The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan( θ/ and the rapidity of the components of the beam, y , are defined in terms of their energy, E ,and longitudinal momentum, p z , as y = 0 . E + p z E − p z . The inner detector is responsible for charged particle tracking and pattern recognition. It accomplishesthis with three distinct detector technologies, the silicon pixels in the innermost layers, the silicon strips (SCT)in the middle layers, and the straw-tube Transition Radiation Tracker (TRT) at the outermost. This system isimmersed in a 2 T solenoidal field that bends charged particles for high precision momentum measurementsdown to 0.5 GeV nominally. Fig. 3.5 shows a graphical representation of the inner detector.The pixel detectors have the highest granularity and sit nearest to the beam-pipe. There are three cylindricallayers in the barrel and three perpendicular disk layers as end-caps on either side of the interaction region. Theminimum pixel size in R − φ × z is × µ m and a total of 80.4 million readout channels. The insertableB-Layer (IBL) [100, 101] was installed for run 2. This additional pixel tracking layer at the innermost radius addsredundancy and precision for displaced vertex finding for the b-tagging program. In order to fit the extra layer,the beam-pipe was replaced with one of smaller diameter in this region. There are four cylindrical SCT layers inthe barrel, each consisting of two perpendicular stereo strip layers. The SCT end-caps are each composed of ninedisk layers of radially oriented strips and a set of stereo strips at an angle of 40 mrad. The total SCT readout hasabout 6.3 million channels.The TRT covers | η | < . and is composed of hollow polyimide drift tubes with 4 mm diameter. Thecathode tubes are concentric around gold plated tungsten wires forming the anode. The tubes were designed tobe filled with a gas mixture of 70% Xe, 27% CO , and 3% O . Charged particles entering the tubes ionizethe gas and the electrons are collected producing the signal. Additionally, low energy transition photons fromsuper-fast electrons would be absorbed by the Xe atoms producing larger signals that would be used for particleidentification (PID) purposes. However, an irreparable gas leak requires the current use of Ar instead of themuch more expensive Xe; this prevents the full PID capabilities from being realized. The barrel is composedof longitudinally oriented 144 cm straw tubes in 73 planes with the wires cut in half around η = 0 , and the4Figure 3.5: A rendering of the ATLAS inner detector barrel (top) and end-cap (bottom) sections [99].end-cap has 37 cm straws oriented radially in wheels making up 160 planes. The TRT system has a total of351,000 readout channels.Track finding begins by clustering charge deposition in the pixels and SCT [102, 103]. These clustersform three-dimensional space-points that are used in the track finding algorithm. Combinatorial tracking seeds5are first created from sets of three space-points fit to helices. From these the impact parameter with-respect-to thecenter of the detector is estimated. A Kalman filter builds track candidates from estimated high purity seeds byincorporating space points from the other layers. Track candidates are then assigned a quality score dependent onhow many clusters were used, how many holes were found and the fit χ . The ambiguity solver then processes thetracks in descending order of their quality trying to disambiguate clusters shared between candidates. Clusterscan be shared by no more than two tracks, and tracks with the higher score get preference. Tracks are removedform contention if they fail to meet a set of basic criteria defining a certain working point . The MinBias trackselection working point, that is used in this thesis, is defined by the following quality cuts:• p T > MeV• | η trk | < . • N Pix ≥ • N SCT ≥ • χ probability > . for p T > GeV• N IBL + N B − Layer > , if both IBL hit and B-layer hit are expected• N IBL + N B − Layer ≥ , if either IBL hit or B-layer hit is not expected• | d | with-respect-to primary vertex less than 1.5 mm• | z sin θ | with-respect-to primary vertex less than 1.5 mmwhere d BL0 and z BL0 are the transverse impact parameter with-respect-to the beam axis and the longitudinaldistance of closest approach to the primary vertex respectively. The electromagnetic (EM) calorimeter, shown in Fig. 3.6 consists of a cylindrical barrel region covering | η | < . and two wheel end-caps covering . < | η | < . . The barrel and two end-caps are each kept6Figure 3.6: A rendering of the ATLAS calorimeter systems [99].in independent cryostats that maintain a temperature of 80 K, sufficient to liquefy argon, with a liquid nitrogenrefrigeration system. The barrel is divided into two symmetric cylinders by a small gap at η = 0 , and the end-capsare divided into two concentric wheels covering . < | η | < . and . < | η | < . respectively. The Pbabsorber has a stacked accordion geometry leaving gaps between the leaves for the LAr and high voltage electrodes.This provides full azimuthal coverage without cracks. The accordion waves are axial in the barrel and vary withradius to maintain a constant gap for the LAr. However, in the end-caps, the waves are radial and the LAr gapis widens, so the wave amplitude and folding angle vary to compensate and yield a linear response. When anelectron or photon encounters the calorimeter, it interacts with the charges in the absorber material to create anelectromagnetic shower, a cascade of photons pair-producing electrons and electrons radiating photons. Chargedparticles moving through the LAr will ionize atoms in the liquid and these ionization electrons are collected onthe electrodes and readout to electronics as signal.The EM calorimeter has three radial layers plus a presampler for most of the coverage. A summary of thecoverage can be found in Table 3.1 and the cumulative material in Fig. 3.8. The first layer is highly granular7Figure 3.7: A diagram of a barrel EM calorimeter module [99].in η allowing for excellent position resolution and shape information of developing electromagnetic showers.Most of the energy is left in the second layer that has moderate η and φ granularity. The third layer is relativelythin and captures only the tail of high energy showers. The excellent granularity and radial segmentation allowsfor identification of electrons and photons from calorimeter shape information. In total there are nine differentshower shape quantities that enter the decision. Photon reconstruction will be discussed in more detail in Sec. 5.The Hadronic calorimeter system is divided into the tile calorimeter (tile) in the barrel covering | η | < . ,the LAr hadronic end-cap calorimeter (HEC) covering . < | η | < . , and the LAr forward calorimeter(FCal) covering . < | η | < . . A summary of the coverage and granularity can be found in Table 3.2, and arepresentation of the total number of interaction lengths taken by each layer is shown in Fig. 3.9.The tile calorimeter comprises a central barrel region covering | η | < . and two extended barrel regionscovering . < | η | < . . The barrel has 64 wedges each spanning ∆ φ ≈ . made of alternating steel andplastic scintillator tiles that are oriented radially and perpendicular to the beam axis. Hadrons moving through thematerial interact strongly with the nuclei inside. The remnants from these collisions can then have interactions8Table 3.1: A summary of the EM calorimeter coverage and layer granularity. Barrel End-cap Layer η Coverage Granularity ∆ η × ∆ φ η Coverage Granularity ∆ η × ∆ φ Presampler | η | < . 53 0 . × . . < | η | < . . × . Layer 1 | η | < . 40 0 . × . . < | η | < . 425 0 . × . . | η | < . 475 0 . × . 025 1 . < | η | < . . × . . < | η | < . . - . × . . < | η | < . . × . Layer 2 | η | < . 40 0 . × . 025 1 . < | η | < . 425 0 . × . . < | η | < . 475 0 . × . 025 1 . < | η | < . . × . . < | η | < . . × . Layer 3 | η | < . 35 0 . × . 025 1 . < | η | < . . × . Figure 3.8: The cumulative EM calorimeter material in radiation lengths as a function of absolute pseudorapid-ity [99].themselves, creating a cascading shower similar to the electromagnetic shower but much more irregular due to thelower cross section and broader range of outcomes for nuclear interactions than electromagnetic ones. Chargedparticles from these hadronic showers create scintillation light in the tiles that is collected into wavelength-shiftingfibers. The fibers are ganged together to form three different readout layers in radius before being coupled tophoto-multiplier tubes and read out to electronics.9Table 3.2: A summary of the hadronic calorimeter coverage and layer granularity.Layer Absorber η Coverage Granularity ∆ η × ∆ φ Scintillator tile calorimeter Layer 1 & 2 Steel | η | < . . × . Layer 3 Steel . × . LAr hadronic end-cap calorimeter Layers 1 & 2 Copper . < | η | < . . × . Layers 3 & 4 . < | η | < . . × . LAr forward hadronic calorimeter Layer 1 Copper . < | η | < . approximately . × . Layer 2 & 3 TungstenSimilar to the EM calorimeter, the HEC also uses LAr to collect ionization electrons and shares its cryostatswith the EM end-caps and FCals. Each side of the HEC has a front wheel and a rear wheel with each wheelcontaining two longitudinal layers. The wheels are made of 32 wedge modules, and each module is made of 24copper absorber plates 25 mm thick. The rear wheels instead have 16 plates at 50 mm each. The gaps for theLAr and high voltage electrodes are each 8.5 mm thick, and thus, the sampling fraction is less for the rear wheels.The gaps contain four electrodes that effectively divide each gap into four drift zones. The configuration of thereadout cells defines an approximately projective geometry back to the center of the detector.Finally, the FCal has one electromagnetic layer and two hadronic layers, each 45 cm thick. Again, the activelayers of these are LAr with the absorber for the EM layer being copper and that of the other two layers beingtungsten. Additionally, a copper shielding plug covers the outside of the third layer to reduce punch throughinto the muon system beyond. Similar to the HEC, the EM FCal layer uses a stacked plate design. However,instead of gaps between the plates, each absorber plate has thousands of holes that house the electrodes. Theelectrodes are copper rods separated from copper tubes by plastic fiber. The LAr permeates the gaps between therods and tubes. The hadronic layers form a similar structure except using the denser tungsten instead of copperabsorber. Additionally, the space between the electrode tubes is filled with tungsten slugs, in order to maximisethe absorbing material and interaction lengths.0Figure 3.9: The cumulative hadronic calorimeter material in nuclear interaction lengths as a function of absolutepseudorapidity [99]. The Minimum Bias Trigger Scintillators (MBTS) provides a low bias and fast readout signal necessary totrigger on MB events in low luminosity running. The detectors are two 2 cm thick polystyrene scintillator disksmounted 3.6 m to either side of the interaction region. The disks are composed of eight sectors where each sectorhas two sections in radius. A representation of one side can be seen in Fig. 3.10. Wavelength shifting fibers areembedded into each sector extending radially. The outer sections cover . < | η | < . , and the inner sectioncovers . < | η | < . . The fibers are coupled to PMTs that read out to the same electronics used in the tilecalorimeter. The LHC is capable of colliding bunches at 40 MHz, and each event is on the order of 1 MB. If ATLASwanted to record every event, the data acquisition system (DAQ) would need to write TBs of data every second.This is unfeasible, so it is necessary for a triggering system to select events to write to disk. The trigger is dividedinto two steps: a fast but coarse hardware based Level-1 (L1), and a slower but more precise software based HighLevel Trigger (HLT).1Figure 3.10: A representation of one side of the Minimum Bias Trigger Scintillators [104].The L1 system is capable of processing the full 40 MHz bunch crossing rate and paring it down to abouta 100 kHz accept rate that gets passed off to the HLT. Simply due to the size of the detector, the time of flight ofthe particles on which L1 decisions are based is longer than the bunch crossing interval. Thus, detector signalsmust be stored in pipeline buffers while the decision is being made. It is of interest in terms of cost and reliabilityto minimize this buffer storage, so the L1 is designed to make decisions with less than 2.5 µ s latency. This isaccomplished using custom electronic processors. The decisions are based on coarsened information from thecalorimeters and muon detectors looking for high p T muons, EM calorimeter clusters, jets, τ -leptons, largemissing transverse energy, and total transverse energy. The Central Trigger Processor (CTP) takes in informationfrom all the L1 object types and is responsible for making the final decision. In total, 256 accept modes arepossible, being combinations of, e.g., flags specifying thresholds that have been met on the L1 objects. Geometricinformation from flagged L1 objects is then passed to the HLT as Regions-of-Interest (ROI) to seed the HLTtrigger decision. A diagram of the L1 flow is plotted in Fig. 3.11.The HLT and DAQ systems interface the detector readout electronics and L1 decisions with the CERNTier-0 mass storage and computing resources. Limitations and requirements are based not just on the capabilitiesof the DAQ, but on the ability of the computer farms at CERN to store and process the volume of data that isoutput. The HLT is divided historically into two sections, the Level-2 (L2) and Event Filter (EV), though both2Figure 3.11: A diagram of the ATLAS L1 trigger flow [99].are implemented in software on servers on site. The L2 takes detector information around ROIs from the L1 andreconstructs these limited regions in detail. In this way L2 decision can be made using a small fraction ( ∼ streams to be written to disk. The final outputbandwidth of the HLT streams tend to be around 1 GB/s. This dissertation is based on data recorded from the p +Pb √ s NN = 8 . TeV collisions delivered by theLHC to ATLAS in November and December 2016. In these collisions, the proton has E = 6 . TeV, whilethe Pb nucleus has E = 6 . TeV per unit charge, resulting in an energy per nucleon of ( Z/A ) × . TeV =82 / × . TeV = 2 . TeV. The resulting nucleon–nucleon collision system has √ s NN = 8 . TeV and thecenter of mass of this system has a rapidity shift with respect to the ATLAS laboratory system of ∆ y = ± . (where the sign is dependent on the direction of the proton). The data comprises two distinct beam orientations:(1) in the first period, called the “ p +Pb” orientation, the Pb beam is moving from negative to positive rapidity,3and the center of mass is boosted by ∆ y = − . , and (2) the reverse orientation, with the Pb beam movingfrom positive to negative rapidity.The dataset is divided into runs of continuous DAQ operation that usually correspond to whole fills of theLHC. The runs are then broken into small chunks called lumi-blocks . Analyzed events are required to pass a set of good run criteria based on the performance of the detector subsystems and the LHC; for this dataset, there are atotal of 30 good runs containing 165 nb − ± p +Pb orientation: 11 runs, run numbers 313063-313435, L int = 56 . nb − • Pb+ p orientation: 19 runs, run numbers 313572-314170, L int = 107 . nb − For consistency when presenting physics results, the proton-going direction defines the positive rapidity direction.One important detail of the detector operation during data-taking is that one quadrant of the HEC onthe A side was disabled. The affected region is approximately +1 . < η lab < . , − π < φ < − π/ (25%of the total A-side HEC acceptance). Specific analysis choices were made to either eliminate this problem or toanalyse any bias this might have caused. hapter 4Centrality Determination A central concept in heavy ion collisions, centrality is a measure of an event’s overall activity or soft par-ticle production. With the use a model such as Glauber, the event activity is translated to geometric quantitiescharacterizing the collision, e.g. the impact parameter, N part , etc.. Thus, centrality provides not only a handleon the scaling of hard and soft particle production mechanisms, but also the shape and geometry of the collisionregion which can be correlated to the final state particle distributions.In ATLAS, the total transverse energy deposited into the forward calorimeter sections (FCal A : 3 . <η < . and FCal C : − . < η < − . ) is used to sample the event activity. In symmetric collision systems,like Pb+Pb, the sum of the transverse energy in both FCals is used. However, for p +Pb, the intrinsic asymmetryof the projectiles as well as the boost of the center of mass frame relative to the detector lead to an asymmetryin the lab pseudorapidity distribution of soft particles. Figure 4.1 shows the correlation between total transverseenergy deposited in the p -going FCal ( Σ E p T ) versus that in the Pb-going FCal ( Σ E Pb T ). At low total energyin both FCals, the correlation is roughly one-to-one, but as the energy in the Pb-going direction increases, theresponse in the p -going direction seems to saturate. This behavior indicates a lack of sensitivity of the p -goingdirection to the overall soft particle production, and therefore, this analysis uses solely Σ E Pb T .The Σ E Pb T distribution is connected with MC Glauber models to correlate the event activity to geometricproperties of the collision. As discussed in Sec. 2.4.1, MC Glauber simulates a nucleus-nucleus collision as acollection of nucleon-nucleon collisions. The event activity distribution is assumed to be parameterized with ascaling in N part (in p +Pb, N coll = N part − ). With this parameterization, the N part distribution is fit to the Σ E Pb T distribution as an N part convolution of the parametric function.5 100 50 100 150 200 [GeV] PbT E S [ G e V ] p T E S Internal ATLAS p+Pb 8.16 TeV Figure 4.1: Correlation of the sum of the energy deposited in the p -going (y-axis) versus Pb-going (x-axis) forwardcalorimeters. The red histogram shows the average of the p -going energy for each Pb-going energy. The analysis is based on the p +Pb data described in Sec. 3.3. Simulated events (MC data) are used to studythe detector response from both inelastic and elastic events. Two sets of minimum bias MC data were used in this analysis. MC event generators, P [43] andH [105] were used to create simulated data. As mentioned in Sec. 2.3.2, the soft particle productionin P is based on the Lund string fragmentation model. Hard processes are leading order perturbativecalculations. Until very recently, P could not simulate heavy ion collisions, and therefore, there was a needfor an extension. The most common extension, H uses a version of P for its nucleon-nucleon collisionsub routines and adds additional modeling of color strings to match measured bulk particle production in largecollision systems.Both generators were used at √ s NN = 8 . TeV with the correct center of mass boost with respect to the labframe to reflect the real data. 100 k P pp events each were generated using non-diffractive, single-diffractive,and double-diffractive processes, and 1 M H p +Pb events were generated in the same configuration but 56different z -vertex positions. Diffractive events are characterized by the exchange of color neutral objects, andthus, one or both of the colliding particles remain intact; These Events account for a large fraction of the totalscattering cross section and must be studied as part of the total energy production. The ATLAS detector responseto the generated events was determined through a full G4 simulation [106, 107], and the simulated eventswere reconstructed in the same way as the data. The data for this analysis was selected using the minimum bias trigger, HLT_mb_sptrk_L1MBTS_1 , thatrequired a hit in one of the MBTS counters and one space point in the tracker as well a one HLT track. Thiscentrality analysis relies on the Glauber geometric model which does not naturally take into account diffractiveor photo-nuclear events. Therefore, it is beneficial to remove them. Photo-nuclear events are such that theboosted electric fields emanating from a colliding particle strike the other as a nearly non-virtual photon. Theyare characterized by the disassociation of one of the projectiles and not the other. Because of the significant chargeenhancement of the Pb nucleus relative to the proton, the photon is much more likely to emanate from the Pbnucleus to strike the proton leaving the nucleus intact. To reject these events, the L1 ZDC trigger bit in the Pbgoing direction is required to have been set, indicating the breakup of the nucleus.Diffractive events are associated with significant pseudorapidity gaps in the particle production. Figures4.2 and 4.3 show the gap distributions measured from the forward edge of the Pb-going and p -going FCal, usingtruth particles and clusters above 200 MeV from the entire calorimeter system, from non-diffractive, single-diffractive, and double-diffractive P data. The separation between non-diffractive and diffractive distribu-tions has a larger magnitude and occurs at a smaller gap size, ∆ η Gap , in the Pb-going direction. In this analysis,we reject events with ∆ η PbGap > . .In-time pileup is when more than one collision occur in a given bunch crossing. To minimize the con-tamination of these events, a reconstructed vertex based rejection is implemented. At least one vertex is requiredin the event and any additional vertices are required to have six or fewer tracks associated with it. Motivatingthis cut, Fig. 4.4 shows a histogram of the number of tracks associated with the secondary vertex, in events withmore that one vertex, from both data and H MC with no simulated pileup. As a check, Fig. 4.5 shows7 Gapp hD Non-diffractiveSingle-diffractiveDouble-diffractive Internal ATLAS PYTHIA8 8.16 TeV GapPb hD Non-diffractiveSingle-diffractiveDouble-diffractive Internal ATLAS PYTHIA8 8.16 TeV Figure 4.2: Edge gaps measured from the forward edge of the calorimeter system ( η = 4 . ) on the p -going ( Left )and Pb-going ( Right ) sides of truth particles above 200 MeV. Gapp hD Non-diffractiveSingle-diffractiveDouble-diffractive Internal ATLAS PYTHIA8 8.16 TeV GapPb hD Non-diffractiveSingle-diffractiveDouble-diffractive Internal ATLAS PYTHIA8 8.16 TeV Figure 4.3: Edge gaps measured from the forward edge of the calorimeter system ( η = 4 . ) on the p -going ( Left )and Pb-going ( Right ) sides of calorimeter clusters above 200 MeV.the distribution of vertex z − z in events with more than one vertex (black). The left plot selects events inwhich the second vertex has greater than 6 tracks, to choose pileup events, (green), and it agrees well with simu-lated pileup events generated by mixing H events (red). Conversely, the right plot selects events passing thepileup rejection (green) compared to the distribution from no pileup H events (red) showing, again, goodagreement.8 vTrk N - 10 110 DataMC Internal ATLAS PYTHIA8 8.16 TeV Figure 4.4: Histogram of the number of tracks associated with the second vertex in data (black) and HIJINGMC with no pileup (red). - - - - z Vertex (z110 Data > 6 vTrk Data NMixed Event Internal ATLAS PYTHIA8 8.16 TeV - - - - z Vertex (z110 Data 6 £ vTrk Data NMC Internal ATLAS PYTHIA8 8.16 TeV Figure 4.5: Distribution of vertex z − z in events with more than one vertex (black). Left: Events in whichthe second vertex has greater than 6 tracks to choose pileup events (green) and agrees well with simulated pileupevents generated by mixing H events (purple). Right: Events passing the pileup rejection (green) comparedto the distribution from no pileup H events (red) showing, again, good agreement.Efficiencies for these requirements are found in P pp simulations and is shown in Fig. 4.6. In total,they exclude 50.8% of the diffractive events while being 98.7% efficiency for the non-diffractive portion.9 T E S FCal 110 C oun t s / . G e V Non-diffractiveSingle-diffractiveDouble-diffractive Internal ATLAS PYTHIA8 8.16 TeV - T E S FCal 00.20.40.60.811.21.4 E ff i c i en cy Non-diffractiveSingle-diffractiveDouble-diffractive Internal ATLAS PYTHIA8 8.16 TeV Figure 4.6: Left: Pb-going FCal total transverse energy distributions from the non-diffractive, single-diffractive,and double-diffractive components from P pp simulations after applying the event selection requirements. Right: Event selection efficiency plotted as a function of FCal Σ E Pb T for non-diffractive, single-diffractive, anddouble-diffractive components. Data taking was separated into two periods: the first in which the Pb nucleus was moving towards FCal A and the proton towards FCal C , the second in which the beam directions were reversed and therefore the Pbnucleus was moving in the directions of FCal C . Noise contributions are determined by examining triggers fromempty beam crossings. These noise distributions are fit to Gaussian functions (Fig. 4.7) from which the meanand width are extracted for each run. The means and widths are plotted in Figure 4.8. The noise widths showa clear separation between the first and second periods showing a characteristic difference between FCal A andFCal C . A slight run dependence is found for the pedestal means and is corrected run-by-run for the rest of theanalysis. Figure 4.9 shows the means after this correction.As has been seen in previous analyses, Σ E Pb T distributions, integrated over entire runs, show a significantnegative energy tail. This tail can be explained by the existence of out-of-time pileup, in which the pulses fromprevious beam crossings overlap in the electronics. The pulses are shaped in a way that cancels this effect onaverage, but can give rise to significant negative energy for events closely following others in time. Out-of-time-pileup has little affect on the positive side of the distribution; However, to prevent the negative side from biasing0 - - - T E S FCal - - - - = -0.101 m = 1.152 s Internal ATLAS p+Pb 8.16 TeVEmpty triggers - - - T E S FCal - - - - = -0.143 m = 1.150 s - - - T E S FCal - - - - = -0.154 m = 1.140 s - - - T E S FCal - - - - = -0.057 m = 1.163 s - - - T E S FCal - - - - = 0.031 m = 1.146 s - - - T E S FCal - - - - = 0.025 m = 1.124 s - - - T E S FCal - - - - = -0.116 m = 1.134 s - - - T E S FCal - - - - = -0.091 m = 1.146 s - - - T E S FCal - - - - = -0.073 m = 1.139 s - - - T E S FCal - - - = -0.112 m = 1.139 s - - - T E S FCal - - - - = -0.098 m = 1.136 s - - - T E S FCal - - - = 0.019 m = 0.865 s - - - T E S FCal - - - - = 0.066 m = 0.869 s - - - T E S FCal - - - - = 0.049 m = 0.890 s - - - T E S FCal - - - - = 0.120 m = 0.887 s - - - T E S FCal - - - - = 0.097 m = 0.882 s Internal ATLAS p+Pb 8.16 TeVEmpty triggers - - - T E S FCal - - - - = 0.137 m = 0.859 s - - - T E S FCal - - - - = 0.201 m = 0.883 s - - - T E S FCal - - - - = 0.219 m = 0.879 s - - - T E S FCal - - - - = 0.271 m = 0.894 s - - - T E S FCal - - - = 0.282 m = 0.887 s - - - T E S FCal - - = 0.245 m = 0.849 s - - - T E S FCal - - - - = 0.245 m = 0.882 s - - - T E S FCal - - - = 0.259 m = 0.896 s - - - T E S FCal - - - = 0.227 m = 0.891 s - - - T E S FCal - - - - = 0.222 m = 0.903 s - - - T E S FCal - - - - = 0.234 m = 0.894 s - - - T E S FCal - - - - = 0.182 m = 0.882 s - - - T E S FCal - - - - = 0.186 m = 0.895 s - - - T E S FCal - - - = 0.215 m = 0.892 s Figure 4.7: Gaussian fits to FCal noise Σ E Pb T distributions from empty triggered events for each run.the global fit, we select only events first in the bunch train, thus ensuring a significant time gap from the precedingevent and no out-of-time pileup. Figure 4.10 shows the Σ E Pb T distribution from all bunch crossings and afterselecting only the first in the train, where the modest negative contribution can be explained by the width of theelectronic noise.1 - - F i t T E Sm First period Second period Internal ATLAS p+Pb 8.16 TeVEmpty triggers 0 5 10 15 20 25 30Run Index0.750.80.850.90.9511.051.11.151.21.25 F i t T E Ss First period Second period Internal ATLAS p+Pb 8.16 TeVEmpty triggers Figure 4.8: Extracted means ( Left ) and widths ( Right ) from Gaussian fits to Σ E Pb T distributions from emptytriggers. The parameters are plotted for each run in chronological order (run index). - - F i t T E Sm First period Second period Internal ATLAS p+Pb 8.16 TeVEmpty triggers Figure 4.9: Extracted means from Gaussian fits to Σ E Pb T distributions from empty triggers after correction.To form the final Σ E Pb T distribution used in this analysis, the Pb-going distributions from each periodare added (i.e. FCal A from period 1 is added to FCal C from period 2). It is therefore necessary that the energyscale from the two calorimeters be consistent. Figure 4.11 shows a comparison of the Σ E Pb T distributions fromeach FCal. It is clear from the ratio that there is a slight discrepancy in the energy scales that is corrected by aconstant scaling factor of 0.989 applied to the energies from FCal C . This is adjusted from this point on in theanalysis.2 - - PbT E S FCal - - - - - All BCIDFirst in train Internal ATLAS p+Pb 8.16 TeVFirst Period - FCal A Figure 4.10: Mean Σ E Pb T from all bunch crossing positions (red) and from only the first position in the bunchtrain. T E - - - - - FCal AFCal C Internal ATLAS p+Pb 8.16 TeV · CT E S PbT E S F C a l A / F C a l C Fit slope = 0.00051 0 20 40 60 80 100 T E - - - - - FCal AFCal C Internal ATLAS p+Pb 8.16 TeV · CT E S PbT E S F C a l A / F C a l C Fit slope = 0.00000 Figure 4.11: Left: Comparison between the Σ E Pb T distributions from each running period, both scaled to unitintegral. Right: The same comparison after applying a scale factor of 0.989 to each entry in the FCal C histogram.The shape of the pseudorapidity distribution of produced particles in these asymmetrical collisions com-bined with the acceptance of the Pb-going FCal lead to a vertex z position dependence on Σ E Pb T distributions.This is simply due to the discrepancy between the fixed (lab) pseudorapidity position relative to the z -translatedphysical pseudorapidity distribution of the produced particles. To quantify this effect, we consider the mean3total Σ E Pb T in bins of vertex z position, shown in Fig. 4.12 for each period (and thus each FCal) separately. Thevertex z dependence is well modeled by a linear function, the slope of which is given in the plot and can be usedto correct for this dependence with a scaling event-by-event. The Σ E Pb T distributions contain this correctionfrom now on. The final Σ E Pb T distribution used in this analysis is given in Fig. 4.13. - - - - > T E S < Slope = -0.0166% +/- 0.0003%First Period - FCal A Internal ATLAS p+Pb 8.16 TeV - - - - > T E S < Slope = 0.0150% +/- 0.0003%Second Period - FCal C Figure 4.12: Mean Σ E Pb T as a function of vertex z from period 1 ( Left ) and period 2 ( Right ). The plots are fitto a line, the parameters of which are used to correct for this effect in the data. PbT E S FCal 110 C oun t s Internal ATLAS p+Pb 8.16 TeV Figure 4.13: Σ E Pb T distribution after all event selection and corrections and integrated over all runs.4 To map the Σ E Pb T distributions to geometric properties of the collisions, it is necessary to introducemodels of individual nucleus-nucleus interactions. Events can then be classified by the N part . The MC Glauberand Glauber-Gribov models used here were described in Sec. 2.4.1. The nucleon-nucleon cross section used forthis analysis corresponds to an extrapolation from the current measurement of the total pp inelastic cross sectionat √ s NN = 8 TeV from the TOTEM collaboration [108] σ pptot = (75 ± 2) mb . (4.1)To review, the Glauber-Gribov model builds on base MC Glauber by incorporating interaction strengthfluctuations. It accomplishes this by introducing a fluctuation in the total cross section ( σ tot ) such that it isdrawn from the probably density function: P ( σ tot ) = N σ tot σ tot + σ exp (cid:16) − σ tot /σ − (cid:17) , (4.2)where σ controls the nominal mean nucleon-nucleon cross-section (cid:104) σ tot (cid:105) , Ω is a dimensionless parameter thatdescribes the magnitude of the cross-section fluctuations, and N is a normalization to ensure unit integral. Theinelastic nucleon-nucleon cross-section σ NN is taken to be a fixed fraction of the total cross-section σ tot accordingto √ s NN = λσ tot , so that P ( √ s NN ) = (1 /λ ) P ( σ tot /λ ) . For each choice of the parameters σ and Ω , we choose λ such that (cid:104) σ tot (cid:105) = (75 ± mb, as in the default Glauber, and Ω = 0.55. In this section, the Glauber model derived N part distributions are connected to the observed data FCal Σ E Pb T distribution by introducing N part scaling parameterizations and performing global fits to the data. As hasbeen assumed in previous analyses, the Σ E Pb T response distribution for any given N part is assumed to follow agamma distribution with parameters k and θ that may depend on N part . The modeled Σ E Pb T distribution isthen computed as the N part convolution of the gamma distributions. In this analysis, we explore two different k ( N part ) and θ ( N part ) parameterizations:• Model 1:5 part N - - - - - - ) pa r t )( d N / d N e v en t ( / N Internal ATLAS p+Pb 8.16 TeV GlauberGlauber-Gribov Figure 4.14: Distribution of N part values from Glauber (with σ NN = (75 ± mb) and Glauber-Gribov (with σ NN = (75 ± mb and Ω = 0 . ) models at √ s NN p +Pb. * k = k N part * θ = θ • Model 2: * k = k + k ( N part − * θ = θ + θ Log ( N part − where, in both models, k and θ are free parameters to be determined from the fit. Model 2 attempts toget a handle on the pp ( N part = 2 ) behavior by fixing the parameters k and θ to those obtained from a fit tothe Σ E Pb T from P pp simulations. P pp simulations, with the same center of mass boost found in p +Pb data, from representativeadmixture non-diffractive, single-diffractive, and double-diffractive events are used to generate a simulated Σ E Pb T distribution, which includes all event selection used in the data except the Pb-going ZDC requirement (The ZDCwas not simulated). Additionally, to exclude events in which ATLAS would not detect or trigger on (and are thusnot included in this analysis), at least one truth particle is required to fall within the Pb-going FCal acceptance.6Fig. 4.15 shows the fit to the noise distribution measured in events in which no truth particles struck the Pb-going FCal. Because this level of noise is slightly less that found in data (Fig. 4.8), the P Σ E Pb T data issmeared with a Gaussian to match the average value found in data. This distribution was then fit to a gammafunction convolved with a Gaussian with a width fixed to this value. Fig. 4.16 gives this distribution and fit. Itis apparent that this functional form is not perfect in describing the data. However it’s simple form and analyticconvolutional properties make it a convenient choice.From this fit, we obtain k and θ used to set the N part = 2 parameters in model 2. - - - T E S c oun t s / . G e V = 0.001 m = 0.71 s Internal ATLAS p + p PYTHIA8 8.16 TeV Figure 4.15: Gaussian fit to the Σ E Pb T noise distribution. Global fits are performed using, as a functional form, the convolution of the N part distributions from theGlauber and Glauber-Gribov models (Fig. 4.14) with gamma distributions who’s parameters are generated bythe two stated scaling models. The fits are made to points above 10 GeV to ensure that any poorly understoodinefficiency or diffractive elements, contributing at low Σ E Pb T , would not influence the fits. Figure 4.17 showsthe fits using traditional Glauber and each scaling model. Figure 4.18 gives the fits using Glauber-Gribov. Theresults of these fits are summarized in Table 4.1. As a check, the fits are computed again, this time fitting above5 GeV instead of 10 GeV. The results of which are summarized in Table 4.2, and the fits are given in Figures 4.19and 4.20.7Table 4.1: Summary of fits to Σ E Pb T data > 10 GeVGlauber model Response model k θ EfficiencyTraditional Glauber model 1 0.361 9.733 0.972Traditional Glauber model 2 0.413 1.413 0.971Glauber-Gribov model 1 0.620 5.788 0.990Glauber-Gribov model 2 0.867 0.014 0.987Table 4.2: Summary of fits to Σ E Pb T data > 5 GeVGlauber model Response model k θ EfficiencyTraditional Glauber model 1 0.351 9.997 0.976Traditional Glauber model 2 0.483 1.112 0.999Glauber-Gribov model 1 0.622 5.820 1.005Glauber-Gribov model 2 0.802 0.132 1.0048 - C oun t s / . G e V PYTHIA8 simulationFit Internal ATLAS Gamma response model GeV T E S p + p Fit to PYTHIA8 = 4.2377 GeV q , part N · k = 0.7632 - [GeV] PbT E S FCal D a t a / F i t Figure 4.16: Σ E Pb T distribution from simulated P events (black) fit with a gamma distribution convolvedwith a Gaussian with width fixed by the noise fit (red). The lower panel gives the ratio of data to fit. c oun t s / . G e V DataFit Internal ATLAS +Pb 8.16 TeV p Traditional Glauber Gamma response model 1 > 10 GeV T E S Fit to = 9.7333 GeV q , part N · k = 0.36083Efficiency = 0.972 [TeV] PbT E S FCal da t a / s i m c oun t s / . G e V DataFit Internal ATLAS +Pb 8.16 TeV p Traditional Glauber Gamma response model 2 > 10 GeV T E S Fit to - 2) part (N · k = 1.526 + 0.413 - 1) GeV part Log(N · = 4.238 + 1.413 q Efficiency = 0.971 [TeV] PbT E S FCal da t a / s i m Figure 4.17: Fit to Σ E Pb T distribution using the Glauber N part distribution and gamma distribution scalingmodel 1 ( Left ) and model 2 ( Right ).9 c oun t s / . G e V DataFit Internal ATLAS +Pb 8.16 TeV p Glauber-Gribov Gamma response model 1 > 10 GeV T E S Fit to = 5.788 GeV q , part N · k = 0.62012Efficiency = 0.990 [TeV] PbT E S FCal da t a / s i m c oun t s / . G e V DataFit Internal ATLAS +Pb 8.16 TeV p Glauber-Gribov Gamma response model 2 > 10 GeV T E S Fit to - 2) part (N · k = 1.526 + 0.867 - 1) GeV part Log(N · = 4.238 + 0.014 q Efficiency = 0.987 [TeV] PbT E S FCal da t a / s i m Figure 4.18: Fit to Σ E Pb T distribution using the Glauber-Gribov N part distribution and gamma distributionscaling model 1 ( Left ) and model 2 ( Right ). c oun t s / . G e V DataFit Internal ATLAS +Pb 8.16 TeV p Traditional Glauber Gamma response model 1 > 5 GeV T E S Fit to = 9.9972 GeV q , part N · k = 0.35081Efficiency = 0.976 [TeV] PbT E S FCal da t a / s i m c oun t s / . G e V DataFit Internal ATLAS +Pb 8.16 TeV p Traditional Glauber Gamma response model 2 > 5 GeV T E S Fit to - 2) part (N · k = 1.526 + 0.483 - 1) GeV part Log(N · = 4.238 + 1.112 q Efficiency = 0.999 [TeV] PbT E S FCal da t a / s i m Figure 4.19: Fit to Σ E Pb T distribution using the Glauber N part distribution and gamma distribution scalingmodel 1 ( Left ) and model 2 ( Right ). c oun t s / . G e V DataFit Internal ATLAS +Pb 8.16 TeV p Glauber-Gribov Gamma response model 1 > 5 GeV T E S Fit to = 5.8197 GeV q , part N · k = 0.62187Efficiency = 1.005 [TeV] PbT E S FCal da t a / s i m c oun t s / . G e V DataFit Internal ATLAS +Pb 8.16 TeV p Glauber-Gribov Gamma response model 2 > 5 GeV T E S Fit to - 2) part (N · k = 1.526 + 0.802 - 1) GeV part Log(N · = 4.238 + 0.132 q Efficiency = 1.004 [TeV] PbT E S FCal da t a / s i m Figure 4.20: Fit to Σ E Pb T distribution using the Glauber-Gribov N part distribution and gamma distributionscaling model 1 ( Left ) and model 2 ( Right ).0 Comparing the simulated distribution for each model to the data provides a data-driven method for esti-mating the event selection efficiency. P simulations in Sec. 4.2 indicate that efficiency losses and any en-hancement due to residual diffractive/photo-nuclear events are primarily constrained to the region Σ E Pb T < .However, the precise centrality designations are sensitive to the total efficiency. Given the variation in efficiencyestimations for each model, a nominal value 98% with variation +2% -1% is assigned, and the centrality desig-nations for the nominal efficiency and variations are given in Table 4.3. (cid:104) N part (cid:105) and (cid:104) T AB (cid:105) Mean N part and T AB are extracted for the regions between each centrality designation (0-1%, 1-5%,5-10%, 10-20%,20-30%, 30-40%, 40-50%, 50-60%, 60-70%, 70-80%, 80-90%, as well as the whole range0-90%). The values are plotted for both traditional Glauber and Glauber-Gribov in Fig. 4.21 and tabulated inTables 4.4 and 4.5. > pa r t < N Traditional GlauberGlauber-Gribov < T AB > Traditional GlauberGlauber-Gribov Figure 4.21: Mean N part ( Left ) and T AB ( Right ) calculated from both Glauber and Glauber-Gribov models andplotted as a function of centrality class.1Table 4.3: Summary of fits to Σ E Pb T data > 5 GeV.Centrality Σ E Pb T cut (98%) Σ E Pb T cut (97%) Σ E Pb T cut (100%)1% 108.51 GeV 108.33 GeV 108.85 GeV5% 78.99 GeV 78.79 GeV 79.39 GeV10% 64.57 GeV 64.35 GeV 65.01 GeV20% 48.50 GeV 48.25GeV 49.00 GeV30% 37.96 GeV 37.68 GeV 38.51 GeV40% 29.79 GeV 29.48 GeV 30.38 GeV50% 22.96 GeV 22.64 GeV 23.60 GeV60% 17.04 GeV 16.69GeV 17.71 GeV70% 11.80 GeV 11.44 GeV 12.49 GeV80% 7.13 GeV 6.77 GeV 7.84 GeV90% 3.07 GeV 2.71 GeV 3.75 GeVTable 4.4: Summary of mean N part values for Glauber and Glauber-Gribov for each centrality class.Centrality Traditional Glauber Glauber-Gribov0-1% . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . Table 4.5: Summary of mean T AB values for Glauber and Glauber-Gribov for each centrality class.Centrality Traditional Glauber Glauber-Gribov0-1% . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . . +0 . . There are three main sources of systematic uncertainty in this analysis. These sources are varied, and theresponse on N part and T AB is measured relative to the nominal values. The variations are as follows:• Uncertainty in efficiency: The efficiency is varied to 97% and 100% corresponding to observed varia-tions in estimates from the fits.• Glauber parameters: * Nucleon-Nucleon cross section ( σ NN ) is varied ± * Woods-Saxon radius and skin depth (R, a) are varied according to their uncertainty and in a waythat preserves their anti-correlation ( (6.62,0.546) → (6.68,0.536) → (6.56,0.556) ) (Fig. 4.23,4.26) * Hard core radius (d min ± Fit model: Alternate fit model 1 is used and relative difference assigned as uncertainty (Fig. 4.24, 4.27)At most peripheral and most central the model variation dominates the uncertainty, whereas in the mid centralityrange, the cross section uncertainty dominates.3 R a t i o t o no m i na l 97% efficiency100% efficiency R a t i o t o no m i na l 97% efficiency100% efficiency Figure 4.22: Systematic variation of N part generated by setting efficiencies to 97% and 100%, and calculatedusing Glauber ( Left ) and Glauber-Gribov ( Right ) of each centrality class. R a t i o t o no m i na l 67 mb NN s 77 mb NN s Woods-Saxon variation 1 67 mb NN s 77 mb NN s Woods-Saxon variation 1Woods-Saxon variation 2 = 0.2 fm min d = 0.6 fm min dWoods-Saxon variation 2 = 0.2 fm min d = 0.6 fm min dWoods-Saxon variation 2 = 0.2 fm min d = 0.6 fm min d R a t i o t o no m i na l 67 mb NN s 77 mb NN s Woods-Saxon variation 1 67 mb NN s 77 mb NN s Woods-Saxon variation 1Woods-Saxon variation 2 = 0.2 fm min d = 0.6 fm min dWoods-Saxon variation 2 = 0.2 fm min d = 0.6 fm min dWoods-Saxon variation 2 = 0.2 fm min d = 0.6 fm min d Figure 4.23: Systematic variation of N part generated by varying Glauber parameters, and calculated using Glauber( Left ) and Glauber-Gribov ( Right ) of each centrality class.4 R a t i o t o no m i na l Gamma scaling model 1 R a t i o t o no m i na l Gamma scaling model 1 Figure 4.24: Systematic variation of N part generated by varying the scaling model to model 1 compared to thenominal model 2, and calculated using Glauber ( Left ) and Glauber-Gribov ( Right ) of each centrality class. R a t i o t o no m i na l 97% efficiency100% efficiency R a t i o t o no m i na l 97% efficiency100% efficiency Figure 4.25: Systematic variation of T AB generated by setting efficiencies to 97% and 100%, and calculated usingGlauber ( Left ) and Glauber-Gribov ( Right ) of each centrality class.5 R a t i o t o no m i na l 67 mb NN s 77 mb NN s Woods-Saxon variation 1 67 mb NN s 77 mb NN s Woods-Saxon variation 1Woods-Saxon variation 2 = 0.2 fm min d = 0.6 fm min dWoods-Saxon variation 2 = 0.2 fm min d = 0.6 fm min dWoods-Saxon variation 2 = 0.2 fm min d = 0.6 fm min d R a t i o t o no m i na l 67 mb NN s 77 mb NN s Woods-Saxon variation 1 67 mb NN s 77 mb NN s Woods-Saxon variation 1Woods-Saxon variation 2 = 0.2 fm min d = 0.6 fm min dWoods-Saxon variation 2 = 0.2 fm min d = 0.6 fm min dWoods-Saxon variation 2 = 0.2 fm min d = 0.6 fm min d Figure 4.26: Systematic variation of T AB generated by varying Glauber parameters, and calculated using Glauber( Left ) and Glauber-Gribov ( Right ) of each centrality class. R a t i o t o no m i na l Gamma scaling model 1 R a t i o t o no m i na l Gamma scaling model 1 Figure 4.27: Systematic variation of T AB generated by varying the scaling model to model 1 compared to thenominal model 2, and calculated using Glauber ( Left ) and Glauber-Gribov ( Right ) of each centrality class. hapter 5Measurement of Direct Photon Production Measurements of particle and jet production rates at large transverse energy are a fundamental method ofcharacterising hard-scattering processes in all collision systems. In collisions involving large nuclei, productionrates are modified from those measured in proton+proton ( pp ) collisions due to a combination of initial- andfinal-state effects. The former arise from the dynamics of partons in the nuclei prior to the hard-scattering process,while the latter are attributed to the strong interaction of the emerging partons with the hot nuclear mediumformed in nucleus–nucleus collisions. As discussed in Sec.2.4.4, modification due to the nuclear environment isquantified by the nuclear modification factor, R AA , defined as the ratio of the cross-section measured in A+A tothat in pp collisions, scaled by the expected difference in the degree of geometric overlap between the systems.Measurements of prompt photon production rates offer a way to isolate the initial-state effects because thefinal-state photons do not interact strongly. These initial-state effects include the degree to which parton densitiesare modified in a nuclear environment [109–111], as well as potential modification due to an energy loss arisingthrough interactions of the partons traversing the nucleus prior to the hard scattering [112, 113]. Constraintson such initial-state effects are particularly important for characterising the observed modifications of stronglyinteracting final states, such as jet and hadron production [89, 114], since they are sensitive to effects fromboth the initial and final state. Due to the significantly simpler underlying-event conditions in proton–nucleuscollisions, measurements of photon rates can be performed with better control over systematic uncertainties thanin nucleus–nucleus collisions, allowing a more precise constraint on these initial-state effects.Prompt photon production has been extensively measured in pp collisions at a variety of collision ener-gies [115–119] at the LHC. It was also measured in lead–lead (Pb+Pb) collisions at a √ s NN = 2 . TeV [25, 26]7at the LHC, and in gold–gold collisions at √ s NN = 200 GeV at RHIC [27], where the data from both collidersindicate that photon production rates are unaffected by the passage of the photons through the QGP. At RHIC,photon production rates were measured in deuteron–gold collisions at √ s NN = 200 GeV [120, 121] and werefound to be in good agreement with pQCD calculations. Additionally, jet production [18, 19] and electroweakboson production [122–124] were measured in nb − of p +Pb collision data at √ s NN = 5 . TeV recordedat the LHC; the former is a strongly interacting final state, while the latter is not. All measurements providedsome constraints on initial-state effects.The data used in this measurement are described in Sec. 3.3. By convention, the results are reported as afunction of photon pseudorapidity in the nucleon–nucleon collision frame, η ∗ , with positive η ∗ correspondingto the proton beam direction, and negative η ∗ corresponding to the Pb beam direction. Because photons aremassless, their pseudorapidity is equal to their rapidity. Furthermore, when discussing detector level quantities, η lab will sometimes be used to refer to the lab coordinates.At leading order, the process p +Pb → γ + X has contributions from direct processes, in which the photonis produced in the hard interaction, and from fragmentation processes, in which it is produced in the partonshower. Beyond leading order the direct and fragmentation components are not separable and only their sum isa physical observable. To reduce contamination from the dominant background of photons mainly from light-meson decays in jets, the measurements presented here require the photons to be isolated from nearby particles.This requirement also acts to reduce the relative contribution of fragmentation photons in the measurement,and thus, the same fiducial requirement must be imposed on theoretical models when comparing with the data.Specifically, as in previous ATLAS measurements [116, 117], the sum of energy transverse to the beam axis withina cone of ∆ R ≡ (cid:112) (∆ η ) + (∆ φ ) = 0 . around the photon, E isoT , is required satisfy E isoT < . . × − E γ T [ GeV ] (5.1)where E γ T is the transverse energy of the photon. At particle level in simulations and calculations, E isoT is cal-culated as the sum of transverse energy of all particles with a decay length above 10 mm, excluding muons andneutrinos. This sum is corrected for the ambient contribution from uncorrelated soft (underlying-event) particles,consistent with the previous measurements [116, 117].8The results report a measurement of the cross-section for prompt, isolated photons in p +Pb collisions.Photons are measured with E γ T > GeV, the isolation requirement detailed above, and in three nucleon–nucleon centre-of-mass pseudorapidity ( η ∗ ) regions, − . < η ∗ < − . , − . < η ∗ < . , and . <η ∗ < . . In addition to the cross-section, the data are compared to a pp reference cross-section derived froma previous measurement of prompt photon production in pp collisions at √ s = 8 TeV that used the identicalisolation condition [116]. The nuclear modification factor R p Pb is derived in each pseudorapidity region, usingan extrapolation for the different collision energy and center-of-mass pseudorapidity selection, and is reported inthe region E γ T > GeV where reference data is available. Furthermore, the ratio of R p Pb in the forward regionto that in the backward region is presented to take advantage of the strong cancellation of systematic uncertainties.The measurements are compared with next-to-leading-order (NLO) pQCD predictions from J [87] usingparton distribution functions (PDF) extracted from global analyses that include nuclear modification effects [58,125]. Additionally, the data are compared with predictions from a model of initial-state energy loss [112, 113,126]. Events are selected for analysis from multiple high-level triggers (HLT) which require a reconstructed pho-ton at the trigger level with E γ T above some minimum threshold. At the trigger level, only a very loose identifica-tion requirement (detailed in Sec. 5.3.2) is imposed to reject hadron backgrounds. These are the HLT_gX_Loose triggers, with the online thresholds X = 15 , , , , (in GeV). All triggers with thresholds less than areprescaled, meaning an event selected by the trigger is recorded only after some number of that same trigger hasfired; this is done in cases in which the requirement would accept too many events and swamp the bandwidth.The five triggers then span the range of the measurement.Events selected by each trigger are used to populate a specific kinematic region of the spectrum mea-surement. Specifically, each E γ T region is filled by the trigger containing the largest number of photons in thekinematic range and which is on its efficiency plateau in the region. In practice, this means that each HLT9Table 5.1: Photon triggers used in analysis, with the corresponding offline E γ T range where they are used, andsampled luminosities in both running periods.Trigger offline E T region L int ( p +Pb period) L int (Pb+ p period) HLT_g15_Loose − − HLT_g20_Loose − − HLT_g25_Loose − − HLT_g30_Loose − − HLT_g35_Loose > GeV 59.88 nb − − trigger solely populates the photon E γ T region which begins GeV above its online threshold value, until ahigher-threshold trigger takes over at higher- E γ T via explicit cuts. In addition, at least one reconstructed ver-tex is required. Table 5.1 summarizes the triggers used, as well as the kinematic regions they populate, and theluminosity sampled by each trigger in each running period.The efficiency of the high-level trigger for selecting offline, loose photons is determined in data. Sincethere is not sufficient minimum bias data to directly determine the HLT efficiencies with high precision, thetrigger efficiency is instead determined separately for each part of the trigger chain, using supporting HLT, L1pass-through and MB triggers in data. The efficiency is always reported as a function of offline photon E γ T , forloose-identified photons.(1) Using minimum bias triggered data ( HLT_mb_sptrk_L1MBTS_1 ), detailed in Sec. 4.2, the efficiencyof the Level-1 EM trigger is determined for different thresholds. Offline loose photons in these eventsare considered to fire the trigger if they are geometrically matched with an L1 EM RoI above the giventhreshold. This efficiency is estimated separately for all of the L1 EM thresholds which seed the HLTtriggers used in this analysis.(2) Using supporting L1 pass-through triggers ( HLT_noalg_L1EM X for different thresholds X ), the ef-ficiency of the HLT trigger without any identification requirement (e.g. etcut ) is evaluated. Thiscondition is checked for different HLT E T thresholds. Offline loose photons in these L1-triggeredevents are geometrically matched to an HLT photon (without any ID requirement) above the giventhreshold.0(3) Using supporting HLT photon triggers without online identification ( HLT_g X _etcut , for differentthresholds X ), the HLT photon efficiency with loose identification is determined. This condition ischecked for different HLT thresholds separately. Offline loose photons in these HLT-etcut triggeredevents are checked to see if the HLT photon they are matched pass the online loose ID selection.In this way, the total efficiency is factorized into three schematic components and examined separatelyin each: (1) the efficiency for an offline photon to be identified at L1; (2) the efficiency for the photon to beidentified at the HLT level; (3) the efficiency of photon to pass online identification cuts. Moreover, efficienciesare evaluated separately for photons in the barrel ( | η | < . ) and end-cap ( . < | η | < . ).Figure 5.1 summarizes the three efficiency components for each of the four HLT triggers used in theanalysis. In the E γ T region where each trigger is used ( GeV above the HLT online threshold), the L1 andHLT without ID efficiencies saturate at 100%. However, the identification at the online level introduces a smallinefficiency. For offline loose identified photons, this last efficiency saturates at % at mid-rapidity and % atforward rapidity. However, when this is evaluated for offline tight identified photons (the signal selection usedin the analysis), these efficiencies are greater than . % in both regions. The resulting inefficiency has a muchsmaller effect on the experimental measurement than the dominant systematic uncertainties, thus, no correctionfor the trigger efficiency is applied or systematic uncertainty assigned.1 g T p T r i gge r E ff i c i en cy Internal ATLAS = 8.16 TeV NN s +Pb, p | < 1.37 g h | L1EM5 fi MB g13_etcut fi L1EM7 g15_loose fi g13_etcut g T p T r i gge r E ff i c i en cy Internal ATLAS = 8.16 TeV NN s +Pb, p | < 2.37 g h L1EM5 fi MB g13_etcut fi L1EM7 g15_loose fi g13_etcut [GeV] g T p T r i gge r E ff i c i en cy ATLAS = 8.16 TeV NN s +Pb, p | < 1.37 g h | L1EM10 fi MB g18_etcut fi L1EM12 g20_loose fi g18_etcut [GeV] g T p T r i gge r E ff i c i en cy ATLAS = 8.16 TeV NN s +Pb, p | < 2.37 g h L1EM10 fi MB g18_etcut fi L1EM12 g20_loose fi g18_etcut [GeV] g T p T r i gge r E ff i c i en cy ATLAS = 8.16 TeV NN s +Pb, p | < 1.37 g h | L1EM12 fi MB g23_etcut fi L1EM16 g25_loose fi g23_etcut [GeV] g T p T r i gge r E ff i c i en cy ATLAS = 8.16 TeV NN s +Pb, p | < 2.37 g h L1EM12 fi MB g23_etcut fi L1EM16 g25_loose fi g23_etcut [GeV] g T p T r i gge r E ff i c i en cy ATLAS = 8.16 TeV NN s +Pb, p | < 1.37 g h | L1EM16 fi MB g28_etcut fi L1EM16 g30_loose fi g28_etcut [GeV] g T p T r i gge r E ff i c i en cy ATLAS = 8.16 TeV NN s +Pb, p | < 2.37 g h L1EM16 fi MB g28_etcut fi L1EM16 g30_loose fi g28_etcut [GeV] g T p T r i gge r E ff i c i en cy ATLAS = 8.16 TeV NN s +Pb, p | < 1.37 g h | L1EM20 fi MB g33_etcut fi L1EM20 g35_loose fi g33_etcut [GeV] g T p T r i gge r E ff i c i en cy ATLAS = 8.16 TeV NN s +Pb, p | < 2.37 g h L1EM20 fi MB g33_etcut fi L1EM20 g35_loose fi g33_etcut Figure 5.1: Trigger efficiency for each “stage” of the total efficiency for HLT loose triggers. Each row shows thestages for a particular HLT loose threshold, while the left and right columns show the efficiency in the barreland end-cap regions. Efficiencies are always shown with respect to offline loose photon. Separate efficiencies areshown for the L1 efficiency in MB events (black), the HLT efficiency without ID in L1 pass-through triggeredevents (red), and the HLT efficiency with online loose ID requirement in HLT trigger photon events without ID(blue).2 Samples of MC simulated events were generated to study the detector performance for signal photons.Proton–proton generators were used as the source of events containing photons. To include the effects of the p +Pb underlying-event environment, these simulated pp events were combined with minimum bias p +Pb eventsfrom data before reconstruction in a process called data overlay . In this way, the simulated events contain theeffects of the p +Pb underlying-event identical to those observed in data.The P 8.186 [127] generator was used to generate the nominal set of MC events, with the NNPDF23LOPDF set [128] and a set of generator parameters tuned to reproduce minimum-bias pp events with the same col-lision energy as that in the p +Pb data (“A14” tune) [129]. A centre-of-mass boost was applied to the generatedevents to bring them into the same laboratory frame as the data. The generator simulates the direct photoncontribution and, through final-state QED radiation in → QCD processes, also includes the fragmentationphoton contributions; these components are defined to be signal photons. Events were filtered in six exclusive E γ T ranges from 17 GeV to 500 GeV.An additional MC sample was used to assess the sensitivity of the measurement to this choice of generator.The S 2.2.4 [130] event generator produces fragmentation photons in a different way from P and wasthus chosen for the comparison. The NNPDF3.0NNLO PDF set [53] was used, and the events were generated inthe same kinematic regions as the P events. These events were generated with leading-order matrix elementsfor photon-plus-jet final states with up to three additional partons, which were merged with the S partonshower.The P and S pp events were passed through a full G4 simulation of the ATLAS de-tector [106, 107]. To model the underlying event (UE) effects, each simulated event was combined with aminimum-bias p +Pb data event and the two were reconstructed together as a single event, using the same al-gorithms as used for the data. These events were split between the two beam configurations in a proportionmatched to that in data-taking. The UE activity levels, as characterized by the FCal Σ E Pb T , are different in thephoton-containing data events from the minimum-bias data events used in the simulation. Thus, the simulatedevents were weighted on a per-event basis to match the UE activity distribution in data.3Generally, distributions in the MC are constructed via a weighted sum of the distribution in each sub-sample, where the weighting accounts for differences in the cross-section ( σ DP ), generator-level filter efficiency( (cid:15) DP ), and total sample statistics ( N DPevt ), e.g. O = (cid:88) DP O DP (cid:0) σ DP /(cid:15) DP N DPevt (cid:1) (5.2)Tables A.1 and A.2 in the Appendix summarize the MC samples used in this analysis. At the generator level, prompt isolated photons are defined as those which are photons (P particlecode = 22 ), final-state, and primary particles. Additionally, the generator-level transverse isolation energy, E isoT ,is defined as the scalar sum of the transverse energies of final-state, primary particles (excluding muons andneutrinos) within a ∆ R < . cone around the photon. To account for the effects of particle level UE on thetruth isolation energy, the ambient-energy-density is determined event-by-event using the jet area method [131],and subtracted from the truth isolation energy before imposing the isolation requirement. Figure 5.2 shows theaverage ambient-energy-density as a function of truth photon E γ T in each pseudorapidity region for both Pand S. This correction ends up having only a sub-percent level effect on the resulting cross sections as canbe seen in the ratios in Figure 5.3. [GeV] T E [ G e V ] æ U E E Æ Pythia8Sherpa * < 1.90 h [GeV] T E [ G e V ] æ U E E Æ Internal ATLAS * < 0.91 h -1.84 < [GeV] T E [ G e V ] æ U E E Æ * < -2.02 h -2.83 < Figure 5.2: Average ambient-energy-density as determined, event-by-event at particle level using the jet areamethod, and plotted as a function of truth photon E γ T in each pseudorapidity region for both P andS.4 [GeV] T E N o m i na l s / J AS s * < 1.90 h [GeV] T E N o m i na l s / J AS s * < 0.91 h -1.84 < Internal ATLAS [GeV] T E N o m i na l s / J AS s * < -2.02 h -2.83 < Figure 5.3: Ratio of resulting photon cross section measurements with and without jet-area subtraction of theUE. Figure 5.4 shows a scatterplot of the generator-level E isoT as a function of E γ T , indicating the region inwhich photons are defined to be isolated. Additionally, it gives an example of how the full isolated photoncross-section is built out of the spectra in individual MC sub-samples. 10 [GeV] g T E0 50 100 150 200 250 300 350 400 450 500 [ G e V ] T i s o E ATLAS T g E [ pb / G e V ] T g / d E s d - - - 10 Internal ATLAS DP17_35DP35_50DP50_70DP70_140DP140_280DP280_500 Figure 5.4: Left: Distribution of generator-level isolation values as a function of generator-level E γ T . All photon E γ T slices are included without cross-section weighting. The dashed line indicates the position of the isolation cut. Right: Isolated photon cross-section at the generator-level in P events. The binning matches the binningused in the analysis, with the (weighted) contribution from each DP sample shown as a different color.5 Photons are reconstructed and identified following a procedure used extensively in previous ATLAS mea-surements [117], of which only the main features are summarised here. Efficiencies for each step of the processare calculated in each period separately to check for period differences, and the final values are combined as theluminosity weighted average. As detailed in Refs. [132, 133], photon candidates are reconstructed from clusters of energy deposited inthe electromagnetic calorimeter in three regions corresponding to the laboratory-frame ( η lab ) positions of thebarrel and forward and backward end-caps (cid:12)(cid:12) η lab (cid:12)(cid:12) < . . The transition region between the barrel and end-capcalorimeters, . < (cid:12)(cid:12) η lab (cid:12)(cid:12) < . , is excluded due to its higher level of inactive material. The measurement ofthe photon energy is based on the energy collected in calorimeter cells in an area of size ∆ η × ∆ φ = 0 . × . in the barrel and ∆ η × ∆ φ = 0 . × . in the end-caps. It is corrected via a dedicated energycalibration [134] which accounts for losses in the material before the calorimeter, both lateral and longitudinalleakage, and for variation of the sampling-fraction with energy and shower depth.The reconstruction efficiency is calculated in MC by computing the fraction of truth isolated photons, N γ TIso , which are reconstructed, N γ TIso , reco , in each E γ T and η bin. The reconstructed photons are required tomatch the truth level photon geometrically within an ∆ R distance of 0.2. (cid:15) reco = N γ TIso , reco N γ TIso (5.3)The efficiency is plotted in Fig. 5.5 showing 99% in the barrel, and 98% in the end caps and similar values for p +Pb and Pb+ p periods. The photons are identified using two sets of calorimeter shower shape requirements corresponding to loose and tight selections described in detail in Ref. [133]. The tight requirements select clusters which are compatiblewith originating from a single photon impacting the calorimeter. Photon identification criteria is designed to6 [GeV] truthT p E ff i c i en cy * < 1.90 h Reco Efficiency [GeV] truthT p E ff i c i en cy * < 0.91 h -1.84 < Internal ATLAS p+Pb PeriodPb+p Period [GeV] truthT p E ff i c i en cy * < -2.02 h -2.83 < Figure 5.5: Reconstruction efficiency for truth isolated photons plotted as a function of E γ T in each center ofmass pseudorapidity slice for both running periods.minimize background from non-prompt sources and is based on the classification of the full shower shape inthe calorimeters. Nine shower shape variables are created using information from the hadronic calorimeter, thelateral shower shape in the second layer of the electromagnetic calorimeter, and the detailed shower shape in thefinely segmented first layer. A pictorial representation of these variables is given in Fig. 5.6. Criteria on each ofthem together form the tight identification category. The loose selection class is designed to be less discriminatingand accept a larger number of background and decay photons. This is done by relaxing some of the second EMand hadronic layer’s shower shape criteria and not using the information from the first layer. In this analysis,the loose selection is only used at the triggering level to select both direct and background photons (which areneeded for the purity determination).The same selection scheme is applied to MC after corrections or fudge factors are imposed to make thedistributions better agree with data. Fig. 5.7 gives an example of one shower shape variable, R η , in data as com-pared with MC before and after fudging for each pseudorapidity region and a representative E γ T bin. Examplesof the rest of the variables can be found in Appendix A.7. Furthermore, when plotting the MC photons, a smalladditional correction is applied as a weight to correct an observed discrepancy between the tight I.D. efficienciesfrom MC and those derived from data driven studies.7Figure 5.6: A pictorial representation of the shower shape variables used for photon identification. h R - - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging h R - - - - < 0.60 Lab h T p h R - - - - < -0.60 Lab h -1.37 < h R - - - - < 1.37 Lab h h R - - - < -1.56 Lab h -1.81 < h R - - - < 1.81 Lab h h R - - - - < -1.81 Lab h -2.37 < h R - - - < 2.37 Lab h Figure 5.7: Shower shape parameter, R η , in each pseudorapidity slice from representative E γ T bin ( GeV ATLAS p+Pb PeriodPb+p Period [GeV] truthT p E ff i c i en cy * < -2.02 h -2.83 < Figure 5.8: Tight identification cut efficiency for reconstructed and truth isolated photons plotted as a functionof E γ T in each center of mass pseudorapidity slice for both running periods. The E isoT is computed from the sum of E T values in topological clusters of calorimeter cells [135] insidea cone of size ∆ R = 0 . centered on the photon. This cone size is chosen to be compatible with a previousmeasurement of photon production in pp collisions at √ s = 8 TeV [116], which is used to construct thereference spectrum for the R p Pb measurement. This estimate excludes an area of ∆ η × ∆ φ = 0 . × . centred on the photon, and is corrected for the expected leakage of the photon energy from this region into theisolation cone. Photons are then declared isolated if they pass the isolation condition identical to the particle levelcondition stated in Eqn. 5.1. Isolation energy in MC is shifted to match data for each E γ T and η bin. Figure 5.9shows the relationship between the reconstructed isolation energy to the truth isolation energy, described above.In section 5.6.1.3, this discrepancy is accounted for by deriving an associated systematic uncertainty.Figure 5.10 shows example E isoT distributions for identified and isolated photons, the corresponding dis-tributions for background photons with the normalisation determined by the double-sideband method, discussedin Sec. 5.4, and the resulting signal-photon distributions after background subtraction, compared with those forgenerator-level photons in MC simulation. The Figure shows the shape of the background distribution withinthe signal region, and the correspondence between the background-subtracted data and the signal-only Pdistributions gives confidence that the simulations accurately represent the data.9 100 5 10 15 20 25 30 [GeV] isoT Truth E10 - [ G e V ] i s o T R e c o E Pythia8 Truth + -0.630 · Reco = 0.607 Simulated Internal ATLAS 100 5 10 15 20 25 30 [GeV] isoT Truth E10 - [ G e V ] i s o T R e c o E Sherpa Truth + -0.530 · Reco = 0.624 Simulated Internal ATLAS Figure 5.9: A 2d histogram of reconstructed isolation energy vs. the truth transverse energy from final-state,primary particles (excluding muons and neutrinos) particles in a cone of 0.4 around the photon. A profile isplotted as a black line and a linear fit to the profile is plotted in red. Left: P data overlay, Right: Sherpadata overlay.The efficiency of the isolation cut is calculated in MC simulations as (cid:15) Iso = N γ TIso , reco , tight , Iso N γ TIso , reco , tight , (5.5)and plotted as a function of truth E γ T in each η bin in Fig. 5.11. The isolation cut efficiency shows a perioddependence of about 1% in the backward region. The disabled HEC region can not be the cause of this discrep-ancy, as it has been removed from the analysis. The root cause of this remains a mystery, and therefore, a flat 1%systematic in the backward region is applied to account for the discrepancy.This analysis applies no detector level UE corrections to the measured isolation energy. However, thesensitivity to this choice was checked by using the jet-area method [131] with topological calorimeter clusters toestimate the ambient UE energy. Subtraction of this energy from photon isolation cones yields a negligible effecton the measurement. The combined reconstruction, tight identification, and isolation efficiency is defined as (cid:15) total = (cid:15) reco × (cid:15) tight × (cid:15) Iso , (5.6)00 - [GeV] IsoT E F r a c t i on o f pho t on s * < 1.90 h g T E 25 < ATLAS - [GeV] IsoT E F r a c t i on o f pho t on s * < 0.91 h -1.84 < Identified photonBackground enhancedBackground subtractedPYTHIA8 - [GeV] IsoT E F r a c t i on o f pho t on s * < -2.02 h -2.83 < - [GeV] IsoT E F r a c t i on o f pho t on s * < 1.90 h g T E 105 < ATLAS - [GeV] IsoT E F r a c t i on o f pho t on s * < 0.91 h -1.84 < Identified photonBackground enhancedBackground subtractedPYTHIA8 - [GeV] IsoT E F r a c t i on o f pho t on s * < -2.02 h -2.83 < Figure 5.10: Distributions of detector-level photon isolation transverse energy E isoT for identified photons indata (black points), background photons scaled to match the data at large E isoT (blue solid line), the resultingdistribution for signal photons scaled so that the maximum value is the same as that for identified photons (greendot-dashed line), and that for photons in simulation which are isolated at the generator level normalised to havethe same integral as the signal photon distribution (red dashed line). Each panel shows a different pseudorapidityregion, while the top and bottom panels show the low- E γ T and high- E γ T range respectively. The vertical errorbars represent statistical uncertainties only.and is plotted as a function of truth E γ T for each η bin in Fig. 5.12. Tables of efficiency values are printed inAppendix A.3.A comparison to the total efficiency calculated using the S data overlay sample is shown for periodA in Fig. 5.13 and period B in Fig. 5.14. The S sample gives an efficiency that is consistent with that fromP in all kinematic regions.01 [GeV] truthT p E ff i c i en cy * < 1.90 h Efficiency ID · Reco Iso [GeV] truthT p E ff i c i en cy * < 0.91 h -1.84 < Internal ATLAS p+Pb PeriodPb+p Period [GeV] truthT p E ff i c i en cy * < -2.02 h -2.83 < Figure 5.11: Isolation cut efficiency for tight identified, reconstructed, and truth isolated photons plotted as afunction of E γ T is each pseudorapidity slice. As a reminder, the photons are only from the region of the detectorin which the HEC was live. 30 40 50 · [GeV] g T E E ff i c i en cy * < 1.90 h 30 40 50 · [GeV] g T E E ff i c i en cy * < 0.91 h -1.84 < Reco ID · Reco Iso · ID · Reco Simulation ATLAS 30 40 50 · [GeV] g T E E ff i c i en cy * < -2.02 h -2.83 < Figure 5.12: Efficiency for simulated photons passing the generator-level isolation requirement, shown as a func-tion of photon transverse energy E γ T with a different pseudorapidity region in each panel. The reconstruction(red circles), reconstruction plus identification (blue squares) and total selection (green triangles) efficiencies areshown separately. The photon energy scale and resolution is also determined in MC simulations. In Fig. 5.15, the meanrelative energy difference of reconstructed to truth E γ T is plotted for tight identified and isolated photons whichquantifies the measured energy scale. The energy scale is within one half of one percent in each region of η .Fig. 5.16 shows reconstructed photon energy resolution as the width of a Gaussian fit to the energy distribution02 [GeV] T E T o t a l e ff i c i en cy PythiaSherpa * < 1.90 h [GeV] T E T o t a l e ff i c i en cy * < 0.91 h -1.84 < Internal ATLAS [GeV] T E T o t a l e ff i c i en cy * < -2.02 h -2.83 < 30 40 50 · [GeV] T E P y t h i a8 ˛ / S he r pa ˛ * < 1.90 h 30 40 50 · [GeV] T E P y t h i a8 ˛ / S he r pa ˛ * < 0.91 h -1.84 < Const = 0.997 Internal ATLAS 30 40 50 · [GeV] T E P y t h i a8 ˛ / S he r pa ˛ * < -2.02 h -2.83 < Const = 0.997 Figure 5.13: Combined reconstruction, tight identification, and isolation cut efficiency for truth isolated pho-tons plotted as a function of E γ T from both P and S data overlay from the p +Pb running period. Top: p +Pb period, Bottom: p +Pb period ratio [GeV] T E T o t a l e ff i c i en cy PythiaSherpa * < 1.90 h [GeV] T E T o t a l e ff i c i en cy * < 0.91 h -1.84 < Internal ATLAS [GeV] T E T o t a l e ff i c i en cy * < -2.02 h -2.83 < 30 40 50 · [GeV] T E P y t h i a8 ˛ / S he r pa ˛ * < 1.90 h 30 40 50 · [GeV] T E P y t h i a8 ˛ / S he r pa ˛ * < 0.91 h -1.84 < Const = 0.999 Internal ATLAS 30 40 50 · [GeV] T E P y t h i a8 ˛ / S he r pa ˛ * < -2.02 h -2.83 < Const = 0.999 Figure 5.14: Combined reconstruction, tight identification, and isolation cut efficiency for truth isolated pho-tons plotted as a function of E T from both P and S data overlay from the Pb+ p running period. Top: Pb+ p period, Bottom: Pb+ p period ratioin every given E γ T bin. It is smaller than 3.5% everywhere in the detector. The scale and resolution are as expected,and therefore, we do not make any additional corrections but apply variations as systematic uncertainties.03 truthT p - - - - - - æ t r u t h T / p r e c o T p Æ < 0.00 h -0.60 < truthT p - - - - - - æ t r u t h T / p r e c o T p Æ < 0.60 h Internal ATLAS truthT p - - - - - - æ t r u t h T / p r e c o T p Æ < -0.60 h -1.37 < truthT p - - - - - - æ t r u t h T / p r e c o T p Æ < 1.37 h truthT p - - - - - - æ t r u t h T / p r e c o T p Æ < -1.56 h -1.81 < truthT p - - - - - - æ t r u t h T / p r e c o T p Æ < 1.81 h truthT p - - - - - - æ t r u t h T / p r e c o T p Æ < -1.81 h -2.37 < truthT p - - - - - - æ t r u t h T / p r e c o T p Æ < 2.37 h Figure 5.15: Mean relative energy difference of reconstructed to truth E γ T for tight identified and isolatedphotons plotted as a function of truth E γ T in each pseudorapidity slice. truthT p ) t r u t h T / p r e c o T ( p s < 0.00 h -0.60 < truthT p ) t r u t h T / p r e c o T ( p s < 0.60 h Internal ATLAS truthT p ) t r u t h T / p r e c o T ( p s < -0.60 h -1.37 < truthT p ) t r u t h T / p r e c o T ( p s < 1.37 h truthT p ) t r u t h T / p r e c o T ( p s < -1.56 h -1.81 < truthT p ) t r u t h T / p r e c o T ( p s < 1.81 h truthT p ) t r u t h T / p r e c o T ( p s < -1.81 h -2.37 < truthT p ) t r u t h T / p r e c o T ( p s < 2.37 h Figure 5.16: Reconstructed photon energy resolution for tight identified and isolated photons plotted as afunction of truth E γ T in each pseudorapidity slice. The dominant sources of electrons in the present kinematic regions are from heavy flavor meson decays,however, the isolation energy condition strongly suppresses this contribution. The primary source of isolatedelectrons are from W ± and Z boson decays as has been noted in previous ATLAS measurements [116, 136]. Mis-04reconstructed electrons are may be mis-identified as converted photons with one track. To study contaminationin the photon container from these mis-reconstructed electrons, a Z → e + e − Monte Carlo sample, with fulldetector simulation, was used to measure the probability to reconstruct electrons as photons.Reconstructed electrons and photons are geometrically matched to truth electrons from Z → e + e − decays. The reconstructed photons are required to satisfy the same identification and isolation conditions usedfor real data in this analysis, and the electrons are required to be pass a loose identification requirement with therecommended track quality cuts. The total per-event-yields of these misidentified photons and electrons as wellas the misidentification rate defined as the ratio of the two spectra are plotted in Fig. 5.17. The misidentificationrate is about 6% in the forward regions and about 2% at mid-rapidity which is consistent with recent studies at13 TeV [137]. [GeV] eT E Truth - - - - - - - 10 1 c oun t s / e v en t / G e V * < 1.90 h [GeV] eT E Truth - - - - - - - 10 1 c oun t s / e v en t / G e V * < 0.91 h -1.84 < [GeV] eT E Truth - - - - - - - 10 1 c oun t s / e v en t / G e V * < -2.02 h -2.83 < [GeV] eT E Truth e fi e / N g fi e N * < 1.90 h [GeV] eT E Truth e fi e / N g fi e N * < 0.91 h -1.84 < [GeV] eT E Truth e fi e / N g fi e N * < -2.02 h -2.83 < Figure 5.17: Top: The total per-event-yields of reconstructed electrons (black) and misidentified photons (red).Bottom: The photon misidentification rate defined as the ratio of the two spectra.05To estimate the electron contamination, we find the cross section of misidentified electrons in the Z → e + e − sample and take the ratio to the measured photon cross section. The contamination is taken as the ratioof these cross sections which is between 0.05% and 0.33% in the forward regions, and 0.05% and 0.12% atmid-rapidity. Figures of the cross sections and contamination are plotted in Fig. 5.18. [GeV] eT E Truth - - - - - 10 110 [ nb ] T E / d s d * < 1.90 h [GeV] eT E Truth - - - - - 10 110 [ nb ] T E / d s d * < 0.91 h -1.84 < [GeV] eT E Truth - - - - - 10 110 [ nb ] T E / d s d * < -2.02 h -2.83 < [GeV] g T E s i gna l gs / ee fi Z g f a k e s * < 1.90 h [GeV] g T E s i gna l gs / ee fi Z g f a k e s * < 0.91 h -1.84 < [GeV] g T E s i gna l gs / ee fi Z g f a k e s * < -2.02 h -2.83 < Figure 5.18: Top: Measured photon cross section from this analysis (black) and misidentified photon crosssection from electrons from Z decays in MC (red). Bottom: The electron contamination defined as the ratio ofthe two spectra.To estimate the contribution from W ± → e ± decays, the ratio of mis-identified electrons from W + Z decays to that of only Z decays is calculated using the contamination values found in the internal note accom-panying the 13 TeV pp inclusive photon results [138], accounting correctly for the factor of two from the Z vs. W decays. These values indicate conservative factors of 4.35 (mid-rapidity) and 4.0 (forward) increases from thecontamination from Z decays only. A conservative estimate of the total contamination is . below 100 GeVand . above 100 GeV in the forward regions, and . for all E γ T in mid-rapidity. These values are taken assystematic uncertainties on the final measurement.06 While investigating Z bosons in the di-electron decay channel in pp collisions at 5.02 TeV, a negative shiftin the mass peak was discovered and was found to be a result of an electron energy scale calibration problem. Theelectron energy scale is parameterized in the following way: E data e = E MC e (1 + α ( cell η , µ )) , (5.7)where α is a function of the pseudorapidity of the calorimeter cell and the pileup rate parameter µ . α is relatedto µ through the OF C ( µ ) parameters. The source of the problem was that the production was run with thedefault OF C ( µ = 20) instead of the appropriate OF C ( µ = 0) for the p +Pb conditions. Fig. 5.19 shows theratio of extracted electron energy from an example 13 TeV run using OF C ( µ = 0) to that using OF C ( µ = 20) showing a strong η dependence. Z boson analysis in 5.02 TeV pp dataATLAS Weekly Meeting New electron energy calibration for 5.02 pp TeV data • egamma experts suggested reprocessing of one 13 TeV run with OFC( μ =0) • from comparing the electron energy and energy calibrations between the nominal and the new reprocessing one can tackle the problem • this was the right way to go - observed strong dependence on electron pseudorapidity plot by Guillaume Unal Figure 5.19: The ratio of extracted electron energy from an example 13 TeV run using OF C ( µ = 0) to thatusing OF C ( µ = 20) .This problem, also affecting photons, is corrected by adding an additional calibration factor to the electronand photon energy scale. Figures 5.20 and 5.21 show this correction applied to a Z mass peak comparison in5.02 TeV pp data at mid- and forward-rapidity. The same corrections are applied in this photon analysis.07 Z boson analysis in 5.02 TeV pp dataATLAS Weekly Meeting 10 • very good agreement after the electron energy calibration update in the Z mass peak for forward Z candidates • no change in central Z boson candidates Validation of the new electron energy calibration for 5.02 pp TeV data Z m C oun t s recoZ Data Z mass |y data ee → Z Internal ATLAS , -1 , 25.3 pb pp =5.02 TeVs | <= 1 recoZ Data Z mass |y Z m60 70 80 90 100 110 120 D a t a / M C NEW Z m C oun t s recoZ Data Z mass |y data ee → Z Internal ATLAS , -1 , 25.3 pb pp =5.02 TeVs | <= 1 recoZ Data Z mass |y Z m60 70 80 90 100 110 120 D a t a / M C OLD Figure 5.20: Di-electron invariant mass distribution in data compared to MC for uncorrected (left) and cor-rected(right) electron energy scale data at mid rapidity. Z boson analysis in 5.02 TeV pp dataATLAS Weekly Meeting 9 • very good agreement after the electron energy calibration update in the Z mass peak for forward Z candidates " Validation of the new electron energy calibration for 5.02 pp TeV data Z m C oun t s recoZ Data Z mass 1 < |y data ee → Z Internal ATLAS , -1 , 25.3 pb pp =5.02 TeVs | < 2.5 recoZ Data Z mass 1 < |y Z m60 70 80 90 100 110 120 D a t a / M C OLD Z m C oun t s recoZ Data Z mass 1 < |y data ee → Z Internal ATLAS , -1 , 25.3 pb pp =5.02 TeVs | < 2.5 recoZ Data Z mass 1 < |y Z m60 70 80 90 100 110 120 D a t a / M C NEW Figure 5.21: Di-electron invariant mass distribution in data compared to MC for uncorrected (left) and corrected(right) electron energy scale data at forward rapidity. Note the different range in y-axis for the ratios in the bottompanels. The differential cross-section is calculated for each E γ T and η ∗ bin as d σ d E γ T = 1 L int E γ T N sig P sig (cid:15) sel (cid:15) trig C MC , where L int is the integrated luminosity, ∆ E γ T is the width of the E γ T bin, N sig is the yield of photon candidatespassing identification and isolation requirements, P sig is the purity of the signal selection, (cid:15) sel is the combinedreconstruction, identification and isolation efficiency for signal photons, (cid:15) trig is the trigger efficiency, and C MC is a MC derived bin-by-bin correction for the change in the E γ T spectrum from photons migrating between bins08in the spectrum due to the width in the energy response. C MC is determined after all selection criteria at bothreconstruction and particle levels are imposed. The efficiencies have been discussed above. The purity and otherfactors are detailed below. The photon purity P sig is determined via a data-driven double-sideband procedure used extensively inprevious measurements of cross-sections for processes with a photon in the final state [116, 117, 139, 140] andsummarised here. A matrix of four designations is made: tight, non-tight, isolated, non-isolated. The non-tightselected photons pass the loose requirements of Ref. [133] but fail certain components of the tight requirements,designed to mostly select background. The non-iso photons are required to have significant isolation energy suchthat E isoT > . . × − E γ T [ GeV ] . (5.8)These designations form four groups: A (tight & iso), B (tight & non-iso), C (non-tight & iso), D (non-tight &non-iso). The majority of signal photons are in the tight, isolated region, defined to be the signal region, whilethe other three regions are dominated by the background. Photon candidates that comprise the background areassumed to be distributed in a way that is uncorrelated along the two axes. The yields in the three non-signalsidebands, with an understanding of the leakage from the signal region into the sidebands, are used to estimatethe yield of background in the signal region and this is combined with the yield in the signal region to extractthe purity.Figure 5.22 shows the sideband yields for the p +Pb and Pb+ p running periods combined (reversing thepseudorapidity of the Pb+ p period) as raw yields and as ratios to the signal region A. These ratios are fit topolynomial forms which are used only to smooth the sideband yields for an alternate purity calculation and arenot used in the calculation of the cross section.Leakage rates of signal photons into the sidebands are estimated in MC and are presented in Fig. 5.23.Comparisons between leakages found from the nominal P sample to those from S can be found inAppendix A.6.09 [GeV] T E C oun t s * < 1.90 h A: Tight - IsoB: Tight - Not IsoC: Non-tight - IsoD: Non-tight - Not Iso [GeV] T E C oun t s * < 0.91 h -1.84 < Internal ATLAS [GeV] T E C oun t s * < -2.02 h -2.83 < [GeV] T E R a t i o * < 1.90 h B/A: Tight - Not IsoC/A: Non-tight - IsoD/A: Non-tight - Not Iso [GeV] T E R a t i o * < 0.91 h -1.84 < Internal ATLAS [GeV] T E R a t i o * < -2.02 h -2.83 < Figure 5.22: Sideband A, B, C, and D yields (Top) and ratios to A (Bottom) from both data taking periodscombined. Photon purity is calculated from these ratios together with leakage fractions. The histograms are fitto polynomial functional forms, though the fits are not used in the cross section calculation.The purity is defined as the ratio of the yield of signal photons to the total photon yield in the tight andisolated region: P = N A , datasignal N A , data (5.9)The yield of signal photons in region A, N A , datasignal , is computed from sideband yields, N X , data , and leakage factors, f X , MC , as N A , datasignal = N A , data − R bkg · (cid:32) ( N B , data − f B , MC N A , datasignal ) · ( N C , data − f C , MC N A , datasignal )( N D , data − f D , MC N A , datasignal ) (cid:33) . (5.10)Thus, to extract N A , datasignal , we can solve the above quadratic. The factor R bkg quantifies the deviation from perfectfactorization and is set to unity to calculate the central purity values and is varied to determine the systematicuncertainty of this assumption on the measurement as described in section 5.6. Because the sideband yields arestatistically limited at high E γ T , the yields from the two periods are combined, respecting the reverse of the beamdirection, before making the calculation directly from the yields and leakage fractions.10 30 40 50 · [GeV] truthT p Lea k age F r a c t i on < -1.56 Lab h -2.37 < sigA / N sigB N sigA / N sigC N sigA / N sigD N 30 40 50 · [GeV] truthT p Lea k age F r a c t i on < 1.37 Lab h -1.37 < Internal ATLAS 30 40 50 · [GeV] truthT p Lea k age F r a c t i on < 2.37 Lab h 30 40 50 · [GeV] truthT p Lea k age F r a c t i on < -1.56 Lab h -2.37 < sigA / N sigB N sigA / N sigC N sigA / N sigD N 30 40 50 · [GeV] truthT p Lea k age F r a c t i on < 1.37 Lab h -1.37 < Internal ATLAS 30 40 50 · [GeV] truthT p Lea k age F r a c t i on < 2.37 Lab h Figure 5.23: Sideband leakage fractions from truth isolated photons in Monte Carlo simulations plotted as afunction of E γ T in each pseudorapidity slice from the p +Pb (Top) and Pb+ p (bottom) running periods.An alternate calculation is made using polynomial fits to the sideband ratios to extrapolate to the pointsabove 75 GeV, and is used for comparison purposes only. In this case, the observed sideband B, C, and Dyields are replaced with the functional forms evaluated at the bin center multiplied by the bin content of A. Thebottom panel of Fig. 5.22 show these ratios along with their fits. The uncertainty in this smoothing is calculatedby determining the 68% (1 σ ) confidence interval around the fit function for each ratio. The value of the upperand lower band at a point is taken as the error, and is propagated through the purity calculation as a statisticalerror bar. The statistical error on the direct calculation is discussed in the next section.The same procedure is carried out using leakages from S, and the resulting purities, shown inFig. 5.24, are consistent with the nominal values within 0.5%. It is worth noting here that N A , datasignal is reallywhat we are after. The purity itself is not used in the cross section measurement, but is a useful performance plotto make.To estimate the statistical uncertainty on the purity, toy MC simulations are used to capture the asymmetri-cal nature of the error. Each toy consists of sample sideband yields randomly generated from Poisson distributions11 30 40 50 · [GeV] T E P u r i t y PythiaSherpa * < 1.90 h 30 40 50 · [GeV] T E P u r i t y * < 0.91 h -1.84 < Internal ATLAS 30 40 50 · [GeV] T E P u r i t y * < -2.02 h -2.83 < [GeV] T E P y t h i a / P S he r pa P Const = 1.000* < 1.90 h [GeV] T E P y t h i a / P S he r pa P Const = 1.000* < 0.91 h -1.84 < Internal ATLAS [GeV] T E P y t h i a / P S he r pa P Const = 1.001* < -2.02 h -2.83 < Figure 5.24: Purities for tight identified and isolated photons calculated via the sideband method with leakagesfrom both P and S data overlay. Top: purities; bottom: ratios.with means set to the measured yield in that sideband, and the leakage fractions which are constant and takenfrom MC. For each toy, the purity is calculated and entered into a finely binned (3000) histogram. 1M toys arethrown for each E γ T and pseudorapidity slice. The error is determined by integrating the distribution to 16% oneither side of the mean to approximate one standard deviation. If there is less than 16% above the mean, the topof the error is set to unity. For the case of N A , datasignal , a completely analogous procedure is carried out, however,because it is not constrained like the purity to be less than one, the statistical uncertainties are expected to besymmetric. Thus, the error is simply taken as the RMS of the distribution. A comparison between the directcalculation and the alternate, smoothed version is shown in Fig. 5.2512 30 40 50 · [GeV] T E P u r i t y * < 1.90 h 30 40 50 · [GeV] T E P u r i t y * < 0.91 h -1.84 < Internal ATLAS ExtrapolatedToy MC 30 40 50 · [GeV] T E P u r i t y * < -2.02 h -2.83 < Figure 5.25: Purities for tight identified and isolated photons calculated via the direct method using toy MCsfor the statistical error, and those calculated using the smoothed sideband method. Because of the non-zero energy resolution for photons in the EM calorimeter, some reconstructed photonswill end up in a E γ T bin not corresponding to its “truth” E γ T . Due to the falling nature of the E γ T spectrum, thisbin sharing is not symmetric and there will be an overall migration of counts towards higher E γ T bins as shownin Fig. 5.26. Fig. 5.27 shows the fraction of photon counts that remain in the same bin after reconstruction (donot migrate) to be about 90%. The saw-tooth jumps are due to jumps in the bin size that affect the migrationfraction. Thus, this effect is small in the case of photons in ATLAS, and therefore, we employ a simple bin-by-bin correction, C MC , as calculated in MC. The correction is calculated using truth matched tight and isolatedphotons and taking the ratio of their reconstructed E γ T over their truth E γ T C MC = N γ, truep T TIso , reco , tight , Iso N γ, recop T TIso , reco , tight , Iso , (5.11)Fig. 5.28 shows that these corrections for each beam configuration are of order a couple percent at low E γ T , but grow to about 5% at high E γ T . Note, the error bars on these corrections are not calculated correctly, asthey have not taken into account the correlation between the numerator and denominator.To smooth the statistical fluctuations, the periods are combined (reversing the pseudorapidity of the secondperiod) and the correct errors are calculated in the following way. The population of i th bin of the truth ( T ) andreconstructed ( R ) E γ T spectra can be expressed as T i = Σ j A ji and T i = Σ j A ij respectively, where A ij are the13 - - - - - - - * < 1.90 h 20 30 40 50 · [GeV] truthT E [ G e V ] r e c o T E Simulation Internal ATLAS * < 1.90 h - - - - - - - * < 0.91 h -1.84 < 20 30 40 50 · [GeV] truthT E [ G e V ] r e c o T E Simulation Internal ATLAS * < 0.91 h -1.84 < - - - - - - - * < -2.02 h -2.83 < 20 30 40 50 · [GeV] truthT E [ G e V ] r e c o T E Simulation Internal ATLAS * < -2.02 h -2.83 < Figure 5.26: Photon E γ T response matrix for tight and isolated truth matched photons from MC data overlay ineach pseudorapidity region. The bin from 17-20 GeV acts as an underflow bin. 30 40 50 · [GeV] truthT E F r a c i on i n d i agona l 30 40 50 · [GeV] truthT E F r a c i on i n d i agona l 30 40 50 · [GeV] truthT E F r a c i on i n d i agona l Figure 5.27: The fraction of photon counts that remain in the same E γ T bin after reconstruction as measured inMC data overlay in each pseudorapidity regionmatrices given in Fig. 5.26. The correction factors for each bin, C i , can then be expressed as C i = R i T i = A ii + Σ j (cid:54) = i A ij T i . (5.12)The reconstructed bin’s contents consist of two populations, (1) those that originated in this bin, and (2) thosethat migrated into it. Binomial errors are assigned to population (1) using the fractions in Fig. 5.27 as thebinomial probability, and Poisson uncertainties are assigned to the counts from (2). The total uncertainty on R i is then the quadrature sum of the two. T i is given Poisson uncertainties which is propagated into C i in the ratio.The corrections, shown in Fig. 5.29, are then fit to a logistic functional form from which the correction factorsare taken. The bin-by-bin errors are simply those found in the above exercise.14 [GeV] T p R e c o / T r u t h * < 1.90 h [GeV] T p R e c o / T r u t h * < 0.91 h -1.84 < Internal ATLAS p+Pb PeriodPb+p Period [GeV] T p R e c o / T r u t h * < -2.02 h -2.83 < Figure 5.28: Bin migration corrections plotted as a function of E γ T in each pseudorapidity region for both runningperiods. Note, the error bars on these data are not calculated correctly, as they have not taken into account thecorrelation between the numerator and denominator. 30 40 50 · [GeV] g T E R e c o / T r u t h * < 1.09 h 30 40 50 · [GeV] g T E R e c o / T r u t h * < -1.84 h Simulation Internal ATLAS 30 40 50 · [GeV] g T E R e c o / T r u t h * < -2.83 h -2.02 < Figure 5.29: Bin migration corrections plotted as a function of E γ T in each pseudorapidity region. The correctionsare fit with a logistic function which is used for the applied corrections.To test the sensitivity of the corrections to differences in the shape of the E γ T spectrum between data andMC, the MC is reweighted to match the shape of that in data. Fig. 5.30 gives a comparison between data andMC showing that the data is slightly steeper than MC. The fits to the ratio in the lower panel are used to reweightthe MC to match the data. Fig. 5.31 shows the correction factors after this reweighting. The difference to thenominal corrections is < . and is considered negligible.15 [GeV] recoT E - - - - - - 10 1 * < 1.09 h DataMC [GeV] recoT E - - - - - - 10 1 * < -1.84 h [GeV] recoT E - - - - - - 10 1 * < -2.83 h -2.02 < [GeV] recoT E D a t a / M C * < 1.09 h [GeV] recoT E D a t a / M C * < -1.84 h [GeV] recoT E D a t a / M C * < -2.83 h -2.02 < Figure 5.30: (Top) A comparison of the photon E T spectrum in data (blue) and MC (red), showing that thedata spectrum is slightly steeper than that of MC. (Bottom) The ratio of the two including an exponential fitwhich is used as a factor to reweight the MC to match the data. 30 40 50 × [GeV] γ T E R e c o / T r u t h * < 1.09 η 30 40 50 × [GeV] γ T E R e c o / T r u t h * < -1.84 η Simulation Internal ATLAS 30 40 50 × [GeV] γ T E R e c o / T r u t h * < -2.83 η -2.02 < Figure 5.31: Bin migration corrections, determined after MC to data spectrum reweighting, plotted as a functionof E γ T in each pseudorapidity region. The corrections show a negligible difference to the nominal values inFig. 5.29.16 R p Pb The nuclear modification factor R p Pb can be expressed as a ratio of cross-sections in the following way: R p Pb = (d σ p +Pb → γ + X / d E γ T ) / ( A · d σ pp → γ + X / d E γ T ) , (5.13)where the geometric factor A is simply the number of nucleons in the Pb nucleus, 208. The reference pp spectrumis constructed by extrapolating a photon spectra measurement from √ s = 8 TeV pp collisions by ATLAS [116]that used the same particle-level isolation requirement. This extrapolation procedure is discussed in detail below. pp Reference Construction A reference cross-section for the prompt photon cross-section in pp collisions at the same energy ( √ s =8 . TeV) and with the same boost of the center of mass frame with respect to the lab frame ( ∆ y = +0 . ),is constructed by extrapolating previously the measured √ s = 8 TeV cross-section by ATLAS [116] using MCsimulation. For the nominal extrapolation, P simulations were used to generate truth-level photon spectrain TeV (without boost) and . TeV (with boost) pp collisions. Both samples use the identical tune (A14)and PDF set (NNPDF23LO), and have a consistent definition of truth-level isolation analogous to that in data.The strategy is then to use the ratios of the MC cross-sections as multiplicative extrapolation factors which canbe applied to the TeV data to construct an . TeV pp reference (with matching boost). Specifically, σ pp, . TeV , boost ( E γ T , η lab ) = σ pp, TeV ( E γ T , η lab ) × σ P , . TeV , boost ( E γ T , η lab ) σ P , TeV ( E γ T , η lab ) (5.14)Note that the TeV data are reported in symmetric selections in η , e.g. | η | < . , whereas the . TeVreference must be constructed in signed- η bins. Therefore, each | η | range in TeV pp data is used to construct a pp reference for two signed η ranges, and the ratios of P distributions are determined in signed η lab ranges.This approach has several advantages: (1) it is a correction derived from the ratio of MC distributions,meaning that any failure of the MC to describe the E γ T , y dependence of the data approximately cancels in theratios, before it is applied to data; (2) the p +Pb to pp comparison ratio is between photon yields measured in thesame physical region of the detector, potentially allowing for a cancellation of systematic uncertainties betweenthe data; (3) this factor simultaneously corrects for the different √ s and center of mass shift at the same time,rather than separate corrections for both effects.17 [GeV] T γ E [ pb / G e V ] T γ / d E σ d − − − − − − − − − − − 10 Internal ATLAS pp Data Pythia8 ) × -1.56 ( ≤ η -2.37 < ) -2 × ≤ η -1.37 < ) -4 × < 2.37 ( η ≤ [GeV] T g E P y t h i a / D a t a ATLAS pp -1.56 £ h -2.37 < 1.37 £ h -1.37 < 2.37 £ h Figure 5.32: Left : Comparison of prompt, isolated photon spectrum measured by ATLAS in √ s = 8 TeV pp data (identical to the points in Fig. 3 in Ref. [116]), to that in P A14 NNPDF23LO at the same energy. Right : P/data ratio in each measured η selection (systematic uncertainties on data not shown).Figure 5.32 shows the central values of the measured TeV ATLAS data compared to that in P foreach (cid:12)(cid:12) η Lab (cid:12)(cid:12) selection in data. It can be seen that P provides a reasonable but not perfect description of the E γ T and η dependence in data, and is typically within % over the range of interest. (Note that the Pcomparison in Ref. [116] is a different tune and PDF set – for our purposes we use the same tune and PDF asthat to derive the corrections for the 8.16 TeV p +Pb analysis.) [GeV] T g E [ pb / G e V ] T g / d E s d - - - - - - - - - - - 10 Internal ATLAS Pythia8 ) · -1.56 ( £ lab h -2.37 < ) -2 · £ lab h -1.37 < ) -4 · < 1.91 ( lab h £ Figure 5.33: Comparison of prompt, isolated photon spectrum in P A14 NNPDF23LO simulation at . TeV (with ∆ y = − . boost) and TeV for each pseudorapidity slice.18 [GeV] g T E E x t r apo l a t i on f a c t o r ( P y t h i a8 ) ATLAS < +2.37 lab h +1.56 < < +1.37 lab h -1.37 < < -1.56 lab h -2.37 < [GeV] T g E [ pb / G e V ] T g / d E s d - - - - - - - - - - - 10 110 10 Internal ATLAS pp Extrapolated 8.16 TeV ) · -1.56 ( £ lab h -2.37 < ) -2 · £ lab h -1.37 < ) -4 · < 2.37 ( lab h £ Figure 5.34: Left : Ratio of prompt, isolated photon spectrum in P A14 NNPDF23LO simulation between . TeV (with ∆ y = − . boost) and TeV for each pseudorapidity slice. Right : Extrapolated √ s =8 . TeV pp reference spectrum with center of mass boost by ∆ y = − . . The spectra are shown for eachpseudorapidity slice.Figure 5.33 compares the spectra as a function of signed η lab between P . TeV (with boost inthe η → −∞ direction) and TeV, while Figure 5.34 shows the ratio of the two as in Eqn. 5.14. It can be seenthat at mid-rapidity or at moderate- E γ T , the ratio of cross-sections is within – % of unity. This is because the η distribution at low or moderate- E γ T is fairly flat, meaning that a boost has little effect on the cross-section atmid-rapidity, and because the cross-section grows only slightly from TeV to . TeV (a 2% difference in √ s ).However, at large- E γ T or at moderate- E γ T and large- | η | , the ratios deviate from unity since the η shape of thephoton spectrum becomes steeper. Here the corrections are up to a factor of in the kinematic region reachedin the p +Pb data.Figure 5.34 shows the resulting reference pp spectra constructed according to Eq. 5.14. These spectra arethe ones used to construct the R p Pb results. Since the extrapolated pp reference is constructed by applying a mul-tiplicative factor to each measured E γ T , η bin, the resulting spectrum inherits the relative systematic uncertaintiesof the original measurements exactly. The sources of systematic uncertainty affecting the measurement are described in this section, which isbroken into two parts discussing the uncertainty in 1) the cross-section and 2) the nuclear modification factor19 R p Pb , including its ratio between forward and backward pseudorapidity regions. Tables including numericalvalues of all contributions to the systematic uncertainties of the cross section, R p Pb , and forward-to-backwardratio can be found in Appendix A.5. The major uncertainties in the cross-section can be divided into two main categories: those affectingthe purity determination, which are dominant at low E γ T where the sample purity is low, and those affecting thedetector performance corrections, which are dominant at high E γ T . All other sources tend to be weakly dependenton E γ T . A summary is shown in Figure 5.35. In each category, the uncertainty is the sum in quadrature of theindividual components; the combined uncertainty is the sum in quadrature of all contributions, excluding thoseassociated with the luminosity. The total uncertainties range from 15% at low and high E γ T , where they aredominated by the purity and detector performance uncertainties respectively, to a minimum of approximately % at E γ T ≈ GeV, where both of these uncertainties are modest. Each contribution to these uncertaintiesare studied in detail below. 30 40 50 · [GeV] g T E - - - - R e l a t i v e un c e r t a i n t y * < 1.90 h ATLAS g T E /d s Relative uncertainty in d 30 40 50 · [GeV] g T E - - - - R e l a t i v e un c e r t a i n t y CombinedPurityDetector performanceOther * < 0.91 h -1.84 < 30 40 50 · [GeV] g T E - - - - R e l a t i v e un c e r t a i n t y Pb Luminosity uncertainty p * < -2.02 h -2.83 < Figure 5.35: Summary of the relative sizes of major sources of systematic uncertainty in the cross-section mea-surement, as well as the combined uncertainty (excluding luminosity), shown as a function of photon transverseenergy E γ T .20 To assess the uncertainty in the purity determination, each boundary defining the sidebands used in thecalculation is varied independently in order to understand the sensitivity of the measurement to the doublesideband binning and correlation assumptions. The dominant uncertainty is that from the in the level of sidebandcorrelation. If there is no correlation, one expects the following relationship of the yield of background photonsin each sideband region: R bkg = N Abkg · N Bbkg N Cbkg · N Dbkg = 1 . (5.15)This condition has been tested in MC and data in previous studies and was found to be accurate to the levelof 10%. This analysis performs the same data-driven check as was done in Ref. [116]. Namely, we dividethe not-isolated background into the following separations analogous to the ABCD distinctions in the puritydetermination:• B: Tight && (7.8 GeV < E γ T < 17.8 [GeV])• D: Non-Tight && (7.8 GeV < E γ T < 17.8 [GeV])• F: Tight && ( E γ T > 17.8 [GeV])• E: Non-Tight && ( E γ T > 17.8 [GeV]) R bkg can now be estimated in the background region as R bkg = N Bbkg · N Ebkg N Dbkg · N Fbkg . (5.16)Fig. 5.36 gives this estimation of R bkg , plotted as a function of E γ T . The results agree with the a 10% variationfound in previous studies, thus we apply ± variation on R bkg and recompute the purities to obtain thesystematic variation. Fig. 5.37 shows the effect of this variation on the purity. This ± variation in thesideband correlation yields a 13% uncertainty in the cross-section in the lowest E γ T range, decreasing to less than % for E γ T > GeV.The inverted photon, non-tight, identification requirement for the background candidates is varied to beless or more restrictive about which shower shapes the background candidates are required to fail. The purities21 [GeV] T E b k g R * < 1.09 h Internal ATLAS [GeV] T E b k g R * < -1.84 h Without leakage [GeV] T E b k g R * < -2.83 h -2.02 < Figure 5.36: R bkg estimated using the BDFE method plotted as a function of E γ T . [GeV] T E P u r i t y Base purity = 1.1 bkg R = 0.9 bkg R * < 1.09 h [GeV] T E P u r i t y * < -1.84 h [GeV] T E P u r i t y * < -2.83 h -2.02 < Figure 5.37: The effect of systematic variations in R bkg when calculating the purity. The base purity is shownas black points and the purity calculated when R bkg is varied up (and down) are shown as magenta up (down)triangles. The plots are shown in the usual pseudorapidity bins.calculated with these variations are shown in Fig. 5.38. As can be seen when plotting the relative deviation ofthese variations in Fig. 5.39, the purity from these variations is statistically limited. To not introduce significantstatistical fluctuations in this systematic variation, the two variations are symmetrized by taking the average ofthe absolute value of each variation (plotted in black). The average points are further smoothed by fitting toconstant functions (blue lines), in the forward and backward regions, and a piece-wise line (in log( x ) ) between20 and 90 GeV and constant between 90 and 550 GeV in the mid-rapidity region. The value of the fit functionsare used as the symmetric uncertainty for these variations. This yields an uncertainty that is less than % for all22 E γ T in the forward and backward rapidity bins, but is significant at mid-rapidity ( − . < η ∗ < . ) where itis 9% in the lowest E γ T bin and decreases to be less than % for E γ T > GeV. [GeV] T E P u r i t y Base purity2-variable failure5-variable failure * < 1.90 h [GeV] T E P u r i t y * < 0.91 h -1.84 < [GeV] T E P u r i t y * < -2.02 h -2.83 < Figure 5.38: The effect of systematic variations in the definition of the non-tight sideband when calculating thepurity. The base purity is shown as black points and the purity calculated with 2 (5) shower shape variable failuremode are shown as orange up (down) triangles. The plots are shown in the usual pseudorapidity bins. [GeV] T E - - - - - R e l a t i v e E rr o r Internal ATLAS * < 1.90 h [GeV] T E - - - - - R e l a t i v e E rr o r * < 0.91 h -1.84 < [GeV] T E - - - - - R e l a t i v e E rr o r * < -2.02 h -2.83 < Figure 5.39: The relative deviation in the purity when varying the non-tight definition (orange). The two varia-tions are symmetrized and averaged and plotted as black points. The averaged points are fit to constant functions(blue lines), in the forward and backward regions, and piece-wise line (in log ( x ) ) between 20 and 90 GeV andconstant between 90 and 550 GeV in the mid-rapidity region. These fits are used as the symmetric error for thesevariations.Variations in the isolation energy threshold of ± GeV have been shown to cover any difference betweensimulations and data [117]. New leakages and purities are then calculated with the new isolation definition.Fig. 5.40 shows the effect of these variations on the purity. The result is a 1–2% effect on the cross-section in the23lowest E γ T range and less than % at higher E γ T . The uncertainty associated with the inverted shower-shape wassmoothed and symmetrised; however, this is derived asymmetrically from the positive and negative variationsseparately. [GeV] T E P u r i t y Base purityBackground Iso cut + 1 GeVBackground Iso cut - 1 GeV * < 1.90 h [GeV] T E P u r i t y * < 0.91 h -1.84 < [GeV] T E P u r i t y * < -2.02 h -2.83 < Figure 5.40: The effect of systematic variations in the definition of the non-iso sideband when calculating thepurity. The base purity is shown as black points and the purity calculated with +1 GeV (-1 GeV) added tothe constant term in the condition are shown as cyan up (down) triangles. The plots are shown in the usualpseudorapidity bins.The variations affecting the purity are summarized in Fig. 5.41 showing the relative deviations for eachvariation. The yellow band gives the quadrature sum of each of these contributions as an asymmetric error band. 30 40 50 · [GeV] T E - - - - - R e l a t i v e E rr o r * < 1.90 h 30 40 50 · [GeV] T E - - - - - R e l a t i v e E rr o r variation bkg RBackground Iso variaionNon-tight variation * < 0.91 h -1.84 < 30 40 50 · [GeV] T E - - - - - R e l a t i v e E rr o r * < -2.02 h -2.83 < Figure 5.41: The relative deviation in the purity when varying R bkg (magenta), the non-isolation definition(cyan), non-tight definition (orange), and their quadratic sum (yellow band). The plots are shown in the usualpseudorapidity bins and both.24 Uncertainties associated with detector performance corrections are dominant at high E γ T . A detailed de-scription of the several components of the photon energy scale and resolution uncertainties are given in Ref. [117].The impact of these on the measurement is determined by varying the reconstructed photon E γ T in simulationwithin the energy scale and resolution uncertainties and deriving alternative correction factors for positive andnegative variations separately. Additionally, the scale factor variation accounts for uncertainties associated withcorrections for small differences in reconstruction, identification and isolation efficiencies observed between dataand simulation [133]. Fig. 5.42 shows the relative deviation for each of these systematic uncertainties overlaid.The yellow band gives the quadrature sum of each of these contributions as an asymmetric error band. Of these,the impact of the energy scale variation is dominant, giving a 10–15% contribution at 500 GeV in the forwardand backward regions, decreasing to less than % at the lowest E γ T . In the mid-rapidity region, the energy scalevariation gives a 5% uncertainty at high E γ T , decreasing to less than % at low E γ T . The scale factor uncertaintiesare about 5% in the forward regions and low E γ T and less than % elsewhere. Systematic uncertainties related to modelling in simulation, luminosity, electron contamination, and othersources tend to be lower than those previously discussed. However, their combined effect is dominant in the mid-rapidity region and between 90 GeV and 250 GeV.Figure 5.9 indicates an undesirable discrepancy between the particle level and detector level isolationdefinitions. Minimizing this gap can potentially reduce model dependencies of the measurement. Recent analyseshave accounted for this by adjusting the particle level definition to match at detector level. However, due to thisanalysis using the 8 TeV pp measurement as a reference, it is important to use the same particle level definition.For this reason, the nominal particle level isolation definition is used for the central values of the measurement,but the effect on the cross section of changing the particle level cut to match the data is added as a systematicuncertainty. That is, the fit from Figure 5.9 is used to derive a mapping to what the particle level cut would beto effectively match the detector level values. Figure 5.43 shows the effect of this redefinition as about 2% at low E γ T , and steadily falling to around 1% at the highest E γ T .25 30 40 50 · [GeV] truthT p P e r c en t E rr o r < -1.56 Lab h -2.37 < Energy scale variationEnergy resolution variationEfficiency SF Uncertanty 30 40 50 · [GeV] truthT p P e r c en t E rr o r < 1.37 Lab h -1.37 < Internal ATLAS 30 40 50 · [GeV] truthT p P e r c en t E rr o r < 2.37 Lab h 30 40 50 · [GeV] truthT p P e r c en t E rr o r < -1.56 Lab h -2.37 < Energy scale variationEnergy resolution variationEfficiency SF Uncertanty 30 40 50 · [GeV] truthT p P e r c en t E rr o r < 1.37 Lab h -1.37 < Internal ATLAS 30 40 50 · [GeV] truthT p P e r c en t E rr o r < 2.37 Lab h Figure 5.42: The relative deviation in the bin migration correction from the systematic variations in the energyresolution (blue) and scale (green) in MC. Additionally plotted is the error on the efficiency associated with theefficiency scale factors (red). The quadratic sum is overlaid as a yellow band. Top: period A; bottom: period B. [GeV] T E N o m i na l s / C o rr e c t ed s * < 1.90 h [GeV] T E N o m i na l s / C o rr e c t ed s * < 0.91 h -1.84 < Internal ATLAS [GeV] T E N o m i na l s / C o rr e c t ed s * < -2.02 h -2.83 < Figure 5.43: Effect on total cross section by changing particle level isolation cut to match the detector level.As discussed in Sec 5.3.6, an uncertainty is assigned to cover the possible contribution of mis-reconstructedelectrons, primarily from the decays of W ± and Z bosons, to the selected photon yield. Based on simulation26studies, and the results of previous measurements [116, 117], this is assigned to be 1.3% for E γ T < GeVin forward pseudorapidity regions, and 0.5% everywhere else. To test the beam orientation dependence, thecross-section is measured using the data from each beam configuration separately. The two measurements agreeat the level of 1%, well above the statistical uncertainty for most E γ T bins. This difference is taken as a global,symmetric uncertainty in the combined results.To quantify the sensitivity of this measurement to the admixture of direct and fragmentation photons inthe MC samples, we calculate the efficiencies and purities after re-weighting these components in the defaultP MC sample. It is worth noting again here that the direct and fragmentation photon distinction is notwell defined beyond leading order in pQCD calculations and cannot be determined experimentally. The defaultfraction of direct photons in the P is plotted in Fig. 5.44, where the fraction of fragmentation photonsis the complement. As an extreme variation, the MC is re-weighted such that the fraction of direct photons isunity, that is, all photons in the sample are direct. Fig 5.45 shows the effect of this variation as the ratio of crosssection with re-weighting to the nominal. The ratios are fit with a constant function and each show a relativevariation of approximately 1% which is taken as a systematic uncertainty. 30 40 50 · 2 [GeV] T E H a r d pho t on f r a c t i on * < 1.90 h h -1.84 < * < -2.02 h -2.83 < Figure 5.44: The default fraction of hard photons in the P MC sample for each rapidity bin, plotted as afunction of photon transverse energy.Finally, the uncertainty in the integrated luminosity of the combined data sample is . %. It is derivedfollowing a methodology similar to that detailed in Ref. [141]. The LUCID-2 detector is used for the baselineluminosity calibrations, and its luminosity scale is calibrated using x-y beam-separation scans [142].27 [GeV] T E N o m i na l s / R e w e i gh t ed s * < 1.90 h m [GeV] T E N o m i na l s / R e w e i gh t ed s * < 0.91 h -1.84 < = 0.995 m Internal ATLAS [GeV] T E N o m i na l s / R e w e i gh t ed s * < -2.02 h -2.83 < = 0.992 m Figure 5.45: Ratios of the resulting cross sections with the direct fraction re-weighting to those from the nominalfraction. R p Pb Uncertainty The nuclear modification factor R p Pb is affected by systematic uncertainties associated with both the p +Pband pp measurements. The uncertainties in the differential cross-section of the pp reference data are obtaineddirectly from Ref. [116] and shown in Fig. 5.46 not including the global luminosity uncertainty of . %. Dueto differences in photon reconstruction, energy calibration, isolation and identification procedures between the pp and p +Pb datasets, the uncertainties are treated as uncorrelated and added in quadrature. [GeV] T g E S ys t e m a t i c U n c . ATLAS pp -1.56 £ h -2.37 < [GeV] T g E S ys t e m a t i c U n c . ATLAS pp £ h -1.37 < [GeV] T g E S ys t e m a t i c U n c . ATLAS pp < 2.37 h £ Figure 5.46: Summary of total systematic uncertainties on previously measured TeVphoton spectrum [116],each panel showing a different | η | selection. (A global luminosity uncertainty of 1.9% is not included.)The uncertainty in the extrapolation of the pp E γ T spectrum at TeV is determined by using an alternativemethod to derive the multiplicative extrapolation factors. J 1.3.1 is used instead of P to produce theratio of the boosted 8.16 TeV to (not boosted) 8 TeV pp cross-sections, which are used as the multiplicative factors28on the pp data. J was run in a mode to produce both the direct and fragmentation photon components.Both the Born and higher order contribution were calculated and summed. The J calculation is runnominally using the CT10 PDF as well as MSTW2008 as an additional source of variation. The variations fromP to J +CT10 are added in quadrature with those from J +CT10 to J +MSTW2008. 30 40 50 · 2 [GeV] g T E - - - - - 10 110 I n t eg r a t ed c r o ss - s e c t i on [ nb ] JETPHOX 1.3.1Direct+Frag = -2.37 to -1.56, 8 TeV lab h = -2.37 to -1.56, boosted 8.16 TeV lab h = -1.37 to +1.37, 8 TeV lab h = -1.37 to +1.37, boosted 8.16 TeV lab h = +1.56 to +2.37, 8 TeV lab h = +1.56 to +2.37, boosted 8.16 TeV lab h [GeV] g T E = h D T e V , s / =+ . h D . T e V , s Simulation ATLAS JETPHOX PYTHIA8 < +2.37 lab h +1.56 < < +1.37 lab h -1.37 < < -1.56 lab h -2.37 < 20 100 500 Figure 5.47: Left: Comparison of the J-calculated cross-section for boosted 8.16 TeV pp and non-boosted8 TeV pp collisions, in the kinematic E γ T and η lab bins used in the analysis. Right: Extracted extrapolation fromJ compared to the nominal values from P.The left side of Fig. 5.47 compares the total integrated cross-section for each kinematic bin used in thisanalysis for (non-boosted) 8 TeV pp and boosted (to ∆ y = − . ) 8.16 TeV pp . The right side shows theboosted 8.16 TeV / 8 TeV ratio, which are the extrapolation factors compared to those from P. Clearly, theyare qualitatively similar in each case, since the overall shape of the η distribution in reasonably well reproducedby multiple theoretical approaches. The difference between these alternate extrapolation factors and the nominalones are used to set a symmetric systematic uncertainty associated with the pp reference as in Fig. 5.48 (sincea different set of extrapolation factors will produce a different reference). Because the values are statisticallyvarying, the histograms are fit to polynomial functions to smooth the variations. The systematic uncertainties upand down are then given by the value of the function at the bin center.A summary of the total uncertainties is given in Fig. 5.49.For the measurement of the ratio of R p Pb values between the forward and backward pseudorapidity re-gions, each systematic variation affecting the purity and detector performance corrections is applied to the nu-merator and denominator in a coherent way, allowing them to partially cancel out in the ratio. All uncertainties29 30 40 50 · [GeV] T p - - - - R e l e t i v e de v i a t i on Slope = -0.002Const = 0.022* < 1.90 h [GeV] T p - - - - R e l e t i v e de v i a t i on Slope = 0.003Const = -0.013* < 0.91 h -1.84 < Internal ATLAS [GeV] T p - - - - R e l e t i v e de v i a t i on Slope = 0.006Const = -0.039* < -2.02 h -2.83 < 30 40 · 2 [GeV] T p - - - - R e l e t i v e de v i a t i on Slope = 0.005Const = -0.019* < 1.90 h 10 [GeV] T p - - - - R e l e t i v e de v i a t i on Slope = -0.000Const = -0.001* < 0.91 h -1.84 < Internal ATLAS 10 [GeV] T p - - - - R e l e t i v e de v i a t i on Slope = -0.005Const = 0.018* < -2.02 h -2.83 < Figure 5.48: Top: Ratio between the constructed pp reference using correction factors from P and thatusing correction factors from J, plotted as a percent of the P values. Bottom: Ratio of extrapolationfactors calculated with J +CT10 to J +MSTW2008. These values are used as asymmetric errorson the extrapolation procedure, and are added in quadrature with the rest of the systematic uncertainties whenplotting the R p Pb . 30 40 50 · [GeV] g T E - - - - - R e l a t i v e U n c e r t a i n t y * < 1.90 h ATLAS Pb p R Relative Uncertainty in 30 40 50 · [GeV] g T E - - - - - R e l a t i v e U n c e r t a i n t y Combinedp+Pb cross sectionp+p cross sectionExtrapolation * < 0.91 h -1.84 < 30 40 50 · [GeV] g T E - - - - - R e l a t i v e U n c e r t a i n t y Pb Luminosity uncertainty p * < -2.02 h -2.83 < Figure 5.49: A breakdown of all systematic uncertainties on the R p Pb measurement.in the other categories, except those from electron contamination and the beam direction difference, are treatedas correlated. For this reason, they cancel out; notably the p +Pb luminosity and pp cross-section uncertaintiescancel out completely. The extrapolation uncertainties are treated as independent and are added in quadrature30to the other uncertainties in R p Pb . The resulting uncertainty ranges from about 5% at the lowest E γ T , where itis dominated by the uncertainty in the purity, to about 3% at mid- E γ T , and again about 5% at high E γ T , whereit is dominated by uncertainty in the energy scale. A summary of the uncertainties in the forward-to-backwardratio is shown in Fig. 5.50. 30 40 50 6070 · · [GeV] g T E - - R e l a t i v e un c e r t a i n t y CombinedPurityDetector performanceReference extrapolationOther BackwardPb p R / ForwardPb p R Relative uncertainty in ATLAS Figure 5.50: Summary of the relative size of major sources of systematic uncertainty in the forward-to-backwardratio of the nuclear modification factor R p Pb , as well as the combined uncertainty, shown as a function of photontransverse energy E γ T . The Reference extrapolation refers to the uncertainty related to the extrapolation of thepreviously measured TeV pp spectrum to . TeV and boosted kinematics. hapter 6Results of the Measurement of Direct Photon Production Photon production cross-sections are shown in Figure 6.1 for photons with E γ T > GeV in threepseudorapidity regions. The measured d σ/ d E γ T values decrease by five orders of magnitude over the complete E γ T range, which extends out to E γ T ≈ GeV for photons at mid-rapidity. In P, photons in this rangetypically arise from parton configurations in which the parton in the nucleus has Bjorken scale variable, x A , inthe range × − (cid:46) x A (cid:46) × − . In the nuclear modified PDF (nPDF) picture, this range probes theso-called shadowing (suppression for x A (cid:46) . ), anti-shadowing (enhancement for . (cid:46) x A (cid:46) . ), and EMC(suppression for . (cid:46) x A (cid:46) . ) regions [58].The data are compared with an NLO pQCD calculation similar to that used in Ref. [111] but using theupdated CT14 [143] PDF set for the free-nucleon parton densities, where the data is similarly underestimatedat low E γ T . J [87] is used to perform a full NLO pQCD calculation of the direct and fragmentationcontributions to the cross-section. The BFG set II [144] of parton-to-photon fragmentation functions are used,the number of massless quark flavours is set to five, and the renormalisation, factorisation and fragmentationscales are chosen to be E γ T . In addition to the calculation with the free-nucleon PDFs, separate calculationsare performed with the EPPS16 [58] and nCTEQ15 [125] nPDF sets. The EPPS16 calculation uses the samefree-proton PDF set, CT14, as the free-nucleon baseline to which the modifications are applied. The predictionis systematically lower than the data by up to 20% at low E γ T but is closer to the data at higher E γ T , consis-tent with the results of such comparisons in pp collisions at LHC energies [116, 117]. A recent calculation ofisolated photon production at NNLO found that the predicted cross-sections were systematically larger at low32 10 [GeV] T E - 10 110 [ pb / G e V ] T E / d s d * < 1.90 h DataJETPHOX + CT14 + EPPS16DataJETPHOX + CT14 + EPPS16 ATLAS -1 +Pb, 165 nb p = 8.16 TeV s 10 [GeV] T E - 10 110 [ pb / G e V ] T E / d s d * < 0.91 h -1.84 < 10 [GeV] T E - 10 110 [ pb / G e V ] T E / d s d * < -2.02 h -2.83 < 30 40 · [GeV] g T E T heo r y / D a t a 30 40 · [GeV] g T E T heo r y / D a t a 30 40 · [GeV] g T E T heo r y / D a t a Figure 6.1: Prompt, isolated photon cross-sections as a function of transverse energy E γ T , shown for differentcentre-of-mass pseudorapidity, η ∗ , regions in each panel. The data are compared with J with the EPPS16nuclear PDF set [58], with the ratio of theory to data shown in the lower panels. Yellow bands correspond tototal systematic uncertainties in the data (not including the luminosity uncertainty), vertical bars correspondto the statistical uncertainties in the data, and the red bands correspond to the uncertainties in the theoreticalcalculation. The green box (at the far right) represents the 2.4% luminosity uncertainty. E γ T than the NLO prediction [145], and thus may provide a better description of the data in this and previousmeasurements.Uncertainties associated with these calculations are assessed in a number of ways. Factorisation, renormal-isation, and fragmentation scales are varied, up and down, by a factor of two as in Ref. [116]. The uncertainty istaken as the envelope formed by the minimum and maximum of each variation in every kinematic region and isdominant in most regions. PDF uncertainties are calculated via the standard CT14 error sets and correspond toa 68% confidence interval. Again following Ref. [116] the sensitivity to the choice of α S is evaluated by varying α S by ± . around the central value of 0.118 in the calculation and PDF. Uncertainties from nPDFs arecalculated from the error sets which correspond to 90% confidence intervals, as described in Ref. [58]. These areconverted into uncertainty bands which correspond to a 68% confidence interval. A summary of each variationis shown in Fig. 6.2.33 30 40 50 · [GeV] g T E - - - R e l a t i v e U n c e r t a i n t y TotalScale uncertainty* < 1.90 h ATLAS 30 40 50 · [GeV] g T E - - - R e l a t i v e U n c e r t a i n t y PDF uncertainties variation s a * < 0.91 h -1.84 < Relative Uncertainty in JETPHOX 30 40 50 · [GeV] g T E - - - R e l a t i v e U n c e r t a i n t y nPDF uncertainties* < -2.02 h -2.83 < Figure 6.2: A breakdown of all systematic uncertainties in the cross-section prediction from J with theEPPS16 nPDF set. R p Pb Results Figure 6.3 shows the nuclear modification factor R p Pb as a function of E γ T in different η ∗ regions. Atforward rapidities ( . < η ∗ < . ), the R p Pb value is consistent with unity, indicating that nuclear effectsare small. In P, photons in this region typically arise from configurations with gluon partons from the Pbnucleus with x A ≈ − . Nuclear modification pulls the pQCD calculation down slightly for E γ T < GeV,above which the modification reverses, indicating a crossover between shadowing and anti-shadowing regions.At mid-rapidity, nuclear effects are similarly small and consistent with unity at low E γ T , but at higher E γ T , thereis a hint that R p Pb is lower. This feature primarily reflects the different up- and down-quark composition of thenucleus relative to the proton and is more important at larger parton x . In this case, the larger relative down-quark density decreases the photon yield. This effect is evident in the J theory curve in blue dash-dottedline, which includes the proton–neutron asymmetry and the free-nucleon PDF set CT14. This effect is mostpronounced at backward pseudorapidity where, in P, the nuclear parton composition is typically a valencequark with x A ≈ . . Here, nPDF modification moves R p Pb above the free-nucleon PDF calculation at low E γ T but below at high E γ T , indicating the crossover from the anti-shadowing to the EMC region.34 30 40 50 · [GeV] g T E P b p R ATLAS -1 +Pb, 165 nb p = 8.16 TeV s pp = 8 TeV, sExtrap. DataData * < 1.90 h 30 40 50 · [GeV] g T E P b p R * < 0.91 h -1.84 < JETPHOX JETPHOX + CT14JETPHOX + CT14 + EPPS16 30 40 50 · [GeV] g T E P b p R * < -2.02 h -2.83 < 30 40 50 · [GeV] g T E P b p R ATLAS -1 +Pb, 165 nb p = 8.16 TeV s pp = 8 TeV, sExtrap. DataData * < 1.90 h 30 40 50 · [GeV] g T E P b p R * < 0.91 h -1.84 < JETPHOX JETPHOX + CT14JETPHOX + nCTEQ15 30 40 50 · [GeV] g T E P b p R * < -2.02 h -2.83 < 30 40 50 · [GeV] g T E P b p R ATLAS -1 +Pb, 165 nb p = 8.16 TeV s pp = 8 TeV, sExtrap. DataData * < 1.90 h 30 40 50 · [GeV] g T E P b p R * < 0.91 h -1.84 < no E-loss = 1.5 fm q l = 0.35 GeV, m = 1 fm q l = 0.35 GeV, m 30 40 50 · [GeV] g T E P b p R * < -2.02 h -2.83 < Figure 6.3: Nuclear modification factor R p Pb for isolated, prompt photons as a function of photon transverseenergy E γ T , shown for different centre-of-mass pseudorapidity, η ∗ , regions in each panel. The R p Pb is measuredusing a reference extrapolated from √ s = 8 TeV pp data (see text). The data are identical in each row, but showcomparisons with the expectations based on J with the EPPS16 nuclear PDF set (top) [58], with thenCTEQ15 nuclear PDF set (middle) [125], and with an initial-state energy-loss calculation (bottom) [112, 113,126]. In all plots, the yellow bands and vertical bars correspond to total systematic and statistical uncertaintiesin the data respectively. In the top and middle panels, the red and purple bands correspond to the systematicuncertainties in the theoretical calculations. The green box (at the far right) represents the combined 2.4% p +Pband 1.9% pp luminosity uncertainties.35The R p Pb calculations including nPDFs consider only the nPDF uncertainty, since previous calculationshave shown that the scale and PDF uncertainties cancel out almost completely in the kinematic region of themeasurement [111], and no non-perturbative corrections are applied. Within the present uncertainties, the dataare consistent with both the free-proton PDFs and with the small effects expected from a nuclear modificationof the parton densities.The R p Pb measurements are also compared with an initial-state energy-loss prediction that is calculatedwithin the framework described in Refs. [112, 113, 126]. In this model, the energetic partons undergo multiplescattering in the cold nuclear medium, and thus lose energy due to this medium-induced gluon bremsstrahlung,before the hard collision. The calculation is performed with a parton–gluon momentum transfer µ = 0 . GeVand mean free path for quarks λ q = 1 . fm. Alternative calculations with a shorter path length ( λ q = 1 fm),and a control version with no initial-state energy loss, are also considered. The data disfavour a large suppressionof the cross-section from initial-state energy-loss effects.The ratio of the R p Pb values between forward and backward pseudorapidity, shown in Figure 6.4, isstudied as a way to reduce the effect of common systematic uncertainties and better isolate the magnitude ofnuclear effects [146]. The remaining systematic uncertainty, discussed in Sec. 5.6.2, is dominated by the referenceextrapolation and treated as uncorrelated between points. Below E γ T ≈ GeV, this corresponds roughly tothe ratio of R p Pb from photons from gluon nuclear parton configurations in the shadowing x A region to thatfrom quark partons in the anti-shadowing region. This can be seen in the top two panels of Figure 6.4, where thenuclear modification (red/purple bands) brings the J calculation below that of the free-nucleon PDF (bluecurve), though the effect from EPPS16 is less significant. In contrast, the behaviour is reversed at higher E γ T wherethe numerator probes the shadowing/anti-shadowing crossover region and the denominator moves deeper intothe EMC region [58]. The data are consistent with the pQCD calculation before incorporating nuclear effects,except possibly in the region E γ T < GeV, which is sensitive to the effects from gluon shadowing. At low E γ T , the data are systematically higher than the calculations which incorporate nPDF effects, but approximatelywithin their theoretical uncertainty. Additionally, in the lower plot of Figure 6.4, the forward-to-backward ratiosare compared with predictions from a model incorporating initial-state energy loss. The data show a preferencefor no or only a limited amount of energy loss.36 30 40 50 60 · · g T E B a ck w a r dp P b R / F o r w a r dp P b R DataJETPHOX + CT14 + EPPS16JETPHOX + CT14DataJETPHOX + CT14 + EPPS16JETPHOX + CT14 ATLAS -1 +Pb, 165 nb p = 8.16 TeV s * < -2.02 h * < 1.90 / -2.83 < h · · g T E B a ck w a r dp P b R / F o r w a r dp P b R DataJETPHOX + nCTEQ15JETPHOX + CT14DataJETPHOX + nCTEQ15JETPHOX + CT14 ATLAS -1 +Pb, 165 nb p = 8.16 TeV s * < -2.02 h * < 1.90 / -2.83 < h · · g T E B a ck w a r dp P b R / F o r w a r dp P b R Datano E-loss = 1.5 fm q l = 0.35 GeV, m = 1 fm q l = 0.35 GeV, m Datano E-loss = 1.5 fm q l = 0.35 GeV, m = 1 fm q l = 0.35 GeV, m ATLAS -1 +Pb, 165 nb p = 8.16 TeV s * < -2.02 h * < 1.90 / -2.83 < h Figure 6.4: Ratio of the nuclear modification factor R p Pb between forward and backward pseudorapidity forisolated, prompt photons as a function of photon transverse energy E γ T . The data are identical in each panel,but show comparisons with the expectations based on J with the EPPS16 nuclear PDF set (top, left) [58]or with the nCTEQ15 nuclear PDF set (top, right) [125], and with an initial-state energy-loss calculation (bot-tom) [112, 113, 126]. The strength of the initial-state energy-loss effect is parameterized by λ q , which representsthe mean free path of partons in the nuclear medium and is smaller for a larger degree of energy loss. In allplots, the yellow bands and vertical bars correspond to total systematic and statistical uncertainties in the datarespectively. In the left and right panels, the red and purple bands correspond to the systematic uncertainties inthe calculations. hapter 7Measurement of Azimuthal Anisotropy7.1 Introduction Small collision systems provide a way to test the interpretation that the v n flow signal at high p T in largesystems is a result of the path-length differential energy loss of hard partons traversing the QGP, as discussed inSec 2.4.4. In small systems, low- p T flow signals match well with expectations from a nearly inviscid hydrodynamicflow of the QGP [5]; however, measurements aimed at observing signatures of jet quenching in have found nosuch effect. The ATLAS experiment has published results on the charged hadron azimuthal anisotropy up to p T ≈ GeV in p +Pb that hint at a non-zero anisotropy extending into the region beyond the usual hydrodynamicinterpretation and into the regime of jet quenching [147]. However, it seems unlikely that there can be differentialjet quenching as a function of orientation relative to the QGP geometry if there is no jet quenching in p +Pbcollisions as observed in the spectra. Thus, there are two related outstanding puzzles, one being the lack ofjet quenching observed in the spectra, if indeed small droplets of QGP are formed, and the other being whatmechanism can lead to high- p T hadron anisotropies other than differential jet quenching.This Chapter presents a measurement of the azimuthal anisotropy of unidentified hadrons as a function of p T and centrality in √ s NN = 8 . TeV p +Pb collisions with the ATLAS detector. The measurement is made usingtwo-particle correlations, measured separately for minimum-bias triggered events and events requiring a jet with p T greater than either 75 GeV or 100 GeV. A standard template fitting procedure [12, 13] is applied to subtractthe non-flow contributions to the azimuthal correlations from particle decays, jets, dijets, and global momentumconservation. To decrease the residual influence of the non-flow correlation in the jet events, a novel procedure isused to restrict the acceptance of particles according to the location of jets in the event. Assuming that the two-38particle anisotropy coefficients are the products of the corresponding single-particle coefficients (factorisation),the elliptic and triangular anisotropy coefficients, v and v , are reported as a function of p T . Additionally, v results are presented as a function of centrality in three different p T ranges. Finally, the fractional contributionto the correlation functions from jet particles is determined as a function of p T . The events used in this analysis fall into two categories: minimum bias and jet events. The minimum biastriggered (MBT) selection is composed of a single trigger requiring at least one high level space-point track and isseeded by an L1 requirement of a hit in either MBTS. A previous iteration of the analysis combined this triggerwith a set of high multiplicity triggers (HMT), to enhance the statistics at high multiplicity. However, the finalresults are restricted to the single trigger because, though the added statistics reduced the statistical uncertainty,combining the triggers introduced systematic uncertainty that negated the statistical gains. A comparison to thecombined trigger approach is given later in the Chapter, and therefore, the HMTs are discussed in this section.The four HMTs used for comparison have varying space point, online track, and pileup suppressionrequirements and are seeded from various L1 total energy requirements. Each trigger is used to populate anexclusive offline range in the number of charged tracks ( N trk ) for which it has recorded the most events. Becausesome triggers were not active during all runs, this optimization is done on a run-by-run basis. The multiplicitydistributions from each MBT trigger for each run are shown in Figures B.1 and B.2 in the Appendix.The efficiency of L1 trigger L1_MBTS_1 can be determined in p +Pb data with respect to HLT_mb_sptrk which is seeded by a random trigger at L1. The efficiency is measured in two different ways: one is the L1_MBTS_1 efficiency, before the trigger prescale is applied, with respect to HLT_mb_sptrk ; the other is the prescale cor-rected efficiency of HLT_mb_sptrk_L1MBTS_1 with respect to HLT_mb_sptrk . Data collected in one singlerun at the beginning of 2016 p +Pb collisions with most of the statistics of HLT_mb_sptrk triggered sampleis used to determine the efficiency. The measured efficiency is shown as a function of multiplicity as shownon the left panel in Figure 7.1. The two measurements show very good consistency indicating that there is no39additional inefficiency at HLT for HLT_mb_sptrk_L1MBTS_1 with respect to L1_MBTS_1 . Due to radiationdamage in 2015 and 2016, the MBTS is not fully efficiency until N ch > . Trigger efficiency corrections for HLT_mb_sptrk_L1MBTS_1 are applied as a function of multiplicity to its triggered sample. The efficiency ofthe HLT requirement of HLT_mb_sptrk is measured as the relative efficiency of HLT_mb_sptrk_L1MBTS_1 with respect to L1_MBTS_1 and shown as a function of multiplicity on the right panel in Figure 7.1. The mea-sured relative efficiency is always which means the HLT requirement of HLT_mb_sptrk is fully efficientin events that satisfy L1_MBTS_1 . ch N R e l a t i v e E ff i c i en cy ATLAS Internal = 8.16 TeV NN s +Pb p Run 313107L1_MBTS_1HLT_mb_sptrk_L1MBTS_1 HLT_mb_sptrk wrt. ch N R e l a t i v e E ff i c i en cy ATLAS Internal = 8.16 TeV NN s +Pb p Run 313107HLT_mb_sptrk_L1MBTS_1 L1_MBTS_1 wrt. Figure 7.1: Left: L1_MBTS_1 trigger efficiency as a function of multiplicity in 2016 p +Pb collisions, mea-sured as the relative efficiencies of L1_MBTS_1 and HLT_mb_sptrk_L1MBTS_1 with respect to HLT_mb_sptrk .Due to radiation damage in 2015 and 2016, the MBTS is not fully efficiency until N ch > . Right: HLT_mb_sptrk_L1MBTS_1 trigger efficiency with respect to L1_MBTS_1 as a function of multiplicity in 2016 p +Pb collisions. No inefficiency observed for the HLT requirement HLT_mb_sptrk with respect to L1_MBTS_1 since the relative efficiency is always .Due to tighter quality cuts applied to tracks offline than those applied online, the track counting at HLTin HMT’s is expected to be fully efficient. The efficiencies of various L1 total energy triggers ( L1_TE ), used toseen the HMTs, are studied as a function of multiplicity as shown in the left panel of Fig. 7.2. The efficienciesare measured as the relative efficiency to MB trigger, HLT_mb_sptrk_L1MBTS_1 . As one can see in the figure,most of the L1_TE triggers are very efficient where a multiplicity cut is applied offline.40 ch N R e l a t i v e e ff i c i en cy L1_TEXHLT_mb_sptrk_L1MBTS_1 wrt. L1_TE20L1_TE50L1_TE90L1_TE120L1_TE160L1_TE200 ATLAS Internal = 8.16 TeV NN s +Pb p [GeV] HI, R=0.4T jet p E ff i c i en cy ATLAS Internal = 8 TeV s +Pb 2016 p HLT_j10_emulateHLT_j20_emulateHLT_j30_emulateHLT_j40_emulateHLT_j50_emulateHLT_j60_emulateHLT_j75_emulateHLT_j100_emulate = -3.2 to 3.2 η Emulated HLT_j Trigger Efficiency Figure 7.2: Left: L1_TEX trigger efficiency as a function of multiplicity in 2016 p +Pb data, measured with respectto HLT_mb_sptrk_L1MBTS_1 . The colored lines correspond to the multiplicity threshold applied offline to eachof the trigger with the same color. Right Jet trigger efficiencies as a function of offline jet p T .The second dataset is selected by a jet trigger requiring a high level jet to pass a 75 GeV or 100 GeV onlinethreshold and is seeded by a L1 jet 20 GeV requirement. The 100 GeV trigger is the lowest threshold unprescaledjet trigger, and thus samples the full luminosity delivered to ATLAS during the running period. Offline, theevents are required to contain a calibrated anti- k t , R = 0 . calorimeter jet with transverse momentum greaterthan 75 GeV or 100 GeV. Jet trigger efficiencies were studied as a function of offline jet p T and shown in theright panel of Fig. 7.2. These studies indicate that the J75 and J100 triggers have greater than 97% efficiency foroffline jets with p T > GeV and p T > GeV respectively. No jet trigger corrections are applied.To minimize bias on the track φ distribution due to the rejection of jets in the disabled sector of theHEC, the offline jet satisfying the threshold is required to have an η < . . Thus, the whole η slice containingthe disabled HEC, including an R = 0 . buffer, is removed from the jet selection. Fig. 7.3 shows the effectof this jet restriction on the track φ distributions. The first row shows the η − φ distribution of tracks, whereeach vertical η slice is self normalized to show the relative structure in φ , and the second row shows the selfnormalized φ distributions. The left column is from MB+HMT events and acts as a baseline, as there can beno jet selection bias. The center shows jet events with no offline jet condition; this shows an obvious bias onthe track distributions due to the jet trigger inefficiency in the disabled HEC region. The right plots are jet41events after making the offline jet selection described in the previous paragraph; in this case, the bias on the trackdistributions is drastically reduced. - - - - - trk h - - - t r k f Internal ATLAS MB+HMT < 3.50 trk T p - - - - - trk h - - - t r k f Internal ATLAS > 100 GeV jet T p < 3.50 trk T p - - - - - trk h - - - t r k f Internal ATLAS > 100 GeV jet T p < 3.50 trk T p Restrict trigger jet3 - - - trk f R e l a t i v e de v i a t i on Internal ATLAS MB+HMT < 3.50 trk T p - - - trk f R e l a t i v e de v i a t i on Internal ATLAS > 100 GeV jet T p < 3.50 trk T p - - - trk f R e l a t i v e de v i a t i on Internal ATLAS > 100 GeV jet T p < 3.50 trk T p Restrict trigger jet Figure 7.3: The η − φ distributions (top) and φ projections (bottom) of tracks in which each η slice is selfnormalized such that the values represent the relative deviation from the mean in φ . The left is from MB+HMTevents, the center is from jet events, and the right is from jet events after the offline jet selection is made.Table 7.1 summarizes the triggers used, offline conditions, and luminosity sampled by each trigger in eachrunning period. Fig. 7.4 shows the multiplicity and track p T distributions for each set of events. Fig. 7.5 showsthe per-event normalized η distributions of tracks for central and peripheral events for each set of trigger selectedevents. In these coordinates, the Pb nucleus is moving towards positive η , the proton toward negative η , andthere is a center-of-mass boost of 0.465 units to the negative direction. In the peripheral case, jet events showan enhancement in particle production due to the presence of jets and the shift of the peak in the direction ofthe boost, whereas the MB+HMT events give a broad and flat distribution. In central events, the fragmentingnucleus dominates the particle production, and there is an enhancement in the nuclear-going direction. In thiscase, the MB+HMT events show a larger yield due to the HMTs.42Table 7.1: Triggers used in analysis, with the sampled luminosities in both running periods. Trigger Offline requirement L int ( p +Pb period) L int (Pb+ p period) HLT_mb_sptrk_L1MBTS_1 N trk < − − HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20 ≤ N trk < − − HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50 ≤ N trk < − − HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120 ≤ N trk < − − HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 ≤ N trk − − HLT_j75_ion_L1J20 p jetT > GeV 3.47 nb − − HLT_j75_L1J20 p jetT > GeV 0 nb − − HLT_j100_ion_L1J20 p jetT > GeV 56.76 nb − − HLT_j100_L1J20 p jetT > GeV 0 nb − − trk N C oun t s MBMB + HMT > 100 GeV jet T p Internal ATLAS - · · trk T p - - - - - - - - - 10 110 e v t N / t r k N MB > 100 GeV jet T p Internal ATLAS Figure 7.4: Multiplicity ( left ) and track p T ( right ) distributions from the two sets of events considered: minbiaswith high multiplicity triggers in green, and those with 100 GeV jets in magenta. - - - - - h h d t r a ck N d e v t N MB + HMT > 100 GeV jet T p Internal ATLAS - - - - - h h d t r a ck N d e v t N MB + HMT > 100 GeV jet T p Internal ATLAS Figure 7.5: dN ch /dη vs η , uncorrected for detector inefficiencies, for central ( left ) and peripheral events ( right )from the two sets of events considered: minbias with high multiplicity triggers in green, and those with 100 GeVjets in magenta.43In-time pileup events are reduced in the same way for the centrality analysis described in Sec. 4.2. Eventsare required to contain at least one vertex, and are rejected if there exists any other vertices with greater than sixtracks associated with it. Contrary to the photon analysis, this measurement is primarily self normalized and corrected and is, there-fore, insensitive to corrections derived from MC simulations. However, reconstruction and selection efficienciesfor primary [148] charged hadrons to meet the track quality criteria, described below, were determined using asample of 3 million minimum-bias p +Pb events simulated by the H generator [84]. Events were generatedwith both beam configurations. The ATLAS detector response to the generated events was determined througha full G4 simulation [106, 107], and the simulated events were reconstructed in the same way as the data.Additionally, a P di-jet data overlay sample is used to check the bias on the jet selection from theUE. In this case, hard QCD P events are filtered at truth level on the requirement that they contain a truthjet with p T > 60 GeV. The detector response is simulated in GEANT4, and the events are mixed with minimumbias data events before being reconstructed in the same way as was described in Sec. 5.2. The correlations studied in this analysis are made between inclusive charged hadrons. These are defined tobe any reconstructed track in the inner detector passing the MinBias track selection working point quality cutsthat are described in Sec. 3.2.1. Charged-particle tracks and collision vertices are reconstructed in the ID usingthe algorithms described in Sec. 3.2.1 and Refs. [102, 103]. Only inner detector tracks with p T > . GeVand | η | < . are used in this analysis. The total number of reconstructed ID tracks satisfying these selectioncriteria in a given event is called the multiplicity or N recch . The MinBias tracking efficiency is measured as theprobability of a truth primary charged pion to be reconstructed as a MinBias track by the ID in the H datasamples described above. The measured efficiencies are shown in Figure 7.6 as a function of prompt pion p T and η . Over the measured kinematic range, the track reconstruction efficiency varies from approximately for the lowest- p T hadrons at large pseudorapidity, to greater than for hadrons with p T > GeV at mid-44rapidity. Dependencies of the tracking efficiency on the event multiplicity and on particle species are ignored inthe nominal analysis but considered in systematic uncertainties. The tracks used in this analysis are re-weighted,track-by-track, to corrected for their inefficiencies. h - - [ G e V ] T p M i n B i a s T r a ck i ng ATLAS Internal Simulation pp MinBias 13 TeV Nominal MinBias p Truth Primary Figure 7.6: Two dimensional reconstruction efficiency of MinBias tracks as a function of track p T and η obtainedfrom MC based prompt charged pions.Jets are reconstructed using energy deposits in the calorimeter system, | η | < . , closely following theprocedure used in other measurements for Pb+Pb and pp collisions [149, 150]. Jets are measured by applyingthe anti- k t algorithm [151, 152] with radius parameter R = 0 . to energy deposits in the calorimeter. Nojets with p T < GeV are considered. An iterative procedure is used to obtain an event-by-event estimateof the η -dependent underlying-event calorimetric energy density, while excluding jets from that estimate. Thejet kinematics are corrected for this background and for the detector response using an η - and p T -dependentcalibration derived from fully simulated and reconstructed P [127] hard-scattering events configured withthe NNPDF23LO parton distribution function set [128] and the A14 set of tuned parameters [129] to modelnon-perturbative effects. An additional, small correction, based on in situ studies of jets recoiling against photons, Z bosons, and jets in other regions of the calorimeter, is applied [153, 154]. Simulation studies show that for jetswith p T > GeV, the average reconstructed jet p T is within 1% of the generator level jet p T and has a relative p T resolution ( σ p T /p T ) below % after the calibration procedure.45 The main technology employed in this analysis is that of two-particle correlations which has been usedextensively within ATLAS [11, 12, 147, 155]. Due to the relatively larger contribution of non-flow correlationsin p +Pb as compared to Pb+Pb, a non-flow subtraction procedure is used to extract the bulk flow correlations.A non-flow template fit method, first used in Ref. [12], is used to separate the flow from non-flow signal. Inthe jet events considered, the non-flow contribution is substantially larger than that of the MBT events, andthe template method is found to be insufficient in describing the non-flow. It is found that by requiring theassociated particles to be separated in η from all jets with p T > GeV, allows the template method to workas expected. Finally, an estimation of the jet particle yields is made in an effort to understand the differencesbetween the results from MBT and jet events. Two-particle correlations are defined here as distributions of particle pair yields. The pairs are definedto be ordered A-B couples of particles-of-interest (particle A) and associate or reference particles (particle B).The particle pair yields are presented as distributions of relative azimuthal angle ( ∆ φ = φ A − φ B ) and relativepseudorapidity ( ∆ η = η A − η B ), normalized by the number of A-particles. This is referred to as a per-particleyield (PPY), Y (∆ φ, ∆ η ) , defined as: Y (∆ φ, ∆ η ) = 1 N A d N pair d∆ φ · d∆ η , (7.1)where N pair is the event-wise yield of particle pairs integrated over all events, and N A is the number of selectedparticles-of-interest integrated over all events. Thus, Y is the average yield of pairs averaged over the number ofA-particles and all events.In practice, due to the limited coverage and imperfect performance of the real detector, there are acceptanceeffects that distort these distributions. These trivial distortions can be removed using the so-called mixed-eventtechnique in which correlations are made between A particles from any given event with B-particles from differentevents. In this way, only trivial pair acceptance correlations will be present as there can be no physics correlation.The B-particles are drawn from events with similar characteristics so that the mixed event correlations faithfully46represent the trivial geometric correlations in the signal distributions. The events are thus mixed in the followingcategories:• collision beam configuration• primary vertex position within 10 mm• multiplicity ranges of N trk within 10 for N trk < and N trk within 20 for N trk > • centrality given by FCal Σ E PbT corresponding to 5% centrality ranges from 0-30%, 10% ranges from30-70%, and the last range from 70-90%To maximize the statistical weight of the mixed events, every signal jet event is mixed with five different qualifiedmix events, which is sufficiently many so that the introduced statistical uncertainty is significantly smaller to thatof the signal distribution. However, for MBT events, the mixed event correction is applied only to estimate asystematic and is only mixed with a single event. Events are abandoned, in both same and mixed event distribu-tions, if there are not exactly five events to mix with so that the events in the mixed distributions are correctlyweighted to those of the signal distributions. After applying the mixed-event based acceptance correction, PPYbecomes: Y (∆ φ, ∆ η ) = KN A (cid:28) d N same / (d∆ φ · d∆ η ) (cid:29) evt (cid:28) d N mixed / (d∆ φ · d∆ η ) (cid:29) evt , (7.2)where N same is the yield of particle pairs with two-particles from the same event, N mixed is the yield of paircombinations of particles from mixed events, and K is a scale factor to conserve the integral of PPY to what itshould be before applying the mixed-event correction. Examples of two-particle correlations in same and mixedevents are shown on the left and middle panels in Figure 7.7, respectively. Both the same and mixed eventdistributions have a trivial triangular shape in ∆ η due to the detector acceptance. An example of PPY aftercorrecting for this acceptance effect using the mixed event distribution is shown on the right panel in Figure 7.7.Because the data were collected using triggers with different prescales and the object reconstruction is notfully efficient, luminosity weights and efficiency corrections are applied to approximate the genuine correlations47 - - - - - hD - fD Internal ATLAS Minbias + HMT < 100 GeV trk T p Same event - - - - - hD - fD Internal ATLAS Minbias + HMT < 100 GeV trk T p Mixed event - - - - - hD - fD Internal ATLAS Minbias + HMT < 100 GeV trk T p Figure 7.7: Example of same event two-particle correlation (left), mixed event two-particle correlation (middle)and per-particle-yield after correction for the acceptance effect.with an ideal detector: Y (∆ φ, ∆ η ) ≡ KN corrA S (∆ φ, ∆ η ) B (∆ φ, ∆ η ) , (7.3)where S (∆ φ, ∆ η ) ≡ (cid:28) d N corrsignal d∆ φ · d∆ η (cid:29) evt, trigger , (7.4) B (∆ φ, ∆ η ) ≡ (cid:28) d N corrmixed d∆ φ · d∆ η (cid:29) evt, trigger , (7.5) N corrsame(mixed) = 1 L triggerint · ε trigger (cid:88) ε A · ε B , (7.6) N corrA = 1 L triggerint · ε trigger (cid:88) ε A , (7.7)where L triggerint is the integrated luminosity of a single trigger as described in Sec. 7.2.1, and ε trigger is the efficiencyof the trigger. L triggerint and ε trigger are applied on a per-event basis. (cid:104)(cid:105) evt indicates the average over many eventscollected by different triggers. Each pair is also weighted by a factor to account for A and B particle reconstructioninefficiency on a per-particle-pair basis, and ε A and ε B are the p T and η dependent tracking reconstructionefficiencies for particle A and B respectively. Fig. 7.8 shows some selected Y (∆ φ, ∆ η ) correlations from MBTand jet events integrated over p T for two different centrality classes.These mixed event corrected two dimensional distributions in Fig. 7.8 are valuable because they providea qualitative picture of the whole correlation space. One can see the strong correlation at small angles ( ∆ η ≈ ∆ φ ≈ ) from decays and jets as well as the broad away-side ( ∆ φ ≈ π ) from the momentum balance of dijets.48 - - - - - hD - fD Internal ATLAS Minbias + HMT < 100 GeV trk T p - - - - - hD - fD Internal ATLAS > 100 GeV jet T p < 100 GeV trk T p - - - - - hD - fD Internal ATLAS Minbias + HMT < 100 GeV trk T p - - - - - hD - fD Internal ATLAS > 100 GeV jet T p < 100 GeV trk T p Figure 7.8: Example of fully corrected per-A-pair yields of two-particle correlations for MBT (left column) andjet (right column) events and peripheral (top row) and central (bottom row) selections.It is also clear in the correlations from central events that there exist a cos(2∆ φ ) modulation that extends the fullrange in ∆ η ; these are the global flow correlations that are key to this measurement. To be quantitative, however, ∆ φ projections must be studied in detail. This is the subject of the next sections. The global correlation signal is extracted from one-dimensional ∆ φ PPY distributions. To reduce theinfluence of short range non-flow correlations, the one dimensional distributions are made by integrating overpairs with large η separation ( ∆ η > ). Long range non-flow is then accounted for via a template fittingprocedure that leverages the difference in the relative non-flow contribution to the PPY between peripheral and49central events. Within the fitting routine, the residual ∆ φ modulation is fit to a truncated Fourier series, thecoefficients of which are the extracted signal. Under the assumption that the two-particle flow signal is theproduct of the signal from the A particle selection and that of the B particle (factorization), the p T dependencecan be extracted by making different A particle p T selections. The one-dimensional ∆ φ PPY, Y (∆ φ ) , is constructed from the ratio of the same event distribution andmixed event distribution, both integrated over | ∆ η | as: Y (∆ φ ) = (cid:82) ∆ h ∆ l S (∆ φ, | ∆ η | ) d | ∆ η | (cid:82) ∆ h ∆ l B (∆ φ, | ∆ η | ) d | ∆ η | , (7.8)where S (∆ φ, | ∆ η | ) and B (∆ φ, | ∆ η | ) are the 2D yields in same and mixed events as defined in Eq. 7.3; ∆ h isthe phase space boundary of ∆ η for the two-particle correlation, which is ∆ h = 5 . in ATLAS; and ∆ l is thelower boundary of the integration which is imposed for purpose of removing short range non-flow contributions.For this analysis, ∆ l = 2 . , which is set to eliminate particle pairs from a single jet or decays.As indicated by Eq. 7.8, the 1D PPY is calculated by integrating S (∆ φ, | ∆ η | ) and B (∆ φ, | ∆ η | ) in ∆ η first and then taking the ratio of the S (∆ φ ) and B (∆ φ ) . The resulting PPY is dominated by contributions at ∆ η ≈ ∆ l due to larger pair yields and is less sensitive to fluctuations at the edge of the ∆ η acceptance. Thisdefinition of PPY is used in previous ATLAS publications [12, 13]. However, one should note that there is adifferent way to define the PPY which treats all ∆ η as having an equal weight. This is accomplished by first takingthe ratio of S (∆ φ, | ∆ η | ) and B (∆ φ, | ∆ η | ) , and then integrating over ∆ η . This alternative definition of PPYis used by the CMS Collaboration [ CMS-HIN-12-015 , 14, 156, 157]. The two definitions result in differentaverage ∆ η due to different relative weight at different ∆ η .The one-dimensional ∆ φ PPY is characterized in terms of Fourier decomposition: Y (∆ φ ) = G (cid:110) ∞ (cid:88) n =1 a n cos( n ∆ φ ) (cid:111) , (7.9)50where a n is the Fourier coefficient at order n and G is the normalization factor corresponding to the integral of Y (∆ φ ) . Parameters a n and G can be obtained from direct Fourier decomposition. As discussed in Section 7.1,the a n parameter extracted from Fourier decomposition contains both flow and non-flow contributions. Quali-tatively, in events with low activity, PPY is driven by particles from dijets jets so a n is dominated by these non-flowcontributions; in events with high activity, the flow contribution in a n becomes comparable with the non-flowcontribution. Quantitatively, the a n parameters are not useful since the flow/non-flow contribution could varywith event activity and particle kinematic selections. So the main goal of two-particle correlation analysis is tosystematically separate the flow from non-flow contributions.The Fourier coefficients, a n , are assumed to be separable into two linearly additive contributions a n = c n + d n , where c n is the flow coefficient quantifying correlations related to the initial geometry and d n is the non-flow coefficient of pair correlations that are dominate by jet particle correlations. Then Eq. 7.9 can be rewrittenas: Y (∆ φ ) = G (cid:26) ∞ (cid:88) n =1 ( c n + d n ) cos( n ∆ φ ) (cid:27) (7.10) = G (cid:26) ∞ (cid:88) n =1 c n cos( n ∆ φ ) (cid:27) + G (cid:26) ∞ (cid:88) n =1 d n cos( n ∆ φ ) (cid:27) (7.11) = G (cid:26) ∞ (cid:88) n =1 c n cos( n ∆ φ ) (cid:27) + GJ (∆ φ ) . (7.12)where the first term in Eq. 7.12 is the flow contribution, and the second term, J (∆ φ ) = 2 (cid:80) ∞ n =1 d n cos( n ∆ φ ) ,is due to non-flow modulations in ∆ φ . It will be shown in the following section that the flow term and non-flowterm scale differently with event activity. By repeating two independent measurements at different event activity,one can separate the flow contribution from non-flow algebraically. The template fit procedure, as used here, has been applied in previous ATLAS measurements [13, 158]to extract c n as defined in Eq. 7.12. Flow and non-flow contributions are distinguished by comparing Y (∆ φ ) between two data selection samples: one at higher event activity, where flow is expected to have a larger influence,and one at lower event activity, where flow is expected to have a smaller influence. Previous measurements [12,51147] have studied this method using different proxies for event activity, namely, charged particle multiplicity, N trk , and the total transverse energy in the Pb-going forward calorimeter, Σ E PbT . For reasons that will bediscussed below 7.3.3, this analysis uses only Σ E PbT . Parameters from central and peripheral correlations will benotated with superscript C and P respectively. Thus ρ n is defined as: ρ n = d C n /d P n , (7.13) ρ n is conjectured to be almost independent of its order n , i.e. ρ n = (cid:37) for all n . In other words, the shape ofnon-flow contribution in Y (∆ φ ) is the same in P and C samples as also discussed in Refs. [13] and [158], i.e. J C (∆ φ ) = (cid:37)J P (∆ φ ) . Two independent PPY in C events and in P events given by: Y P (∆ φ ) = G P J P (∆ φ ) + G P (cid:110) ∞ (cid:88) n =1 c P n cos( n ∆ φ ) (cid:111) , (7.14) Y C (∆ φ ) = G C J C (∆ φ ) + G C (cid:110) ∞ (cid:88) n =1 c C n cos( n ∆ φ ) (cid:111) , (7.15)can be combined using J C (∆ φ ) = (cid:37)J P (∆ φ ) : Y C (∆ φ ) = G C (cid:37)G P Y P (∆ φ ) + G C (1 − (cid:37) ) (cid:110) ∞ (cid:88) n =1 (cid:16) c C n − (cid:37)c P n − (cid:37) (cid:17) cos( n ∆ φ ) (cid:111) (7.16)One can re-parameterize Eq. 7.16 to match with the following form as used in Refs. [13] and [158]: Y C (∆ φ ) = F temp Y P (∆ φ ) + G temp (cid:26) ∞ (cid:88) n =1 c temp n cos( n ∆ φ ) (cid:27) . (7.17)One then obtains the physical meanings of parameters F temp , G temp , and c temp n used in Eq. 7.16 in terms of G C , G P and (cid:37) as: F temp = G C (cid:37)G P , (7.18) G temp = G C (1 − (cid:37) ) , (7.19) c temp n = c C n − (cid:37)c P n − (cid:37) . (7.20)Motivated by previous measurements of the first-order flow correlation being small while the non-flowcontribution at first-order is at its largest, the first order flow correlation, c , contribution is ignored. One can52think of it being absorbed in d (cid:48) = d + c ∼ d . The C sample PPY is eventually fit as follows: Y C (∆ φ ) = F temp Y P (∆ φ ) + G temp (cid:110) (cid:88) n =2 c temp n cos( n ∆ φ ) (cid:111) = F temp Y P (∆ φ ) + Y ridge (∆ φ ) , (7.21)where Y ridge (∆ φ ) = G temp (cid:110) (cid:80) n =2 c temp n cos( n ∆ φ ) (cid:111) isolates the pure flow correlation. The parametersin Eq. 7.21, F temp , G temp , and c temp n , are obtained from fitting Y C (∆ φ ) using Y P (∆ φ ) as a template via aglobal χ minimization. Thus, this approach is often referred to as the template fit method [12, 13]. The flowcorrelation coefficient of particles in C events is reported as: v n,n = c C n = c temp n − (cid:37) ( c temp n − c P n ) (7.22)where c P n is the correlation coefficient in the P sample. Here c C n is replaced by the symbol v n,n to be consistentwith previous publications [12, 13].A brief summary of the assumptions and caveats of using the template fit method is listed below:• Assumption 1: The non-flow shape doesn’t change with event activity, namely ρ n = (cid:37) ;• Assumption 2: The first order flow contribution is negligible compared to non-flow contribution: c =0 or a = d ;• If the flow correlation coefficient doesn’t dependent on event activity, v n,n = c temp n , a one-step correctionshould be applied: v n,n = c temp n − (cid:37) ( c temp n − c P n ) . v n Extraction Assuming Factorization If the two-particle momentum correlations originate from a global field, as is the case for collective expan-sion, the v n,n will factorise such that v n,n ( p A T , p B T ) = v n ( p A T ) · v n ( p B T ) . By assuming this relation and making specific p T selections on A- and B-particles, the single-particle v n ( p A T ) canbe obtained from v n ( p A T ) = v n,n ( p A T , p B T ) / (cid:113) v n,n ( p B T , p B T ) , v n,n ( p A T , p B T ) is determined with A- and B-particles having p T in range p A T and p B T , respectively, and v n,n ( p B T , p B T ) is determined with A- and B-particles both having p T in range p B T . In this analysis, this range isnominally p B T > . GeV, although the dependence of the extracted anisotropy on this choice is explored inChapter 8. Previous ATLAS measurements [12, 147] have studied template non-flow extraction using both chargedparticle multiplicity and Σ E PbT as proxies for event activity, and find similar results for p +Pb. This is also trueof this analysis; similar results are found for each case when considering the MBT selection of events. However,in jet selected events, a bias on the jet shape is found when selecting low multiplicity events. Fig. 7.9 shows anexample of the output of the template fitting procedure for MBT events. The left plot uses multiplicity for lowand high event activity, and the right uses Σ E PbT centrality ranges. In each case, the P templates seem to beworking well, and adding the harmonic modulation describes the C selection. The resulting v n,n are roughlyconsistent with each other.In contrast, Fig. 7.10 shows the same comparison for jet events. On the left, for multiplicity selected Pand C, the awayside structure of the P reference is much sharper than the C selection, and the fit is quite poor.On the right, the P and C selections are made with Σ E PbT centrality ranges. In this case, the template seemsto do a better job describing the awayside shape of the C. The residual discrepancy in the awayside is discussedbelow in Sec. 7.3.4.The problem when using multiplicity selections seems to come from a jet shape bias. In essence, the Pselection is requiring a high p T jet to be present in addition to there being a low number of particles. This selectsjets that tend to fragment harder, i.e. into fewer, higher p T particles that form more columnated shapes. Jets tendto be emitted at mid-rapidity, overlapping with the tracking acceptance, facilitating this correlation. When theselections are made using Σ E PbT , the jet to Σ E PbT correlation is much weaker because the FCal is so far forwardin rapidity. For this reason, the rest of this analysis will only make template event selections based on Σ E PbT .54 − φΔ ) φ Δ ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 4.00 A T p ± = 0.011307 v 0.000076 ± = 0.002316 v /NDF = 0.979274 χ − φ Δ − ) φ Δ ( L M Y F - G ) - φ Δ ( Y Low multiplicity: 0-40High multiplicity: >240 − φΔ ) φ Δ ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 4.00 A T p ± = 0.011370 v 0.000057 ± = 0.002039 v /NDF = 1.520806 χ − φ Δ − − ) φ Δ ( L M Y F - G ) - φ Δ ( Y Peripheral: 60-90%Central: 0-5% Figure 7.9: Template fitting output for MBT events. Both require ∆ η > and the A particles to have .
ATLAS < 4.00 A T p ± = 0.002150 v 0.000333 ± = 0.005608 v /NDF = 10.580478 χ − φ Δ − − ) φ Δ ( L M Y F - G ) - φ Δ ( Y Low multiplicity: 0-40High multiplicity: >240 − φΔ ) φ Δ ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 4.00 A T p ± = 0.005006 v 0.000126 ± = 0.002427 v /NDF = 3.357070 χ − φ Δ − − ) φ Δ ( L M Y F - G ) - φ Δ ( Y Peripheral: 60-90%Central: 0-5% Without jet-associated restriction Figure 7.10: Template fitting output for jet events. Both require ∆ η > and the A particles to have . with respect all jets in the event with p T > 15 GeV.In the simple two component model discussed above, this selection would keep correlations from UE-UE and HS-UE pair combinations but reduce the contribution from HS-HS correlations. Fig. 7.12 gives acomparison between the cases with (right) and without (left) this restriction. It is clear that the restriction gives areduction in statistics. However, the obvious discrepancy on the awayside is gone, and the flow signal is a muchgreater fraction of the total correlation. Furthermore, the extracted parameters are significantly different; the v , is smaller because the fit is not trying to account for the depletion on the awayside, which allows v , to rise. In the previous section, a simple two component picture of a p +Pb jet event was discussed. The UEparticles arise from soft interactions correlated with the overlapping nuclear geometry; a subset of the particlesform jets emanating from a hard scattering (HS) of partons uncorrelated with the global geometry. In thiscase, the correlation functions are constructed from pairs pulled from this mixture. Under the two componentassumption, pairs can be formed in the following four combinations:• A: UE, B: UE (UE-UE)• A: UE, B: HS (UE-HS)• A: HS, B: UE (HS-UE)57 - - - - - jet hD Track 050010001500200025003000 · Internal ATLAS - - - - - jet hD Track 10 Internal ATLAS Figure 7.11: The distribution of track ∆ η with respect to both the leading and sub-leading jets in 70-90% centraljet events. To minimize the contamination from other jets in the event, the tracks are required to have | ∆ φ | < π/ with respect to the jet being compared to. The red dashed lines are quadratic fits to the histogram in the regions(-3.5,-1.5) and (1.5,3.5), respectively, and are included to guide the eye. The vertical blue dashed lines representthe nominal values of the B particle ∆ η cut. The left plot is on a linear y scale and the right plot has a log y scale.• A: HS, B: HS (HS-HS)The following details the methodology used to estimated the relative particle pair yields of each contributionunder minimal assumptions and taking inspiration from previous ATLAS measurements of the underlying in pp collisions event [159–162].Consider dividing the φ tracking acceptance into regions oriented by either the leading jet or leading track,in the case of MBT events that contain no jets with p T > GeV. Define the following regions relative to thisleading vector:• towards: ( | ∆ φ jet | < π ) ∪ ( | ∆ φ jet | > π ) • transverse: π < | ∆ φ jet | < π A graphical representations of these divisions is shown in Fig. 7.13, where the leading p T object is representedas a yellow triangle. Then, under the assumption that 1) HS particles are completely contained in the towards58 - fD ) f D ( Y cent Y Fit peri YF + G (0) peri YF + ridge2 Y (0) peri YF + ridge3 Y ATLAS -1 = 8.16 TeV, 165 nb NN s+Pb p < 4.0 GeV A T p – = 5.01 · v 0.13 – = 2.43 · v /NDF = 3.36 c - fD - - ) f D ( pe r i Y F - G ) - f D ( Y - fD ) f D ( Y cent Y Fit peri YF + G (0) peri YF + ridge2 Y (0) peri YF + ridge3 Y ATLAS -1 = 8.16 TeV, 165 nb NN s+Pb p < 4.0 GeV A T p – = 5.33 · v 0.47 – = 1.82 · v /NDF = 1.27 c | > 1 Bj hD | - fD - - ) f D ( pe r i Y F - G ) - f D ( Y Figure 7.12: Template fitting output for jet events. Both require ∆ η > and the A particles to have . with respectto all jets with p T > 15 GeV in the event. In the upper panels, the open circles show the scaled and shifted Ptemplate with uncertainties omitted from the plot, the closed circles show the C data, and the red line shows thefit (template and harmonic functions). The blue dashed line shows the nd order harmonic component and theyellow dashed line shows the total harmonic function. The lower panels show the difference between the C dataand the scaled and shifted P template.region, and 2) the UE particles are uniformly distributed in the φ acceptance, the following relations follow: N UE = 2 N trans N HS = N toward − N trans , where, N UE , and N HS are the single particle yields from UE and HS processes respectively.59Figure 7.13: A graphical representation of the transverse and towards azimuthal regions relative to a high p T object, shown as a yellow triangle.The total yield of particle pairs can be decomposed in terms of products of the numbers of A ( N A ) and B( N B ) particles in the following way: P total = N A · N B (7.23) = ( N AHS + N AUE ) · ( N BHS + N BUE ) (7.24) = N AHS · N BHS + N AHS · N BUE + N AUE · N BHS + N AUE · N BUE . (7.25)In the current case, because we enforce a ∆ η gap and the detector acceptance is finite, N A = N A ( η A ) and N B = N B ( η A , ∆ η ) . That is, the yield of B particles, N B , depends on η A , and the particle separation, ∆ η .Thus, the products in 7.23 must take into account these dependencies: N AX · N BY = (cid:90) . − . d N AX ( η A )d η A (cid:34) (cid:90) d N BY ( η A , | ∆ η | )d η A d | ∆ η | d | ∆ η | (cid:35) d η A (7.26)Using the above assumptions and counting scheme, the pair yields of each combination may be estimatedon a statistical basis, averaged over events. It is not possible to identify individual particles as originating fromthe UE or a HS using this method. It should be noted that the assumptions used in this derivation are likely notperfect; for example, the UE is not uniformly distributed in φ , event by event, due to the presence of azimuthalanisotropy. The leading object may be more likely to be oriented with the anisotropy, in which case the UE yieldwould be underestimated and the HS yield overestimated. However, the analysis proceeds with the assumptionsas given and includes no additional uncertainty for this potential effect.60 The sensitivity of each choice impacting the analysis is studied by making variations. The uncertaintiesare determined by assessing the difference between the nominal value of v or v and the value after a givenvariation. Unless otherwise stated, the uncertainties are defined as asymmetric one-standard-deviation errors.The final uncertainty is the quadrature sum of the uncertainty from each individual source. The variations aredivided into three categories:• Performance of the event triggers and tracking objects,• Signal extraction, including choices made in the 2PC and template procedure,• Jet selection.In order to reduce the impact of statistical fluctuations, in most cases, the relative differences are smoothedusing a bin-wise Gaussian convolution with width equal to one bin index. I.e. the value at any point is replacedby the Gaussian-weighted average of neighboring points. Below is a synopsis of the variations, as well as acomparison between the v results versus p T . Comparisons with the v results may be found in App. B.2, and asummary of the uncertainties in v as a function of centrality may be found in App. B.3. The sensitivity to the MBTS trigger efficiency correction and track efficiency corrections, is studied bychecking the results with and without the corrections. Fig. 7.14 shows the results with and without the trackingand MBTS trigger (in the MBT case) corrections for both MBT and jet events. The effects of the correctionare an almost negligible decrease in v values. As a systematic variation on the corrections, the difference of theresults with the corrections (nominal) to that without is taken as an uncertainty.The 2016 p +Pb running period contained a bias to the tracking due to weak modes in the detector align-ment. In these cases, the detector can be misshapen in a way that cannot be fully accounted for by the alignmentprocedure because they leave the global χ invariant. This leads to systematic problems with the track q/p andsagitta that can be accounted for by applying bias corrections to tracks as a function of their angular position61 - · 10 [GeV] T p - - v With efficiency correctionWithout efficiency correction Internal ATLAS MB [GeV] A T p - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v With efficiency correctionWithout efficiency correction Internal ATLAS > 75 GeV JetT p [GeV] A T p - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v With efficiency correctionWithout efficiency correction Internal ATLAS > 100 GeV JetT p [GeV] A T p - - - R e l a t i v e d i ff e r en c e Figure 7.14: v versus p T for MBT (left), 75 GeV jet (center), and 100 GeV jet (right) events with and withouttrigger and tracking efficiency corrections.to simulate the impact of such weak modes. A comparison of the final results with and without this correctionis shown in Fig 7.15. The MBT and 75 GeV jet events show a negligible difference, however, the 100 GeV jetevents show a significant effect. Because it is not clear why the correction should affect the 100 GeV jet eventsand not the others, the difference is added as a systematic for the 100 GeVjet v results only. - · 10 [GeV] T p - - v Without sagitta correctionWith sagitta correction Internal ATLAS Minbias [GeV] A T p - - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v Without sagitta correctionWith sagitta correction Internal ATLAS > 75 GeV JetT p [GeV] A T p - - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v Without sagitta correctionWith sagitta correction Internal ATLAS > 100 GeV JetT p [GeV] A T p - - - - R e l a t i v e d i ff e r en c e Figure 7.15: v versus p T for MBT (left), 75 GeV jet (center), and 100 GeV jet (right) events with and withoutsagitta tracking correction.The combined uncertainties for this category are plotted in Fig. 7.16.62 - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS MB Efficiency correctionsTotal - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p Efficiency correctionsTotal - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p Efficiency correctionsSagitta tracking biasTotal Figure 7.16: Combined performance uncertainty, plotted as the absolute difference in v between the varied andnominal selections, for MBT (left), 75 GeV jet (center), and 100 GeV jet (right) events. The following applies to the mixed event corrections described in Sec. 7.3.1. Because the 1D correlationfunctions are generated by first integrating over ∆ η for the same and mixed events separately, and then dividing,the mixed event corrections do not correct for any ∆ η acceptance effect in the final results. However, there aredetector imperfections that are potentially being corrected for in ∆ φ . To understand the magnitude of the effectof this correction on the results, the analysis is run with and without the correction. Fig. 7.17 gives the resultsof this test and shows a modest but systematic effect at high p T in the case of the jet events, but an insignificanteffect elsewhere. Because it is unclear what may cause the p T dependence of the correction, the difference is takenas a systematic uncertainty.The event mixing introduces additional statistical uncertainty in the results. Therefore, for the case of theMBT events, the results without the mixed event corrections are taken as nominal - adding any difference to thecorrected as a systematic uncertainty. Conversely, due to the systematic difference observed for the jet events, thecorrected are used as the nominal values and add the difference to the uncorrected as a systematic uncertainty.The template method relies on there being a different fraction of flow and non-flow particles in the P andC selections. Here we test the sensitivity to this fraction by changing the P reference selection. The nominal − reference is varied to use:• − • − - · 10 [GeV] T p - - v No mixed event correctionWith mixed event correction Internal ATLAS MB [GeV] AT p - - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v With mixed event correctionNo mixed event correction Internal ATLAS > 75 GeV JetT p [GeV] AT p - - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v With mixed event correctionNo mixed event correction Internal ATLAS > 100 GeV JetT p [GeV] AT p - - - - R e l a t i v e d i ff e r en c e Figure 7.17: v versus p T for both MBT (left), 75 GeV jet (center), and 100 GeV jet (right) events with thenominal values using the mixed event correction, and variation without the correction. The solid blue points inthe sub-panels are the differences after smoothing.Fig. 7.18 gives the result of this comparison. The maximum difference above and below the nominal case aretaken as one standard deviation systematic uncertainties. - · 10 [GeV] T p - - v ATLAS MB Reference selection [GeV] A T p - - - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v ATLAS > 75 GeV JetT p Reference selection [GeV] A T p - - - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v ATLAS > 100 GeV JetT p Reference selection [GeV] A T p - - - - - R e l a t i v e d i ff e r en c e Figure 7.18: v versus p T for both MBT (left), 75 GeV jet (center), and 100 GeV jet (right) events with thenominal and two varied P reference selections. The solid blue and red points in the sub-panels are the differencesafter smoothing.The combined uncertainties for this category are plotted in Fig. 7.19.64 - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS MB Event mixingReference selectionTotal - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p Event mixingReference selectionTotal - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p Event mixingReference selectionTotal Figure 7.19: Combined signal extraction uncertainty, plotted as the absolute difference in v between the variedand nominal selections, for MBT (left), 75 GeV jet (center), and 100 GeV jet (right) events. The reconstructed jets used in this analysis have been corrected for the average UE energy falling withinthe jet cone. However, this subtraction does not account for any azimuthal modulation of the UE. Therefore,the jets that happen to fall within the flow plane, will have, on average, more energy than those out of plane.This analysis selects jets based on their p T , thus, there will be more events with jets correlated to the UE flowplane passing the threshold. Because jets are partially composed of charged particles, this will enter the analysisas a positive contribution that will be strongest at high track p T . Additionally, the UE energy is not stronglydependent on jet energy, and thus, the p T bias on the jets will be a larger percent for lower p T jets. Therefore,this bias effect should be strongest for lower p T jets.To quantify this effect on the end results, we utilize the di-jet data overlay sample in which the jet processesare generated in P, and are mixed with real data underlying events. If events are selected based on a p T threshold made on the reconstructed jets (as in data) the sample jets will have been biased by the genuine flow ofthe data UE in a quantitatively similar way to jets in data. The magnitude of the effect is quantified by correlatingtracks matched to truth P particles with tracks coming from the data UE. If there is no bias, the correlationshould be zero since the P events are embedded randomly. Events are categorized by the presence of areconstructed jet above either 75 or 100 GeV, as in data, and correlation functions are generated in exactly thesame way as in data events except that the A-particles are required to be truth P particles, and B-particles65are required to be data particles. Fig. 7.20 gives the v from this study, overlaid with the results from the jetdatasets as a function of p T . - · 10 [GeV] T p - - v Nominal dataDO: MC-data correlations Internal ATLAS > 75 GeV JetT p [GeV] A T p - - - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v Nominal dataDO: MC-data correlations Internal ATLAS > 100 GeV JetT p [GeV] A T p - - - - - R e l a t i v e d i ff e r en c e Figure 7.20: v versus p T for 75 GeV (left) and 100 GeV (right) jet events from data compared to those foundusing the MC data overlay sample. The red line is a fit to all points above 3 GeV, and acts as an estimate for theamount of the v signal can be attributed to the jet-UE bias.As expected, the effect is largest for the lower threshold jet events and at high track p T . The effect issignificant in magnitude, however it accounts for only about 20% of the high p T signal in 100 GeV events, andabout 30% in the 70 GeV events. This is accounted for as a systematic uncertainty rather than a correction tothe central values. The points are used as the uncertainty below 3 GeV and the constant fit is used above. Forthe centrality dependent v results, the value determined in the 0-5% central case is conservatively used for allcentralities.The nominal selection criteria for jet events is an offline jet with p T > GeV or p T > GeV to bepresent in the region of η < . . This p T threshold is varied to p T > GeV and p T > GeV, respectively,to study the sensitivity to any slight jet trigger inefficiency or resolution effect. Fig. 7.21 shows the comparisonof results with the varied jet threshold. The differences are taken as systematic uncertainties.In jet events, the nominal B particle jet rejection cut made for all jets above 15 GeV. To understand thesensitivity to this choice, the threshold is varied to 20 GeV, and the difference to the nominal results is taken asa systematic uncertainty. The results using each cut value are compared in Fig. 7.22.66 - · 10 [GeV] T p - - v > 75 [GeV] (nominal) jetT p > 80 [GeV] jetT p Internal ATLAS > 75 GeV JetT p [GeV] A T p - - - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v > 100 [GeV] (nominal) jetT p > 105 [GeV] jetT p Internal ATLAS > 100 GeV JetT p [GeV] A T p - - - - - R e l a t i v e d i ff e r en c e Figure 7.21: v versus p T for 75 GeV (left) and 100 GeV (right) jet events with offline jet p T thresholds variationsof +5 GeV. The solid blue points in the sub-panels are the differences after smoothing. - · 10 [GeV] T p - - v Reject jets > 15 GeV (nominal)Reject jets > 20 GeV Internal ATLAS > 75 GeV JetT p [GeV] AT p - - - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v Reject jets > 15 GeV (nominal)Reject jets > 20 GeV Internal ATLAS > 100 GeV JetT p [GeV] AT p - - - - - R e l a t i v e d i ff e r en c e Figure 7.22: v versus p T for 75 GeV (left) and 100 GeV (right) jet events with the nominal and varied ∆ η jet p T selection. The solid blue points in the sub-panels are the differences after smoothing.The threshold p T for jets used in the rejection scheme is 15 GeV. Given this low threshold, it is conceivablethat a significant portion of these jets are single hadrons on the tail of the UE particle distribution. To study thisfurther, the number of charged tracks with ∆ R < . from the jet axis is determined. Figure 7.23 shows themultiplicity distributions of jets in different p T windows from 100 GeV jet events with two different centralityselections. The legends also report the fraction of these jets containing only a single track.67 JetTrk N00.020.040.060.080.10.120.140.16 Internal ATLAS < 20; 5.1% single particle jet T p 15 < 0% - 5% central Internal ATLAS < 25; 3.7% single particle jet T p 20 < 0% - 5% central Internal ATLAS < 30; 3.1% single particle jet T p 25 < 0% - 5% central Internal ATLAS < 35; 2.6% single particle jet T p 30 < 0% - 5% central Internal ATLAS < 40; 2.3% single particle jet T p 35 < 0% - 5% central Internal ATLAS < 45; 2.2% single particle jet T p 40 < 0% - 5% central JetTrk N00.020.040.060.080.10.120.140.160.180.2 Internal ATLAS < 20; 11.5% single particle jet T p 15 < 70% - 90% central Internal ATLAS < 25; 8.4% single particle jet T p 20 < 70% - 90% central Internal ATLAS < 30; 6.5% single particle jet T p 25 < 70% - 90% central Internal ATLAS < 35; 5.4% single particle jet T p 30 < 70% - 90% central Internal ATLAS < 40; 4.4% single particle jet T p 35 < 70% - 90% central Internal ATLAS < 45; 3.9% single particle jet T p 40 < 70% - 90% central Figure 7.23: The number of charged tracks with ∆ R < . from the jet axis jets in different p T windows from100 GeVjet events. The left plot show the results from events from 0-5% central events and the right is for70-90% central events. The solid blue points in the sub-panels are the differences after smoothing.To estimate the sensitivity of the results to differences in jet multiplicity, all jets used in the jet rejectionscheme are required to contain more than two tracks. The results of this test are plotted in Fig. 7.24. Thedifference from this test to the nominal scheme is taken as a systematic uncertainty on the final results. - · 10 [GeV] T p - - v Reject jets > 15 GeV (nominal) > 2 jet trk N && Internal ATLAS > 75 GeV JetT p [GeV] AT p - - - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v Reject jets > 15 GeV (nominal) > 2 jet trk N && Internal ATLAS > 100 GeV JetT p [GeV] AT p - - - - - R e l a t i v e d i ff e r en c e Figure 7.24: v versus p T for 75 GeV (left) and 100 GeV (right) jet events with the nominal and varied associ-ated particle rejection jet multiplicity selection. The solid blue points in the sub-panels are the differences aftersmoothing.As mentioned in Sec. 3.3, a sector of the HEC was disabled for this running period. Since the analysisuses calorimeter jet objects to reject B tracks from correlations, it is possible that the reduced response in this68sector is allowing jets in that should be removed. To check for a bias, the analysis is run only using B tracks with η < . in the lab frame and compared with the nominal results. Fig. 7.25 gives the result of this comparison.There is a significant difference in each case, however, the trends at high p T are opposite for the two jet samples.It is unclear what mechanism could have opposite effects for the two jet triggered events. As this difference couldbe due to jet bias, the difference is propagated as a systematic uncertainty. - · 10 [GeV] T p - - v Nominal < 1.56 LabTrack B h Internal ATLAS > 75 GeV JetT p [GeV] A T p - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v Nominal < 1.56 LabTrack B h Internal ATLAS > 100 GeV JetT p [GeV] A T p - - - R e l a t i v e d i ff e r en c e Figure 7.25: v versus p T for 75 GeV (left) and 100 GeV (right) events comparing the nominal results to thosegenerated from tracks with an η < . in the lab frame. The solid blue points in the sub-panels are thedifferences after smoothing.The combined uncertainties for this category are plotted in Fig. 7.26. - · AT p - - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p cut T p Jet cut T p Jet rejection low Jet multiplicity > 2 < 1.56 LabTrack B h Jet UE biasTotal - · AT p - - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p cut T p Jet cut T p Jet rejection low Jet multiplicity > 2 < 1.56 LabTrack B h Jet UE biasTotal Figure 7.26: Combined jet selection uncertainty for MBT (left), 75 GeV jet (center), and 100 GeV jet (right)events.69 As mentioned in Sec. 7.3.2.1, a separation in η between A and B particles is imposed to reduce thecontamination from short range non-flow correlations. The nominal gap is | ∆ η | > , as has been used innumerous previous analyses. To understand the effect of this choice on the results, the flow extraction is madefrom correlations using different selections of | ∆ η | for three different selections in A particle p T :• Low p T : 0.5 < p T < 2 GeV• Mid p T : 2 < p T < 9 GeV• High p T : 9 < p T < 100 GeVFig. 7.27 gives the result of this comparison, plotting v vs. | ∆ η | for the three p T selections for all three datasets. hD Track-track |00.020.040.060.080.10.120.140.16 v < 2 A T p A T p A T p Internal ATLAS Minbias0 - 5% central hD Track-track |00.020.040.060.080.10.120.140.16 v < 2 A T p A T p A T p Internal ATLAS > 75 GeV JetT p hD Track-track |00.020.040.060.080.10.120.140.16 v < 2 A T p A T p A T p Internal ATLAS > 100 GeV JetT p Figure 7.27: v versus | ∆ η | in low (orange), mid (blue), and high (red) p T ranges for MBT (left), 75 GeV jet(center), and 100 GeV jet (right) events.One sees in Fig. 7.27 a slow change in v as the | ∆ η | cut is varied around the nominal cut of 2. Becausethe separation cut is changing the η distribution of tracks entering the correlations, as can be seen in Fig. 7.28,it is reasonable to expect this small change. However, when the cut becomes too small, one sees a change in thetrend; this is particularly obvious in the jet events. This dramatic change is interpreted as a breakdown in thetemplate assumptions and what we wish to avoid. The fact that the nominal cut value is well on the plateau givesconfidence that the method is unbiased by the short-range correlations. The cut can be interpreted as a definitionof the fiducial region of the measurement, and, therefore, do not include an uncertainty from this variation.70 - - - - - B h = 1.690 æ | B h | Æ | > 1.2: hD Track-track | = 1.717 æ | B h | Æ | > 1.4: hD Track-track | = 1.745 æ | B h | Æ | > 1.6: hD Track-track | = 1.775 æ | B h | Æ | > 1.8: hD Track-track | = 1.805 æ | B h | Æ | > 2.0: hD Track-track | = 1.836 æ | B h | Æ | > 2.2: hD Track-track | = 1.869 æ | B h | Æ | > 2.4: hD Track-track | = 1.902 æ | B h | Æ | > 2.6: hD Track-track | = 1.937 æ | B h | Æ | > 2.8: hD Track-track | Internal ATLAS Figure 7.28: The η distribution of associated (B) tracks used to generate correlation functions from 100 GeV jetevents for several different values of track-track gap requirements. For each variation, the mean of | η | is reportedquantifying the change in the distributions.The associated particle jet rejection scheme requires there to be a separation in η of at least 1 unit betweenthe B particle and all jets with p T > 15 GeV. Much like the previous check, we study the effect of this choiceof separation on the results. The flow extraction is made from correlations using different selections of jet-track| ∆ η | for three different selections in A particle p T :• Low p T : 0.5 < p T < 2 GeV• Mid p T : 2 < p T < 9 GeV• High p T : 9 < p T < 100 GeVFig. 7.29 gives the result of this comparison, plotting v vs. | ∆ η | for the three p T selections for the two jetdatasets.Fig. 7.29 shows a slow change in v as the | ∆ η | cut is varied around the nominal cut of 1 unit. Becausethe separation cut is changing the η distribution of tracks entering the correlations, as can be seen in Fig. 7.30,it is reasonable to expect this small change. Again the fact that the nominal cut is on a plateau gives confidencethat the method is unbiased by the jet correlations. There is larger variation in the mid p T transition regionwhere the results are sensitive to changes in the UE-HS particle fractions. As before, this cut can be interpretedas a definition of the fiducial region of the measurement, and do not to incorporate a variation of it into theuncertainties.71 hD Jet-track |00.020.040.060.080.10.120.140.16 v < 2 A T p A T p A T p Internal ATLAS > 75 GeV JetT p hD Jet-track |00.020.040.060.080.10.120.140.16 v < 2 A T p A T p A T p Internal ATLAS > 100 GeV JetT p Figure 7.29: v versus | ∆ η | in low (orange), mid (blue), and high (red) p T ranges for 75 GeV jet (left), and100 GeV jet (right) events. - - - - - B h = 1.751 æ | B h | Æ | > 0.8: hD Jet-track | = 1.779 æ | B h | Æ | > 0.9: hD Jet-track | = 1.805 æ | B h | Æ | > 1.0: hD Jet-track | = 1.829 æ | B h | Æ | > 1.1: hD Jet-track | = 1.852 æ | B h | Æ | > 1.2: hD Jet-track | = 1.910 æ | B h | Æ | > 1.5: hD Jet-track | Internal ATLAS Figure 7.30: The η distribution of associated (B) tracks used to generate correlation functions from 100 GeV jetevents for several different values of jet-track gap requirements. For each variation, the mean of | η | is reportedquantifying the change in the distributions.The results should be independent of the detector configuration, and therefore should be consistent be-tween the two running periods (in which the p +Pb beam configurations were reversed). To check this, the resultsare determined for 100 GeV jet events in period 1 (run number < 313500) and period 2 (run number > 313500)separately. The left side of Fig. 7.31 shows a comparison between these two selections. There appears to be aslight bias towards higher values in period 1 vs. period 2 at high p T . Because the observed difference from theB particle disabled HEC rejection described in Sec. 7.4.3 is a selection made in the lab frame, the bias might bewhat is causing the slight period dependence. The right side of Fig. 7.31 shows the comparison again, but withthe condition that B particles are restricted to have η Lab < . . Since this check removes the apparent bias, the72effect is attributed to the disabled HEC which is accounted for in Sec. 7.4.3. Therefore no additional systematicis applied. - · 10 [GeV] T p - - v Period 1Period 2 Internal ATLAS > 100 GeV JetT p [GeV] A T p - - - R e l a t i v e d i ff e r en c e /NDF = 1.606 c - · 10 [GeV] T p - - v Period 1Period 2 Internal ATLAS > 100 GeV JetT p [GeV] A T p - - - R e l a t i v e d i ff e r en c e /NDF = 0.981 c Figure 7.31: Comparison of v results from data from period 1 and 2 separately. The right plot is after theassociated particles are restricted to have η Lab < . , and the left is without restriction. The red dashed linesare the result of a constant fit for which the χ /N DF is quoted on the figure.Fig. 7.3 shows small η − φ dependent tracking performance differences. To understand the sensitivityto any residual effects not removed by the event mixing scheme, φ flattening maps are generated using dataand applied, particle-by-particle, when constructing the correlation functions. The corrections are derived bynormalizing track φ distributions in ∆ η = 0 . slices for tracks within a given p T range. These correction mapsare generated for MBT and jet events independently and are plotted in Figures B.26- B.28 in App. B.5. Fig. 7.32gives the results with and without the corrections for the 75 GeV and 100 GeV jet events. As one would hope,the additional flattening yielded negligible differences to the nominal results, and no additional uncertainty isapplied.In addition to the nominal associated particle jet rejection scheme, others have been checked. Fig. 7.33shows a comparison between the nominal “all” jet rejection, and one where only the leading and sub-leading (in p T ) jets are rejected. There is a clear difference between 1.5 and 3 GeV where the all jet rejection case peaks at ahigher value than the 2-jet case. This could be due to a higher concentration UE-UE correlations. At high p T ,the 2-jet rejection yields a systematically higher value. It is not known if this is due to residual non-flow or adifference in the signal distribution being sampled. However, the all-jet rejection yields a larger suppression in73 - · 10 [GeV] T p - - v Not flattened (nominal)Flattened Internal ATLAS > 75 GeV JetT p [GeV] A T p - - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v Not flattened (nominal)Flattened Internal ATLAS > 100 GeV JetT p [GeV] A T p - - - - R e l a t i v e d i ff e r en c e Figure 7.32: v versus p T for both 75 GeV (left) and 100 GeV (right) jet events with the nominal values andthose with flattening corrections applied.the awayside non-flow peak in the correlation functions, making the extraction less sensitive to inconsistenciesin the non-flow subtraction. Thus, we choose to use the all-jet scheme with no additional uncertainty. - · 10 [GeV] T p - v Internal ATLAS > 75 GeV jetT p All jet rejection (nominal)2 jet rejection - · 10 [GeV] T p - v Internal ATLAS > 100 GeV jetT p All jet rejection (nominal)2 jet rejection Figure 7.33: v versus p T for 75 GeV (left) and 100 GeV (right) jet events with the nominal ”all” jet rejectionand those in which only the leading and sub-leading (in p T ) jets are used in the B particle rejection.One might think that the simple two jet rejection scheme that rejects from the leading and sub-leading(in p T ) jets might not be as efficient in removing the jet non-flow as if you require the jets to be in oppositehemispheres. For this check, the basic two jet rejection is compared with a variant where the sub-leading jet mustbe in the opposite side in φ (| ∆ φ | > π/ ). Fig. 7.34 gives the result of this comparison showing almost nodifference for 100 GeV jet events.74 - · 10 [GeV] T p - v Internal ATLAS > 100 GeV jetT p Figure 7.34: v versus p T 100 GeV jet events with the simple two jet rejection compared to those generated withthe two opposite jet rejection.As mentioned in Sec. 7.2.1, high multiplicity triggers were used to record events with multiplicities abovea certain threshold. Because we are using the Σ E PbT to categorize events, if we use these triggers, our central andperipheral selections would be formed from a combination of triggers and the multiplicity distributions would beunnatural. Figure 7.35 gives a comparison of the results between the nominal selections from the MBT datasetand those from the MBT+HMT. If the MB+HMT is corrected for it’s prescale differences, the results agree withjust the MB. However comparing the MBT with the uncorrected MBT+HMT gives noticeable differences -particularly in the transition region between 2 GeV and 9 GeV. Since there is no statistical benefit in using theprescale corrected MBT+HMT, the MBT only is used for simplicity. The resultant variation from each source of uncertainty is added in quadrature asymmetrically. A summaryof the sources as well as the total uncertainty in v is plotted in Fig. 7.36. Likewise, the total uncertainty in the v determination is plotted in Fig.7.37.To determine the uncertainty in the particle pair yield fractions, the calculation is done after each variation,and each difference is considered an independent source. The variations relevant to the pair yield determinationin MBT events are:• Efficiency corrections75 - · 10 [GeV] T p - - v MBMB+HMT Internal ATLAS [GeV] A T p - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v MBMB+HMT prescale corrected Internal ATLAS [GeV] A T p - - - R e l a t i v e d i ff e r en c e Figure 7.35: v versus p T for MBT and MBT+HMT events. The right figure gives the MBT+HMT after triggerprescale correction, and the left is uncorrected. - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS MB PerformanceSignal extractionTotal - · AT p - - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p PerformanceSignal extractionJet selectionTotal - · AT p - - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p PerformanceSignal extractionJet selectionTotal Figure 7.36: The relative uncertainty in v from all sources versus p T for MBT (left), 75 GeV jet (center), and100 GeV jet (right) events. The combined uncertainty is shown as the black curve. - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS MB PerformanceSignal extractionTotal - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p PerformanceSignal extractionJet selectionTotal - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p PerformanceSignal extractionJet selectionTotal Figure 7.37: The relative uncertainty in v from all sources versus p T for MBT (left), 75 GeV jet (center), and100 GeV jet (right) events. The combined uncertainty is shown as the black curve.76and the variations relevant to the jet events are:• Efficiency corrections• Jet p T cut• B particle rejection jet low p T cut• B particle rejection jet multiplicity cutSummary figures for UE-UE and HS-UE pair combinations are shown in Fig. 7.38. - · AT p - - - - - R e l a t i v e d i ff e r en c e Internal ATLAS MB+HMTBulk - Bulk pairs Track EfficiencyTrans minTrans maxTotal - · AT p - - - - - R e l a t i v e d i ff e r en c e Internal ATLAS > 75 GeV jetT p Bulk - Bulk pairs Track EfficiencyTrans minTrans max cut T p Jet cut T p Jet rejection low Jet multiplicity > 2Total - · AT p - - - - - R e l a t i v e d i ff e r en c e Internal ATLAS > 100 GeV jetT p Bulk - Bulk pairs Track EfficiencyTrans minTrans max cut T p Jet cut T p Jet rejection low Jet multiplicity > 2Total - · AT p - - - - - R e l a t i v e d i ff e r en c e Internal ATLAS MB+HMTJet - Bulk pairs Track EfficiencyTrans minTrans maxTotal - · AT p - - - - - R e l a t i v e d i ff e r en c e Internal ATLAS > 75 GeV jetT p Jet - Bulk pairs Track EfficiencyTrans minTrans max cut T p Jet cut T p Jet rejection low Jet multiplicity > 2Total - · AT p - - - - - R e l a t i v e d i ff e r en c e Internal ATLAS > 100 GeV jetT p Jet - Bulk pairs Track EfficiencyTrans minTrans max cut T p Jet cut T p Jet rejection low Jet multiplicity > 2Total Figure 7.38: The relative uncertainty in UE-UE (top) and HS-UE (bottom) pair fractions in 0-5% central eventsfrom all sources versus p T for MBT (left), 75 GeV jet (center), and 100 GeV jet (right) events. The combineduncertainty is shown as the black curve. hapter 8Results of the Measurement of Azimuthal Anisotropy Figure 8.1 shows the extracted second- ( v ) and third-order ( v ) anisotropy coefficients for the MBTevents compared to those from both 75 and 100 GeV selections of jet events plotted as a function of A-particle p T in the range . < p T < GeV. Each set of values is from events with the same 0–5% centrality selection.Points are located on the horizontal axis at the mean p T of tracks within any given bin. The v and v coefficientsincrease as a function of p T in the low p T region ( p T < 2–3 GeV), then decrease (2–3 < p T < 9 GeV), and finallyplateau for high p T ( p T > 9 GeV). The v coefficients are consistent with being independent of p T for p T >9 GeV, while the larger uncertainties in the values of v preclude any strong conclusion. - · 10 [GeV] AT p - v MBT > 75 GeV jetT p > 100 GeV jetT p ATLAS -1 , 165 nb = 8.16 TeV NN s+Pb p - · 10 [GeV] AT p - v MBT > 75 GeV jetT p > 100 GeV jetT p ATLAS -1 , 165 nb = 8.16 TeV NN s+Pb p Figure 8.1: Distribution of v (left) and v (right) plotted as a function of the A-particle p T . Values from MBTevents are plotted as black squares, and those from events with jet p T > GeV and events with jet p T > GeVare plotted as blue circles and orange diamonds respectively. Statistical uncertainties are shown as narrow verticallines on each point, and systematic uncertainties are presented as colored boxes behind the points.78The v results show agreement within uncertainties between the MBT and jet events for the low p T ( p T (cid:46) GeV) and high p T ( p T (cid:38) GeV) regions. For the intermediate p T region, the MBT events yielda higher v value than jet events, although the trends are qualitatively similar. Similarly to v , the v resultsshow agreement between the MBT and jet events for p T < GeV, and higher values from MBT events for p T > GeV.As mentioned in Section 7.3.2.3, if the measured anisotropy originates from a global momentum field,the v and v values, extracted for a given p A T range, will be independent of B-particle selection. This assumption - · 10 [GeV] AT p - v < 1 GeV B T p B T p 1 < < 3 GeV B T p 2 < > 0.4 GeV (nominal) B T p ATLAS -1 , 165 nb = 8.16 TeV NN s+Pb p MBT - · 10 [GeV] AT p - v < 1 GeV B T p B T p 1 < < 3 GeV B T p 2 < > 0.4 GeV (nominal) B T p ATLAS -1 , 165 nb = 8.16 TeV NN s+Pb p > 75 GeV jetT p - · 10 [GeV] AT p - v < 1 GeV B T p B T p 1 < < 3 GeV B T p 2 < > 0.4 GeV (nominal) B T p ATLAS -1 , 165 nb = 8.16 TeV NN s+Pb p > 100 GeV jetT p Figure 8.2: Measured v values plotted as a function of the A-particle p T for MBT events (top), events with jet p T > GeV (bottom left), and events with jet p T > GeV (bottom right). The nominal values (closed blackcircles) are overlaid with points generated by making different B-particle p T selections: . < p B T < GeV (blueopen circles), < p B T < GeV (open violet squares), and < p B T < GeV (open red triangles). The pointswith different B-particle p T selections are offset slightly from the nominal horizontal-axis positions to make theuncertainties visible.79of factorization is explicitly tested by carrying out the analysis for different selections of p B T . Figure 8.2 showsthe v values, from each event trigger, for the nominal results using p B T > . GeV overlaid with results using . < p B T < GeV, < p B T < GeV, and < p B T < GeV. The test shows factorization breaking at the levelof 5% for p A T < GeV in MBT events. However, at higher p A T , the differences grow with p A T to be 10–100%from the nominal values. For jet events, factorization holds within about 10–20% for all values of p A T , except for < p A T < GeV in p jet T > GeV events, where it is within about 30–40%. Although the large uncertaintiesprevent strong conclusions from being drawn, there is a hint of a difference in behavior at high p A T where thefactorization breaking is greater for MBT events than for jet events. This result could be due to the B-particlejet rejection scheme used for the jet events. Correlations resulting from hard-process, e.g. from back-to-backjets, are expected to specifically violate the factorization assumption, though P studies have shown that itmight be possible for hard processes to approximately pass factorization tests [163]. The B-particle jet rejectiondramatically limits the contribution from these processes from entering the correlation functions in jet events.However, the correlations from MBT events have no such rejection, and could, therefore, be more susceptible tohard-process correlations at high p A T .Figure 8.3 shows v plotted as a function of centrality for MBT events and both classes of jet events.The results are divided into three regions in A-particle p T : 0.5 < p T < 2 GeV, 2 < p T < 9 GeV, and 9 < p T <100 GeV. The v results show agreement, within uncertainties, between the MBT and jet events for p T selections . < p T < GeV and p T > GeV for all centralities and are found to be nearly independent of centrality. For < p T < GeV, the MBT events give a higher v value than the jet events, and all three sets show a trend tolower values of v as the collisions become more peripheral.80 - v MBT > 75 GeV jetT p > 100 GeV jetT p ATLAS -1 , 165 nb = 8.16 TeV NN s+Pb p < 2 GeV A T p - v MBT > 75 GeV jetT p > 100 GeV jetT p ATLAS -1 , 165 nb = 8.16 TeV NN s+Pb p < 9 GeV A T p - v MBT > 75 GeV jetT p > 100 GeV jetT p ATLAS -1 , 165 nb = 8.16 TeV NN s+Pb p < 100 GeV A T p Figure 8.3: Distribution of v plotted as a function of centrality for MBT events (black squares), events with jet p T > GeV (blue circles), and events with jet p T > GeV (orange diamonds). The results are obtained inthree different selections of the A-particle p T : . < p T < GeV (top left), < p T < GeV (top right), and < p T < GeV (bottom). Statistical uncertainties are shown as narrow vertical lines on each point, andsystematic uncertainties are presented as colored boxes behind the points. Focusing on the overall p T dependence of the anisotropies, Figure 8.4 (left panel) shows v and v coeffi-cients from events with jet p T > GeV compared with theoretical calculations from Ref. [23]. This theoreticalcalculation, within the jet quenching paradigm, invokes a stronger parton coupling to the QGP near the tran-sition temperature, which helps to reduce the tension in simultaneously matching the nucleus–nucleus high- p T hadron spectrum suppression and the azimuthal anisotropy v . The calculation tests two different initial p +Pbgeometries referred to as ‘size a’ and ‘size b’, where the latter has a smaller initial QGP volume. The predictions81 AT p - - n v Zhang, Liao size a v size b v size a v size b v v v ATLAS -1 , 165 nb = 8.16 TeV NN s+Pb p T p P b p R = 5.02 TeV NN s+Pb p = 5.02 TeV NN sp+Pb pPb R ATLAS Pb-sidecoll pPb Q ALICE Zhang, Liao: size aZhang, Liao: size b Figure 8.4: Coefficients v and v (left panel) and R p Pb (right panel) plotted as a function of particle p T for p +Pb collisions. The left panel is for central 0–5% events from the jet p T > GeV event sample. Statisticaluncertainties are shown as narrow vertical lines on each point, and systematic uncertainties are presented ascolored boxes behind the points. The left panel has two sets of curves showing theoretical predictions from ajet quenching framework with two different initial geometries in 0–4% central collisions [23]; the upper two(red/orange) are v for ‘size a’ (dotted) and ‘size b’ (dash-dotted) configurations, and the lower two (blue) are v where the ‘size a’ (dash-dotted) and ‘size b’ (dashed) curves are nearly indistinguishable from each other. Theright panel shows R p Pb data from ATLAS [164] and Q p Pb data from ALICE [165]. Theoretical calculations(red/orange lines) from Ref. [23] are also shown in this panel; the dotted line gives the results of the ‘size a’configuration and the dash-dotted line gives the results of the ‘size b’ configuration.are slightly lower than the data for both v and v , and the ‘size a’ curve is within two standard deviations ofall points. However, in the right panel of Figure 8.4, the same calculation predicts a substantial suppression ofhigh- p T hadrons, as expressed by the quantity R p Pb = d N p Pb / d p T d y/ ( T p Pb × d σ pp / d p T d y ) where T p Pb represents the nuclear thickness of the Pb nucleus, as determined via a Monte Carlo Glauber calculation [7].Shown in comparison are published experimental results from ATLAS and ALICE for R p Pb in central eventsthat are consistent with no nuclear suppression, i.e. R p Pb = 1 [164, 165]. The ALICE experiment uses thenotation Q p Pb for the same quantity to describe a bias that may exist due to the centrality categorization. Thereare uncertainties in the experimental measurements related to the centrality or multiplicity selection in p +Pb col-lisions, particularly in determining the nuclear thickness value T p Pb . However, there is no indication of the large R p Pb suppression predicted by the jet quenching calculation. Thus, the jet quenching calculation is disfavored asit cannot simultaneously describe the non-zero high- p T azimuthal anisotropy and the lack of yield suppression.82Figure 8.5 shows the MBT v and v coefficients compared with theoretical calculations from Ref. [5].The calculations are derived from two opposite limits of kinetic theory. The low momentum bands representzeroth-order hydrodynamic calculations for high-multiplicity p +Pb events that give quantitative agreement with v up to p T = 2 GeV while predicting values of v that are too high. Above some high p T threshold, hadrons areexpected to result, not from hydrodynamics, but instead from jets where the resulting partons have the oppositelimit than in hydrodynamics, i.e. a large mean free path. To model this region, a non-hydrodynamic ‘eremitic’expansion calculation (see Ref. [5] for the detailed calculation), shown as the bands at high p T , indicates slowlydeclining v and v coefficients. The dashed lines are a simple Padé-type fit connecting the two regimes [5]. Thetrends are qualitatively similar to those in the data, although there is not quantitative agreement. In particular,the calculation predicts values of v and v substantially below the experimental results for p T = - · AT p - n v Romatschke v Fluid v Fluid v Eremitic v Eremitic v Pade v Pade v Fluid v Fluid v Eremitic v Eremitic v Pade v Pade v v ATLAS -1 , 165 nb = 8.16 TeV NN s+Pb p Figure 8.5: Coefficients v and v plotted as a function of p T for central 0–5% p +Pb collisions from the MBTevent sample. Theoretical calculations relevant to the low- p T regime from hydrodynamics and to the high- p T regime from an ‘eremitic’ framework from Romatschke [5] are also shown. The lines are Padé-type fits connectingthe two regimes, where the red dotted line is for v and the blue dash-dotted line is for v . Statistical uncertaintiesare shown as narrow vertical lines on each point, and systematic uncertainties are presented as colored boxesbehind the points.83hydrodynamic regime result in better quantitative agreement with the anisotropy coefficients at low p T [71, 166].It is worth highlighting that traditional parton energy-loss calculations connect the high- p T v with a suppressionin the overall yield of high- p T particles. The same is true with this eremitic calculation, and thus, it should alsobe in contradistinction to p +Pb high p T experimental data indicating almost no suppression, i.e. jet quenching.Another possible source of the high- p T anisotropies could lie in an initial-state effect, potentially encodedin a model such as P. Shown in Figure 8.6 is a P calculation with hard pp events overlaid onminimum-bias p +Pb events generated in the default Angantyr framework [167]. It is emphasized that this ver-sion of P does not include the recently developed string–string interaction, or so-called string shoving [168].The generator-level charged particles are then processed with the entire analysis procedure, including the non-flow template fit. The result is a negative v , for all momenta, in contradistinction to the experimental data.Further investigation reveals that P run in ‘hard’ scattering mode has correlations with large pseudorapidityseparation between particle pairs as a result of the specific implementation of initial-state radiation. This corre-lation is reduced in high-multiplicity events because of the large number of uncorrelated UE particles, and thusresults in a negative v , after subtracting the non-flow contribution. The term ‘hard’ refers to P run with the following settings: HardQCD:all=on , PartonLevel:MPI=off , and containing ajet with p T > GeV. - fD ) f D ( Y cent Y Fit peri YF + G (0) peri YF + ridge2 Y (0) peri YF + ridge3 Y PYTHIA8 = 8.16 TeV NN s+Pb p < 1.75 GeV A T p – = -5.05 · v 0.05 – = 0.69 · v /NDF = 1.20 c - fD - ) f D ( pe r i Y F - G ) - f D ( Y - fD ) f D ( Y cent Y Fit peri YF + G (0) peri YF + ridge2 Y (0) peri YF + ridge3 Y PYTHIA8 = 8.16 TeV NN s+Pb p < 100 GeV A T p 45 < 0.10 – = -0.10 · v 0.10 – = -0.20 · v /NDF = 1.04 c - fD - ) f D ( pe r i Y F - G ) - f D ( Y - · 10 [GeV] AT p - - - - - - - - , v NN s PYTHIA8 +Pb Angantyr UE p > 100 GeV jet T p hard pp Figure 8.6: Predictions of azimuthal anisotropy from P using the same two-particle formalism used for thedata results. The events combine minimum-bias p +Pb underlying events generated in the Angantyr frameworkwith hard pp events that require the presence of a jet with p T > GeV. The two top plots show examplecorrelation functions, with template fits, from a low particle- p T selection (top left) and a high particle- p T selection(top right). In the upper panels of the two top plots, the open circles show the scaled and shifted peripheraltemplate with uncertainties omitted, the closed circles show the central data, and the red histogram shows thefit (template and harmonic functions). The blue dashed line shows the second-order harmonic component, Y ridge2 , and the orange dashed line shows the third-order harmonic component, Y ridge3 respectively). The lowerpanels show the difference between the central data and the peripheral template along with the second and thirdharmonic functions. The resulting v , , v , , and global fit χ /NDF values are reported in the legends, whereNDF = 35 . The bottom plot shows the extracted v , values as a function of A-particle p T .85 p +Pb and Pb+Pb Data Figure 8.7 shows the published Pb+Pb results for v as a function of p T in the 20–30% centrality selec-tion [80] compared to the v from both the MBT p +Pb data and p +Pb containing a jet with p T > GeV. ThisPb+Pb centrality range is selected because the spatial elliptic eccentricity is approximately the same as in 0–5%centrality p +Pb collisions [169], despite having a much larger total particle multiplicity. The overall trends forPb+Pb v as a function of p T are qualitatively similar to those presented here for p +Pb from MBT events andthe jet events with jet p T > GeV. Both sets of the p +Pb values are scaled by a single multiplicative factor(1.5) to match the Pb+Pb rise at low p T . The MBT p +Pb results quantitatively agree with those from the Pb+Pbsystem for . < p T < GeV, except for a slight difference in the peak value near p T ≈ GeV. For p T aboveabout 8 GeV, the Pb+Pb results indicate a slow decline of v values with increasing p T , while the p +Pb resultsexhibit more of a plateau. Strikingly, the overall behavior of the v values are quite similar. - · 10 [GeV] AT p v -1 , 165 nb = 8.16 TeV NN s+Pb p ATLAS = 5.02 TeV NN sPbPb +Pb MBT p · jetT p +Pb p · Figure 8.7: Scaled p +Pb v values plotted as a function of the A-particle p T overlaid with v from 20–30%central Pb+Pb data at √ s NN = 5.02 TeV [80]. Results from MBT and jet p T > GeV p +Pb events are plottedas black squares and orange diamonds, respectively, and those from Pb+Pb are plotted as green circles. Statisticaluncertainties are shown as narrow vertical lines on each point, and systematic uncertainties are presented ascolored boxes behind the points.As detailed in Sections 2.4.3 and 2.4.4, the physics interpretations of the Pb+Pb elliptic anisotropies arehydrodynamic flow at low p T , differential jet quenching at high p T , and a transition between the two in the86intermediate region of approximately < p T < GeV. Since these effects all relate to the initial QGPgeometric inhomogeneities, a common shape with a single scaling factor for p +Pb could indicate a commonphysics interpretation albeit with a different initial average geometry. This scaling factor of 1.5, as empiricallydetermined, may be the result of slightly different initial spatial deformations, or from the much larger Pb+Pboverall multiplicity, which enables a stronger translation of spatial deformations into momentum space. For thehigh p T region, this presents a conundrum in that it is difficult for differential jet quenching to cause the v anisotropy in p +Pb collisions when there is no evidence for jet quenching overall. These measurements showingnon-zero high p T v in p +Pb collisions in the absence the jet quenching observed in Pb+Pb collisions suggestthere might be additional contributions to v at high p T in Pb+Pb collisions. Returning to the issue of the difference in the intermediate p T region between the p +Pb MBT and jetevent results, the source of hadrons in this region should be considered. As detailed in Sec. 7.3.5, in a highlysimplified picture one can classify hadrons as originating from hard scatterings (HS) or from the underlying event(UE). Thus, pairs of particles of A and B types can come from the combinations HS–HS, HS–UE, UE–HS, andUE–UE. Figure 8.8 presents the measured pair fractions for both MBT and jet, 0–5% central events plottedas a function of the A-particle p T . In each case UE–UE pairs dominate the correlation functions at low p T ,and HS–UE combinations dominate at high p T . Combinations with HS B-particles are sub-dominant, becausethere are fewer jet particles than UE particles in central events; for the jet selected events, these combinationsare further suppressed by the B-particle jet rejection condition. Figure 8.9 shows the dominant contributionsfrom the MBT and jet events overlaid. Although the same qualitative behavior is found in each case, the pointat which the HS–UE pairs become dominant over the other combinations is at a lower p T for jet events than forMBT events.This behavior can also be seen in Figure 8.10, in which the pair fractions are plotted as a function ofcentrality, and again, the values for MBT and jet events are overlaid. The centrality-dependent results are plottedfor low, medium, and high A-particle p T ranges in the same way as in Figure 8.3. At low p T , pair fractions fromMBT and jet events agree, and in the mid- p T transition region, MBT events have a larger UE–UE contribution87 - · 10 [GeV] AT p P a i r f r a c t i on ATLAS = 8.16 TeV NN s+Pb p MBT, 0-5% central UE - UE pairsHS - UE pairsHS - HS pairsUE - HS pairs -1 = 165 nb int L - · 10 [GeV] AT p P a i r f r a c t i on ATLAS = 8.16 TeV NN s+Pb p > 75 GeV jetT p -1 = 165 nb int L UE - UE pairsHS - UE pairsHS - HS pairsUE - HS pairs - · 10 [GeV] AT p P a i r f r a c t i on ATLAS = 8.16 TeV NN s+Pb p > 100 GeV jetT p -1 = 165 nb int L UE - UE pairsHS - UE pairsHS - HS pairsUE - HS pairs Figure 8.8: Particle pair yield composition fractions for MBT events (top), events with jet p T > GeV (bottomleft), and events with jet p T > GeV (bottom right) plotted as a function of the A-particle p T . Green andblue open circles represent HS–HS and UE–HS pairs, respectively, and red and violet closed circles representUE–UE and HS–UE pairs, respectively. Statistical uncertainties are shown as narrow vertical lines on each point,and systematic uncertainties are presented as colored boxes behind the points.and smaller HS–UE contribution compared to jet events. At high p T , central events show a difference betweenUE–UE and HS–UE that is reduced in more-peripheral events and absent for more peripheral than 25% cen-trality. The overall trend of the pair fractions with centrality is quite similar to that of v shown in Figure 8.3, i.e.little centrality dependence for low and high p T and significant centrality dependence in addition to MBT–jetevent ordering in the mid- p T transition region.Thus, a potential explanation for the lower v and v in the intermediate p T region is simply that, inthat region, the HS particles have lower anisotropy coefficients than UE particles, and MBT events have a larger88 - · 10 [GeV] AT p P a i r f r a c t i on ATLAS = 8.16 TeV NN s+Pb p -1 = 165 nb int L MBT > 75 GeV jetT p > 100 GeV jetT p UE - UE pairsHS - UE pairs Figure 8.9: Underlying event–underlying event (UE–UE) (open circles) and hard scatter–underlying event (HS–UE) (open squares) particle-pair yield composition fractions for MBT events (black), events with jet p T > GeV (blue), and events with jet p T > GeV (orange) plotted as a function of the A-particle p T . Statisticaluncertainties are shown as narrow vertical lines on each point, and systematic uncertainties are presented ascolored boxes behind the points.fraction of UE–UE pairs than jet-triggered events. In the low and high p T regions, the same types of pairsdominate in both the MBT and jet-triggered events, namely UE–UE and HS–UE respectively, and hence theanisotropy coefficients agree between the event samples. If this explanation is correct, it also aids in understandingFigure 8.7 in which there is a significant difference between the p +Pb jet event v and the Pb+Pb v in theintermediate p T region, because the relative pair fractions are potentially different.This particle mixing picture is attractive in that it naturally explains the general shape of the v ( p T ) and v ( p T ) distributions as well as the ordering of the different event samples. However, it is noted that the corre-spondence between the differences in the flow coefficients and pair fractions is not quantitative; the differencesin the flow coefficients are fractionally much larger than the differences in the pair fractions. Thus, there areeither additional sources of correlation or our assumptions are violated in some way (e.g. the two assumed HSand UE sources are too simplistic or the measured pair fractions do not accurately represent the sources, as isdiscussed in Sec. 7.3.5). That said, for particle p T > GeV, where particle production in any model is thought89 P a i r f r a c t i on ATLAS -1 , 165 nb = 8.16 TeV NN s+Pb p MBT > 75 GeV jetT p > 100 GeV jetT p < 2 GeV A T p UE - UE pairsHS - UE pairs P a i r f r a c t i on ATLAS -1 , 165 nb = 8.16 TeV NN s+Pb p MBT > 75 GeV jetT p > 100 GeV jetT p < 9 GeV A T p UE - UE pairsHS - UE pairs P a i r f r a c t i on ATLAS -1 , 165 nb = 8.16 TeV NN s+Pb p MBT > 75 GeV jetT p > 100 GeV jetT p < 100 GeV A T p UE - UE pairsHS - UE pairs Figure 8.10: Underlying event–underlying event (UE–UE) (open circles) and hard scatter–underlying event(HS–UE) (open squares) particle-pair yield composition fractions for MBT events (black), events with jet p T > GeV (blue), and events with jet p T > GeV (orange) plotted as a function of event centrality. The resultsare obtained in three different selections of the A-particle p T : . < p T < GeV (top left), < p T < GeV(top right), and < p T < GeV (bottom). Statistical uncertainties are shown as narrow vertical lines on eachpoint, and systematic uncertainties are presented as colored boxes behind the points.to arise mainly from jet fragmentation, the non-zero v demonstrates that a positive correlation exists betweenhard (high p T ) and soft (low p T ) particles, irrespective of the pair fractions. hapter 9Conclusions This dissertation presented a study of 8.16 TeV p +Pb collisions generated at CERN’s Large Hadron Col-lider and measured with the ATLAS detector. This study consisted of two novel measurements of particles overa broad range of energy scales, probing initial- and final-state nuclear phenomena; these results are published asRefs. [29, 30].A measurement of the cross section and nuclear modification factor, R p Pb , of prompt and isolated photonswas detailed in Chapters 5 and 6. These results span < E γ T < GeV and were presented from threenucleon–nucleon center-of-mass frame rapidity ranges: forward ( . < η ∗ < . ), middle ( − . < η ∗ < . ), and backward ( − . < η ∗ < − . ). The cross sections, shown in Fig. 6.1, are compared to next-to-leading order pQCD calculations from J using CT14 parton distribution functions [143] with EPPS16nuclear modifications [58]. The theoretical predictions show a discrepancy of 20% at low E γ T that becomesnegligible at high E γ T . This discrepancy is of a similar level as has been observed from previous measurements in pp collisions [116, 117].To isolate the nuclear effects, R p Pb was constructed in the same kinematic range using a pp reference ex-trapolated from 8 TeV data [116]. The results, shown in Fig. 6.3 with forward-over-backward ratios in Fig. 6.4, arelargely consistent with theoretical predictions using both free nucleon PDFs (including effects from the proton–neutron asymmetry of the Pb nucleus) and nuclear modified PDFs. At mid-rapidity and E γ T ≈ GeV, corre-sponding to the shadowing range in nPDFs, the data hint at a preference for the slight modification predicted, butthis is insignificant given the uncertainties in the data. The data are also compared to a prediction from a modelof initial-state energy loss in which the colliding parton in the proton loses energy via gluon bremsstrahlung as it91moves through the nucleus before interacting to create the photon [112, 113, 126]. The data show a preferencefor no energy loss, limiting the allowed amount of initial-state multiple scattering in theoretical models.These photon results are now part of the world data that can be used in the global fit analyses to createfuture refinements of nPDFs. A precise understanding of the partonic structure of nucleons, and the initial statein general, is crucial to the ability to distinguish QGP-related final-state effects when studying strongly inter-acting probes. With this in mind, it would be interesting for future efforts to study prompt photon productiondifferentially in centrality. Not only would this be an especially clean test of Glauber modeling and T AB scaling,the results would be able to confirm that the centrality dependent modification measured in the jet spectra inRef. [18] is indeed the result of an initial-state effect.The second result, presented in Chapters 7 and 8, is a measurement of the azimuthal anisotropy coeffi-cients, v and v , from two-particle correlations of charged hadrons. By selecting events based on the presence ofa high- p T jet, this measurement is able to extend over an unprecedented range in particle p T , for small systems.Fig. 8.1 shows the observation of non-zero elliptic flow reaching p T ≈ GeV. In the context of the standardparadigm, in which anisotropy at low p T is due to a hydrodynamic response to the nuclear geometry and thesignal at high p T is the result of path-length differential jet quenching, this is quite surprising because there isno observed energy loss in p +Pb. Furthermore, this does not appear to be a question of R p Pb measurementsensitivity, since Fig. 8.4 shows that in order to have a level of anisotropy similar to the data, the R p Pb must besuppressed to a level that is inconsistent with measurements (at least within this model).This result casts doubt on the common explanation of the v n signal at high p T in large systems [22–24];at least in the sense that differential energy loss might not be the only component. Moreover, new questionsare raised about the potential origin of the signal in p +Pb. Are final-state effects ruled out? It seems clear thatdroplets of QGP are being formed in small systems; is it possible that the signal is a result of an interactionwith the QGP that does not manifest signs of energy loss? Measurements of jet fragmentation, such as thatof Ref. [170], leave little room for the modification of the particle p T and angular structure within jets. Newprecision measurements of jet or particle yields relative to photons, which are known to be unmodified, wouldprovide the strongest limits to date on possible final-state effects. These measurements could also help to answer92the, perhaps, more general but related question about whether it is possible to create droplets of QGP matterwithout any final state modification to the strongly interacting high- p T objects.On the other hand, the high- p T anisotropy could be due to a speculative initial-state correlation betweenhigh- and low- x partons in the colliding bodies. It is clear from Fig. 8.6 that there are mechanisms included inP’s implementation of initial-state radiation that produce long range azimuthal correlations; however, thesecorrelations are diluted at higher centrality in disagreement with the data. Alternative approaches based on theCGC gluon saturation model have shown that, in p +Pb collisions, it’s possible for initial-state momentum corre-lations to result in significant v for heavy-flavor quarks that can only be produced through hard processes [171].It would be interesting to know if a model similar to this is able to generate correlations of the same type andcentrality scaling behavior as the present data.Lastly, a simple two-component model of particle production was introduced to help explain the observeddiscrepancy in v n between MB and jet events in the mid- p T transition region. In this model, particles originatefrom either the bulk underlying event or from jet-like hard scatterings. Then, the hypothesis is that the particlesin any given range of p T will have a certain fraction of UE and HS particles. Under the presumption of dijet-likeHS particle production, the relative yields of particle pairs from each combination of the classes were estimated,as shown in Figures 8.8, 8.9, and 8.10. These pair fractions show a difference between MB and jet events in themid- p T range, qualitatively consistent with the behavior of the v n values. This raises a question: if the correlationsare a linear combination of two components and the relative fractions of the components are known, can oneextract the pure UE-UE and HS-UE correlations? In this case, the data are incompatible with this picture. Asstated in Sec. 8.3, the differences in the v n are larger than the differences in the pair fractions, and thus, the pairfractions alone are not able to account for the differences in the flow coefficients. However, this model makes itclear that the high- p T flow correlations that are reported in Fig. 8.1 are correlations between particles from hardjet fragmentation and the soft underlying event, and they are not correlations between hard particles themselves.As to what mechanism might cause such a relationship, it is hoped that future theoretical and experimental effortswill shed light and that this work will have contributed to a deeper understanding of the universe. ppendix AMeasurement of Direct Photon SpectraA.1 MC Data E T slice [GeV] σ DP [nb] (cid:15) DP N DPevt p +Pb Data Overlay samples, 8.16 TeV( ∆ y = − . boost) mc15_pPb8TeV.423100.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP17_35* × × − × mc15_pPb8TeV.423101.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP35_50* × × − × mc15_pPb8TeV.423102.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP50_70* × × − × mc15_pPb8TeV.423103.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP70_140* × × − × mc15_pPb8TeV.423104.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP140_280* × × − × mc15_pPb8TeV.423105.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP280_500* × × − × Pb+ p Data Overlay samples, 8.16 TeV( ∆ y = +0 . boost) mc15_pPb8TeV.423100.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP17_35* × × − × mc15_pPb8TeV.423101.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP35_50* × × − × mc15_pPb8TeV.423102.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP50_70* × × − × mc15_pPb8TeV.423103.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP70_140* × × − × mc15_pPb8TeV.423104.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP140_280* × × − × mc15_pPb8TeV.423105.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP280_500* × × − × Generator-only pp signal samples, 8 TeV( ∆ y = 0 , no boost) mc15_8TeV.423104.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP17_35.evgen* × × − . × mc15_8TeV.423104.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP35_50.evgen* × × − . × mc15_8TeV.423104.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP50_70.evgen* × × − . × mc15_8TeV.423104.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP70_140.evgen* × × − . × mc15_8TeV.423104.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP140_280.evgen* × × − . × mc15_8TeV.423104.Pythia8EvtGen_A14NNPDF23LO_gammajet_DP280_500.evgen* × × − . × E T slice [GeV] σ [nb] (cid:15) N evt p +Pb Data Overlay samples, 8.16 TeV( ∆ y = − . boost) mc15_pPb8TeV.420154.Sherpa_224_NNPDF30NNLO_SinglePhotonPt15_35_EtaFilter* × × − × mc15_pPb8TeV.420155.Sherpa_224_NNPDF30NNLO_SinglePhotonPt35_50_EtaFilter* × × − × mc15_pPb8TeV.420156.Sherpa_224_NNPDF30NNLO_SinglePhotonPt50_70_EtaFilter* × × − × mc15_pPb8TeV.420157.Sherpa_224_NNPDF30NNLO_SinglePhotonPt70_140_EtaFilter* × × − × mc15_pPb8TeV.420158.Sherpa_224_NNPDF30NNLO_SinglePhotonPt140_280_EtaFilter* × × − × mc15_pPb8TeV.420159.Sherpa_224_NNPDF30NNLO_SinglePhotonPt280_500_EtaFilter* × × − × Pb+ p Data Overlay samples, 8.16 TeV( ∆ y = +0 . boost) mc15_pPb8TeV.420154.Sherpa_224_NNPDF30NNLO_SinglePhotonPt15_35_EtaFilter* × × − × mc15_pPb8TeV.420155.Sherpa_224_NNPDF30NNLO_SinglePhotonPt35_50_EtaFilter* × × − × mc15_pPb8TeV.420156.Sherpa_224_NNPDF30NNLO_SinglePhotonPt50_70_EtaFilter* × × − × mc15_pPb8TeV.420157.Sherpa_224_NNPDF30NNLO_SinglePhotonPt70_140_EtaFilter* × × − × mc15_pPb8TeV.420158.Sherpa_224_NNPDF30NNLO_SinglePhotonPt140_280_EtaFilter* × × − × mc15_pPb8TeV.420159.Sherpa_224_NNPDF30NNLO_SinglePhotonPt280_500_EtaFilter* × × − × A.2 Cross section calculation data Table A.3: Table of components in the N sigA calculation in center of mass rapidity range (1 . < η ∗ < . .Yields are each quoted after prescale correction E T low E T high N A N B N C N D f B f C f D N sigA Error (%)20 GeV 25 GeV 672821 124311 466354 153628 0.0018 0.0808 0.0003 317642 6.84925 GeV 35 GeV 395205 109405 206615 123121 0.0029 0.0555 0.0002 223596 3.16935 GeV 45 GeV 97645 37004 35378 37037 0.0027 0.0434 0.0002 65274 1.06045 GeV 55 GeV 33865 15524 9627 16394 0.0030 0.0356 0.0002 25653 0.99755 GeV 65 GeV 14147 7448 3284 8627 0.0029 0.0317 0.0002 11641 1.29965 GeV 75 GeV 6629 3913 1419 4936 0.0040 0.0305 0.0002 5646 1.77575 GeV 85 GeV 3471 2214 664 3112 0.0046 0.0289 0.0002 3064 2.29485 GeV 105 GeV 3138 2178 510 3146 0.0050 0.0277 0.0003 2841 2.308105 GeV 125 GeV 1222 936 193 1537 0.0050 0.0252 0.0003 1122 3.595125 GeV 150 GeV 623 484 78 947 0.0073 0.0271 0.0008 591 4.758150 GeV 175 GeV 278 217 34 458 0.0067 0.0262 0.0004 265 7.063175 GeV 200 GeV 148 115 7 228 0.0077 0.0275 0.0006 146 9.213200 GeV 250 GeV 94 95 5 211 0.0083 0.0269 0.0005 93 11.542250 GeV 350 GeV 49 41 1 95 0.0092 0.0267 0.0009 49 15.643350 GeV 550 GeV 7 2 3 19 0.0141 0.0309 0.0012 6 44.508 Table A.4: Table of components in the N sigA calculation in center of mass rapidity range ( − . < η ∗ < . .Yields are each quoted after prescale correction E T low E T high N A N B N C N D f B f C f D N sigA Error (%)20 GeV 25 GeV 2417784 456241 1687869 549793 0.0026 0.0740 0.0002 1091930 3.36325 GeV 35 GeV 1382959 331933 796584 403765 0.0028 0.0464 0.0002 760835 1.58135 GeV 45 GeV 346858 110494 135962 125226 0.0029 0.0291 0.0001 233566 0.53045 GeV 55 GeV 120035 46681 34341 49597 0.0031 0.0232 0.0001 89853 0.49655 GeV 65 GeV 49222 22303 11437 23128 0.0034 0.0193 0.0001 38981 0.73465 GeV 75 GeV 23190 11638 4694 12382 0.0033 0.0180 0.0001 19123 0.92375 GeV 85 GeV 12160 6336 2044 7450 0.0038 0.0168 0.0001 10583 1.14985 GeV 105 GeV 10890 6222 1695 7675 0.0037 0.0160 0.0001 9648 1.173105 GeV 125 GeV 4192 2590 572 3424 0.0041 0.0159 0.0001 3807 1.808125 GeV 150 GeV 2159 1458 247 2184 0.0044 0.0161 0.0001 2017 2.399150 GeV 175 GeV 936 631 83 1072 0.0045 0.0156 0.0001 896 3.508175 GeV 200 GeV 438 312 29 559 0.0055 0.0156 0.0001 426 5.013200 GeV 250 GeV 362 270 18 519 0.0055 0.0148 0.0002 355 5.435250 GeV 300 GeV 116 109 5 202 0.0063 0.0154 0.0004 114 9.443300 GeV 350 GeV 46 45 2 78 0.0062 0.0153 0.0003 45 15.146350 GeV 400 GeV 21 24 1 42 0.0069 0.0147 0.0003 21 22.602400 GeV 550 GeV 13 21 1 23 0.0078 0.0167 0.0002 13 28.655 N sigA calculation in center of mass rapidity range ( − . < η ∗ < − . .Yields are each quoted after prescale correction E T low E T high N A N B N C N D f B f C f D N sigA Error (%)20 GeV 25 GeV 590254 129265 393165 140692 0.0043 0.0796 0.0003 249931 7.23225 GeV 35 GeV 343385 97396 175942 108025 0.0044 0.0594 0.0002 196530 2.99735 GeV 45 GeV 85099 32817 30019 34787 0.0050 0.0451 0.0004 59531 1.06845 GeV 55 GeV 28773 14329 7915 14802 0.0063 0.0362 0.0002 21945 1.15155 GeV 65 GeV 11520 6673 2776 7482 0.0056 0.0318 0.0004 9325 1.41865 GeV 75 GeV 5164 3378 1141 4107 0.0065 0.0320 0.0004 4346 1.96275 GeV 85 GeV 2521 1917 511 2520 0.0068 0.0305 0.0003 2186 2.63785 GeV 105 GeV 2143 1740 378 2625 0.0066 0.0277 0.0004 1930 2.673105 GeV 125 GeV 799 654 114 1116 0.0078 0.0295 0.0003 746 4.160125 GeV 150 GeV 331 331 46 581 0.0086 0.0229 0.0009 309 6.405150 GeV 175 GeV 118 128 29 269 0.0081 0.0245 0.0005 105 11.186175 GeV 200 GeV 57 42 2 103 0.0088 0.0250 0.0004 57 14.639200 GeV 250 GeV 28 43 1 71 0.0095 0.0221 0.0010 28 20.170250 GeV 350 GeV 10 6 1 21 0.0087 0.0226 0.0010 10 33.534350 GeV 550 GeV 0 1 1 1 0.0168 0.0247 0.0009 0 0 A.3 P- Efficiency data Table A.6: Table of efficiency values in period A in center of mass rapidity range (1 . < η ∗ < . . E T low E T high (cid:15) Reco (cid:15) Reco × ID (cid:15) Reco × ID × Iso Bin migration20 GeV 25 GeV 0.9647 0.7931 0.7845 1.012425 GeV 35 GeV 0.9721 0.8644 0.8542 1.010635 GeV 45 GeV 0.9730 0.8969 0.8848 1.004945 GeV 55 GeV 0.9743 0.9216 0.9073 0.995955 GeV 65 GeV 0.9749 0.9235 0.9093 0.994665 GeV 75 GeV 0.9771 0.9257 0.9090 0.991175 GeV 85 GeV 0.9760 0.9278 0.9093 0.999585 GeV 105 GeV 0.9743 0.9301 0.9121 0.9960105 GeV 125 GeV 0.9706 0.9276 0.9097 1.0023125 GeV 150 GeV 0.9800 0.9306 0.9137 0.9846150 GeV 175 GeV 0.9765 0.9278 0.9035 0.9989175 GeV 200 GeV 0.9768 0.9214 0.8954 1.0071200 GeV 250 GeV 0.9792 0.9263 0.8984 0.9984250 GeV 350 GeV 0.9771 0.9189 0.8874 0.9951350 GeV 550 GeV 0.9812 0.9138 0.8758 1.0002Table A.7: Table of efficiency values in period B in center of mass rapidity range (1 . < η ∗ < . . E T low E T high (cid:15) Reco (cid:15) Reco × ID (cid:15) Reco × ID × Iso Bin migration20 GeV 25 GeV 0.9628 0.7847 0.7756 1.012425 GeV 35 GeV 0.9694 0.8552 0.8430 1.010635 GeV 45 GeV 0.9704 0.8906 0.8773 1.004945 GeV 55 GeV 0.9692 0.9129 0.8980 0.995955 GeV 65 GeV 0.9709 0.9117 0.8971 0.994665 GeV 75 GeV 0.9707 0.9113 0.8956 0.991175 GeV 85 GeV 0.9720 0.9198 0.9024 0.999585 GeV 105 GeV 0.9716 0.9230 0.9031 0.9960105 GeV 125 GeV 0.9702 0.9214 0.9009 1.0023125 GeV 150 GeV 0.9725 0.9241 0.8999 0.9846150 GeV 175 GeV 0.9726 0.9201 0.8959 0.9989175 GeV 200 GeV 0.9701 0.9159 0.8902 1.0071200 GeV 250 GeV 0.9727 0.9157 0.8868 0.9984250 GeV 350 GeV 0.9763 0.9124 0.8816 0.9951350 GeV 550 GeV 0.9752 0.9068 0.8684 1.000299Table A.8: Table of efficiency values in from both running periods as the luminosity weighted average in centerof mass rapidity range (1 . < η ∗ < . . E T low E T high (cid:15) Reco (cid:15) Reco × ID (cid:15) Reco × ID × Iso Bin migration20 GeV 25 GeV 0.9635 0.7876 0.7787 1.015025 GeV 35 GeV 0.9703 0.8584 0.8469 1.003435 GeV 45 GeV 0.9713 0.8928 0.8799 1.007745 GeV 55 GeV 0.9710 0.9159 0.9012 0.989955 GeV 65 GeV 0.9723 0.9158 0.9013 0.991065 GeV 75 GeV 0.9729 0.9162 0.9002 0.997675 GeV 85 GeV 0.9733 0.9226 0.9048 0.998885 GeV 105 GeV 0.9726 0.9255 0.9062 0.9917105 GeV 125 GeV 0.9703 0.9235 0.9039 0.9932125 GeV 150 GeV 0.9751 0.9263 0.9047 0.9899150 GeV 175 GeV 0.9739 0.9228 0.8985 0.9958175 GeV 200 GeV 0.9724 0.9178 0.8920 0.9938200 GeV 250 GeV 0.9750 0.9193 0.8908 0.9944250 GeV 350 GeV 0.9766 0.9146 0.8836 0.9846350 GeV 550 GeV 0.9773 0.9092 0.8710 0.9888Table A.9: Table of efficiency values in period A in center of mass rapidity range (0 . < η ∗ < − . . E T low E T high (cid:15) Reco (cid:15) Reco × ID (cid:15) Reco × ID × Iso Bin migration20 GeV 25 GeV 0.9812 0.8142 0.8039 1.016825 GeV 35 GeV 0.9858 0.8766 0.8660 1.006335 GeV 45 GeV 0.9884 0.9193 0.9078 1.013245 GeV 55 GeV 0.9894 0.9311 0.9202 0.998055 GeV 65 GeV 0.9903 0.9406 0.9280 1.003565 GeV 75 GeV 0.9902 0.9424 0.9303 0.999475 GeV 85 GeV 0.9897 0.9436 0.9295 1.000085 GeV 105 GeV 0.9901 0.9430 0.9300 0.9957105 GeV 125 GeV 0.9896 0.9426 0.9281 1.0041125 GeV 150 GeV 0.9895 0.9415 0.9274 0.9995150 GeV 175 GeV 0.9909 0.9425 0.9288 0.9974175 GeV 200 GeV 0.9910 0.9421 0.9261 0.9922200 GeV 250 GeV 0.9911 0.9397 0.9241 0.9995250 GeV 300 GeV 0.9915 0.9360 0.9187 0.9900300 GeV 350 GeV 0.9928 0.9401 0.9244 0.9937350 GeV 400 GeV 0.9926 0.9403 0.9222 0.9991400 GeV 550 GeV 0.9926 0.9366 0.9179 0.993500Table A.10: Table of efficiency values in period B in center of mass rapidity range (0 . < η ∗ < − . . E T low E T high (cid:15) Reco (cid:15) Reco × ID (cid:15) Reco × ID × Iso Bin migration20 GeV 25 GeV 0.9803 0.8045 0.7928 1.016825 GeV 35 GeV 0.9843 0.8690 0.8546 1.006335 GeV 45 GeV 0.9875 0.9164 0.9018 1.013245 GeV 55 GeV 0.9885 0.9311 0.9161 0.998055 GeV 65 GeV 0.9896 0.9382 0.9219 1.003565 GeV 75 GeV 0.9896 0.9405 0.9246 0.999475 GeV 85 GeV 0.9899 0.9420 0.9257 1.000085 GeV 105 GeV 0.9898 0.9434 0.9271 0.9957105 GeV 125 GeV 0.9898 0.9433 0.9269 1.0041125 GeV 150 GeV 0.9905 0.9418 0.9251 0.9995150 GeV 175 GeV 0.9907 0.9427 0.9256 0.9974175 GeV 200 GeV 0.9905 0.9387 0.9191 0.9922200 GeV 250 GeV 0.9908 0.9407 0.9233 0.9995250 GeV 300 GeV 0.9921 0.9401 0.9222 0.9900300 GeV 350 GeV 0.9924 0.9380 0.9187 0.9937350 GeV 400 GeV 0.9921 0.9375 0.9183 0.9991400 GeV 550 GeV 0.9923 0.9339 0.9127 0.9935Table A.11: Table of efficiency values in from both running periods as the luminosity weighted average in centerof mass rapidity range (0 . < η ∗ < − . . E T low E T high (cid:15) Reco (cid:15) Reco × ID (cid:15) Reco × ID × Iso Bin migration20 GeV 25 GeV 0.9806 0.8079 0.7966 1.020325 GeV 35 GeV 0.9848 0.8717 0.8586 1.009235 GeV 45 GeV 0.9878 0.9174 0.9038 1.011245 GeV 55 GeV 0.9888 0.9311 0.9175 1.003255 GeV 65 GeV 0.9899 0.9390 0.9240 1.004765 GeV 75 GeV 0.9898 0.9411 0.9266 0.998475 GeV 85 GeV 0.9898 0.9426 0.9270 0.998985 GeV 105 GeV 0.9899 0.9433 0.9281 0.9982105 GeV 125 GeV 0.9897 0.9431 0.9273 1.0015125 GeV 150 GeV 0.9902 0.9417 0.9259 1.0007150 GeV 175 GeV 0.9908 0.9427 0.9267 0.9969175 GeV 200 GeV 0.9907 0.9399 0.9215 0.9984200 GeV 250 GeV 0.9909 0.9404 0.9236 0.9984250 GeV 300 GeV 0.9919 0.9387 0.9210 0.9909300 GeV 350 GeV 0.9926 0.9387 0.9207 0.9924350 GeV 400 GeV 0.9923 0.9384 0.9196 0.9979400 GeV 550 GeV 0.9924 0.9348 0.9145 0.993101Table A.12: Table of efficiency values in period A in center of mass rapidity range ( − . < η ∗ < − . . E T low E T high (cid:15) Reco (cid:15) Reco × ID (cid:15) Reco × ID × Iso Bin migration20 GeV 25 GeV 0.9641 0.7957 0.7834 1.004725 GeV 35 GeV 0.9651 0.8542 0.8406 1.006935 GeV 45 GeV 0.9692 0.8890 0.8723 0.997245 GeV 55 GeV 0.9710 0.9168 0.8966 0.999855 GeV 65 GeV 0.9725 0.9169 0.8990 0.984565 GeV 75 GeV 0.9737 0.9164 0.8965 1.003475 GeV 85 GeV 0.9715 0.9183 0.8939 0.994285 GeV 105 GeV 0.9706 0.9219 0.9005 0.9918105 GeV 125 GeV 0.9778 0.9304 0.9082 0.9741125 GeV 150 GeV 0.9723 0.9347 0.9034 1.0134150 GeV 175 GeV 0.9695 0.9213 0.8954 0.9998175 GeV 200 GeV 0.9762 0.9304 0.9067 0.9879200 GeV 250 GeV 0.9764 0.9204 0.8868 0.9700250 GeV 350 GeV 0.9807 0.9218 0.8992 0.9758350 GeV 550 GeV 0.9692 0.9184 0.8850 0.9819Table A.13: Table of efficiency values in period B in center of mass rapidity range ( − . < η ∗ < − . . E T low E T high (cid:15) Reco (cid:15) Reco × ID (cid:15) Reco × ID × Iso Bin migration20 GeV 25 GeV 0.9633 0.7774 0.7600 1.004725 GeV 35 GeV 0.9685 0.8483 0.8261 1.006935 GeV 45 GeV 0.9721 0.8916 0.8660 0.997245 GeV 55 GeV 0.9732 0.9159 0.8871 0.999855 GeV 65 GeV 0.9718 0.9168 0.8877 0.984565 GeV 75 GeV 0.9731 0.9182 0.8864 1.003475 GeV 85 GeV 0.9745 0.9253 0.8923 0.994285 GeV 105 GeV 0.9753 0.9307 0.8970 0.9918105 GeV 125 GeV 0.9764 0.9324 0.8962 0.9741125 GeV 150 GeV 0.9762 0.9415 0.9046 1.0134150 GeV 175 GeV 0.9756 0.9324 0.8942 0.9998175 GeV 200 GeV 0.9764 0.9287 0.8887 0.9879200 GeV 250 GeV 0.9806 0.9374 0.8998 0.9700250 GeV 350 GeV 0.9758 0.9297 0.8940 0.9758350 GeV 550 GeV 0.9842 0.9346 0.8882 0.981902Table A.14: Table of efficiency values in from both running periods as the luminosity weighted average in centerof mass rapidity range ( − . < η ∗ < − . . E T low E T high (cid:15) Reco (cid:15) Reco × ID (cid:15) Reco × ID × Iso Bin migration20 GeV 25 GeV 0.9636 0.7837 0.7680 1.012025 GeV 35 GeV 0.9673 0.8503 0.8311 1.014335 GeV 45 GeV 0.9711 0.8907 0.8682 0.998745 GeV 55 GeV 0.9725 0.9162 0.8903 1.001755 GeV 65 GeV 0.9720 0.9169 0.8916 0.994265 GeV 75 GeV 0.9733 0.9176 0.8899 1.007175 GeV 85 GeV 0.9735 0.9228 0.8929 0.997685 GeV 105 GeV 0.9737 0.9277 0.8982 0.9981105 GeV 125 GeV 0.9769 0.9317 0.9003 0.9896125 GeV 150 GeV 0.9749 0.9392 0.9042 1.0063150 GeV 175 GeV 0.9735 0.9285 0.8946 1.0035175 GeV 200 GeV 0.9763 0.9293 0.8949 0.9891200 GeV 250 GeV 0.9792 0.9315 0.8953 0.9878250 GeV 350 GeV 0.9775 0.9270 0.8958 0.9915350 GeV 550 GeV 0.9791 0.9290 0.8871 0.986903 A.4 P- Purity data Table A.15: Table of inputs for the purity calculation for the forward-rapidity bin, showing raw sideband yields N X , sideband leakage fractions from MC f X , and the final purity with asymmetrical errors. E T low E T high N A N B N C N D f B f C f D P Error low Error high20 GeV 25 GeV 5889 1125 3971 1330 0.0012 0.0794 0.0000 0.46208 0.03633 0.0366725 GeV 35 GeV 11080 3165 5674 3481 0.0022 0.0562 0.0002 0.56502 0.01927 0.0197335 GeV 45 GeV 40297 15559 13560 16229 0.0020 0.0429 0.0003 0.70741 0.00666 0.0063445 GeV 55 GeV 33865 15524 9627 16394 0.0030 0.0349 0.0002 0.75702 0.00577 0.0062355 GeV 65 GeV 14147 7448 3284 8627 0.0026 0.0288 0.0000 0.82074 0.00699 0.0070165 GeV 75 GeV 6629 3913 1419 4936 0.0040 0.0293 0.0001 0.85083 0.00908 0.0089275 GeV 85 GeV 3471 2214 664 3112 0.0054 0.0309 0.0001 0.88414 0.00939 0.0096185 GeV 105 GeV 3138 2178 510 3146 0.0049 0.0257 0.0001 0.90414 0.00839 0.00861105 GeV 125 GeV 1222 936 193 1537 0.0042 0.0224 0.0003 0.91650 0.01225 0.01175125 GeV 150 GeV 623 484 78 947 0.0053 0.0282 0.0012 0.94999 0.01174 0.01126150 GeV 175 GeV 278 217 34 458 0.0065 0.0254 0.0006 0.95451 0.01626 0.01674175 GeV 200 GeV 148 115 7 228 0.0080 0.0289 0.0002 0.99172 0.02047 0.01803200 GeV 250 GeV 94 95 5 211 0.0076 0.0234 0.0006 0.98667 0.01492 0.01358250 GeV 350 GeV 49 41 0 95 0.0101 0.0238 0.0013 1.00000 0.01325 0.00000350 GeV 550 GeV 7 2 3 19 0.0142 0.0299 0.0012 0.95173 0.12248 0.04827 Table A.16: Table of inputs for the purity calculation for the mid-rapidity bin, showing raw sideband yields N X ,sideband leakage fractions from MC f X , and the final purity with asymmetrical errors. E T low E T high N A N B N C N D f B f C f D P Error low Error high20 GeV 25 GeV 20811 3883 14457 4723 0.0021 0.0726 0.0001 0.45889 0.01964 0.0193625 GeV 35 GeV 38920 9694 21698 11671 0.0020 0.0462 0.0001 0.56032 0.01057 0.0104335 GeV 45 GeV 143333 48218 52076 53646 0.0024 0.0294 0.0001 0.69322 0.00347 0.0035345 GeV 55 GeV 120035 46681 34341 49597 0.0026 0.0241 0.0001 0.74893 0.00318 0.0028255 GeV 65 GeV 49222 22303 11437 23128 0.0029 0.0191 0.0001 0.79154 0.00879 0.0092165 GeV 75 GeV 23190 11638 4694 12382 0.0024 0.0184 0.0001 0.82471 0.00546 0.0055475 GeV 85 GeV 12160 6336 2044 7450 0.0035 0.0163 0.0001 0.86987 0.00562 0.0053885 GeV 105 GeV 10890 6222 1695 7675 0.0032 0.0169 0.0001 0.88651 0.00526 0.00574105 GeV 125 GeV 4192 2590 572 3424 0.0031 0.0158 0.0000 0.90802 0.00727 0.00773125 GeV 150 GeV 2159 1458 247 2184 0.0042 0.0168 0.0001 0.93449 0.00824 0.00776150 GeV 175 GeV 936 631 83 1072 0.0040 0.0152 0.0001 0.95658 0.00883 0.00917175 GeV 200 GeV 438 312 29 559 0.0052 0.0150 0.0001 0.97136 0.01111 0.01089200 GeV 250 GeV 362 270 18 519 0.0056 0.0163 0.0002 0.98262 0.00887 0.00913250 GeV 300 GeV 116 109 5 202 0.0062 0.0165 0.0004 0.98559 0.01384 0.01416300 GeV 350 GeV 46 45 2 78 0.0054 0.0155 0.0002 0.98382 0.02757 0.01618350 GeV 400 GeV 21 24 1 42 0.0067 0.0158 0.0003 0.98173 0.05298 0.01827400 GeV 550 GeV 13 21 0 23 0.0071 0.0168 0.0002 1.00000 0.13625 0.00000 N X , sideband leakage fractions from MC f X , and the final purity with asymmetrical errors. E T low E T high N A N B N C N D f B f C f D P Error low Error high20 GeV 25 GeV 5129 1077 3337 1210 0.0033 0.0754 0.0001 0.45545 0.03870 0.0383025 GeV 35 GeV 9725 2766 4719 3061 0.0023 0.0565 0.0001 0.59365 0.01890 0.0191035 GeV 45 GeV 34925 14443 11258 14714 0.0042 0.0449 0.0003 0.71708 0.00683 0.0071745 GeV 55 GeV 28773 14329 7915 14802 0.0050 0.0327 0.0002 0.75954 0.00629 0.0067155 GeV 65 GeV 11520 6673 2776 7482 0.0039 0.0300 0.0002 0.80766 0.00791 0.0080965 GeV 75 GeV 5164 3378 1141 4107 0.0049 0.0326 0.0002 0.84178 0.01003 0.0099775 GeV 85 GeV 2521 1917 511 2520 0.0056 0.0317 0.0003 0.86760 0.01235 0.0126585 GeV 105 GeV 2143 1740 378 2625 0.0049 0.0287 0.0002 0.90088 0.01063 0.01037105 GeV 125 GeV 799 654 114 1116 0.0070 0.0276 0.0000 0.93230 0.01305 0.01295125 GeV 150 GeV 331 331 46 581 0.0104 0.0261 0.0014 0.93536 0.01961 0.01939150 GeV 175 GeV 118 128 29 269 0.0065 0.0253 0.0006 0.89538 0.04013 0.03987175 GeV 200 GeV 57 42 2 103 0.0065 0.0250 0.0000 0.99597 0.01522 0.00403200 GeV 250 GeV 28 43 1 71 0.0103 0.0285 0.0007 0.99559 0.03534 0.00441250 GeV 350 GeV 10 6 0 21 0.0062 0.0295 0.0003 1.00000 0.08575 0.00000350 GeV 550 GeV 0 0 0 0 0.0117 0.0272 0.0009 0.00000 0.00000 0.00000 A.5 Total systematic uncertainty data Table A.18: Table of components of the total systematic uncertainty on the cross section shown as percents foreach p T bin in center of mass rapidity range (0 . < η ∗ < − . . E T low E T high E-scale low E-scale high Purity low Purity high Other low Other high Total low Total high20 GeV 25 GeV 12.67 12.63 6.20 6.29 3.56 3.56 14.54 14.5525 GeV 35 GeV 8.24 8.15 3.12 3.39 3.53 3.53 9.49 9.5035 GeV 45 GeV 4.45 4.40 3.05 2.77 3.51 3.51 6.43 6.2745 GeV 55 GeV 3.48 3.45 3.53 3.46 3.48 3.48 6.06 6.0055 GeV 65 GeV 2.43 2.42 3.56 3.57 3.45 3.45 5.52 5.5365 GeV 75 GeV 2.05 2.04 3.91 3.74 3.42 3.42 5.59 5.4675 GeV 85 GeV 1.62 1.63 3.79 3.86 3.40 3.40 5.34 5.3985 GeV 105 GeV 1.40 1.41 4.09 4.43 3.15 3.15 5.35 5.62105 GeV 125 GeV 1.30 1.30 4.74 4.93 3.12 3.12 5.82 5.98125 GeV 150 GeV 1.05 1.05 4.85 4.74 3.09 3.09 5.85 5.75150 GeV 175 GeV 1.02 1.02 6.34 6.64 3.06 3.06 7.12 7.39175 GeV 200 GeV 0.90 0.90 6.92 6.33 3.03 3.03 7.61 7.08200 GeV 250 GeV 0.91 0.91 7.34 8.65 3.01 3.01 7.99 9.20250 GeV 350 GeV 0.89 0.89 9.26 8.46 2.98 2.98 9.77 9.01350 GeV 550 GeV 1.13 1.04 12.06 14.55 2.95 2.95 12.46 14.88 Table A.19: Table of components of the total systematic uncertainty on the cross section shown as percents foreach p T bin in center of mass rapidity range (0 . < η ∗ < − . . E T low E T high E-scale low E-scale high Purity low Purity high Other low Other high Total low Total high20 GeV 25 GeV 15.67 15.52 3.08 3.07 2.98 2.98 16.25 16.1025 GeV 35 GeV 11.10 11.02 1.64 1.67 2.95 2.95 11.60 11.5335 GeV 45 GeV 7.33 7.31 1.52 1.54 2.92 2.92 8.03 8.0245 GeV 55 GeV 5.58 5.58 1.54 1.47 2.90 2.90 6.47 6.4655 GeV 65 GeV 4.28 4.26 1.63 1.54 2.87 2.87 5.40 5.3665 GeV 75 GeV 3.23 3.23 1.61 1.52 2.84 2.84 4.59 4.5675 GeV 85 GeV 2.22 2.21 1.75 1.62 2.81 2.81 3.99 3.9385 GeV 105 GeV 1.59 1.58 1.48 1.46 2.79 2.79 3.54 3.52105 GeV 125 GeV 1.36 1.37 2.06 1.63 2.76 2.76 3.70 3.49125 GeV 150 GeV 1.14 1.14 2.08 2.19 2.74 2.74 3.62 3.68150 GeV 175 GeV 1.01 1.01 2.74 2.45 2.71 2.71 3.98 3.79175 GeV 200 GeV 0.95 0.95 2.61 2.53 2.68 2.68 3.86 3.80200 GeV 250 GeV 0.92 0.91 2.84 2.60 2.66 2.66 3.99 3.83250 GeV 300 GeV 0.91 0.91 3.29 3.26 2.63 2.63 4.31 4.28300 GeV 350 GeV 0.91 0.91 3.36 2.95 2.60 2.60 4.35 4.04350 GeV 400 GeV 0.92 0.92 3.71 3.21 2.58 2.58 4.61 4.22400 GeV 550 GeV 0.90 0.90 5.91 5.48 2.55 2.55 6.50 6.12 p T bin in center of mass rapidity range ( − . < η ∗ < − . . E T low E T high E-scale low E-scale high Purity low Purity high Other low Other high Total low Total high20 GeV 25 GeV 13.31 13.09 5.18 5.20 3.90 3.90 14.80 14.6225 GeV 35 GeV 7.35 7.29 2.88 2.89 3.87 3.87 8.79 8.7435 GeV 45 GeV 4.34 4.21 3.16 3.29 3.83 3.83 6.60 6.5845 GeV 55 GeV 3.43 3.42 3.17 3.37 3.80 3.80 6.02 6.1255 GeV 65 GeV 2.66 2.62 3.46 3.71 3.77 3.77 5.77 5.9065 GeV 75 GeV 2.17 2.18 3.82 3.38 3.73 3.73 5.77 5.4975 GeV 85 GeV 1.81 1.81 4.10 4.00 3.70 3.70 5.81 5.7485 GeV 105 GeV 1.44 1.46 3.91 4.14 3.46 3.46 5.41 5.59105 GeV 125 GeV 1.15 1.16 3.47 4.32 3.42 3.42 5.01 5.63125 GeV 150 GeV 1.15 1.13 4.89 4.35 3.39 3.39 6.06 5.63150 GeV 175 GeV 1.48 1.51 5.46 5.86 3.35 3.35 6.58 6.92175 GeV 200 GeV 0.88 0.88 6.24 5.85 3.32 3.32 7.12 6.78200 GeV 250 GeV 0.88 0.88 6.46 7.56 3.28 3.28 7.30 8.29250 GeV 350 GeV 0.88 0.88 9.04 8.28 3.24 3.24 9.64 8.94350 GeV 550 GeV 0.88 0.88 10.35 12.53 3.21 3.21 10.87 12.96 Table A.21: Table of components of the total systematic uncertainty on R p Pb shown as percents for each p T binin center of mass rapidity range (0 . < η ∗ < − . . E T low E T high p+Pb CS low p+Pb CS high p+p CS low p+p CS high Extrapolation low Extrapolation high Total low Total high25 GeV 35 GeV 9.17 9.17 11.52 11.74 1.20 1.20 14.77 14.9435 GeV 45 GeV 5.99 5.99 7.97 7.97 0.88 0.88 10.02 10.0145 GeV 55 GeV 5.50 5.50 5.94 5.95 0.64 0.64 8.12 8.1355 GeV 65 GeV 4.93 4.93 4.69 4.74 0.44 0.44 6.82 6.8665 GeV 75 GeV 5.08 5.08 4.16 4.21 0.27 0.27 6.57 6.6175 GeV 85 GeV 4.62 4.62 3.87 3.89 0.12 0.12 6.03 6.0485 GeV 105 GeV 5.13 5.13 3.80 3.82 0.07 0.07 6.39 6.40105 GeV 125 GeV 4.74 4.74 3.83 3.83 0.28 0.28 6.10 6.10125 GeV 150 GeV 5.03 5.03 4.04 4.03 0.47 0.47 6.47 6.46150 GeV 175 GeV 5.74 5.74 4.83 4.83 0.66 0.66 7.53 7.53175 GeV 200 GeV 6.36 6.36 4.96 4.95 0.81 0.81 8.10 8.10200 GeV 250 GeV 6.88 6.88 5.51 5.49 1.01 1.01 8.87 8.86250 GeV 350 GeV 7.90 7.90 7.32 7.09 1.32 1.32 10.86 10.70350 GeV 550 GeV 10.63 10.63 10.95 10.36 1.77 1.77 15.36 14.95 Table A.22: Table of components of the total systematic uncertainty on R p Pb shown as percents for each p T binin center of mass rapidity range (0 . < η ∗ < − . . E T low E T high p+Pb CS low p+Pb CS high p+p CS low p+p CS high Extrapolation low Extrapolation high Total low Total high25 GeV 35 GeV 11.34 11.34 12.13 12.22 0.53 0.53 16.61 16.6835 GeV 45 GeV 7.71 7.71 8.21 8.24 0.64 0.64 11.28 11.3045 GeV 55 GeV 6.11 6.11 5.82 5.83 0.73 0.73 8.47 8.4855 GeV 65 GeV 5.00 5.00 4.37 4.38 0.81 0.81 6.69 6.7065 GeV 75 GeV 4.15 4.15 3.48 3.48 0.87 0.87 5.48 5.4975 GeV 85 GeV 3.48 3.48 3.02 3.03 0.92 0.92 4.70 4.7185 GeV 105 GeV 3.06 3.06 2.66 2.66 0.99 0.99 4.18 4.18105 GeV 125 GeV 3.18 3.18 2.52 2.51 1.07 1.07 4.19 4.19125 GeV 150 GeV 3.09 3.09 2.53 2.54 1.14 1.14 4.16 4.16150 GeV 175 GeV 3.53 3.53 2.61 2.62 1.21 1.21 4.55 4.56175 GeV 200 GeV 3.41 3.41 2.70 2.70 1.27 1.27 4.53 4.53200 GeV 250 GeV 3.57 3.57 2.79 2.76 1.34 1.34 4.72 4.71250 GeV 300 GeV 3.93 3.93 2.92 2.89 1.42 1.42 5.10 5.08300 GeV 350 GeV 3.99 3.99 3.15 3.11 1.49 1.49 5.29 5.27350 GeV 400 GeV 4.28 4.28 3.40 3.39 1.55 1.55 5.69 5.67400 GeV 550 GeV 6.28 6.28 3.73 3.75 1.64 1.64 7.49 7.49 R p Pb shown as percents for each p T binin center of mass rapidity range ( − . < η ∗ < − . . E T low E T high p+Pb CS low p+Pb CS high p+p CS low p+p CS high Extrapolation low Extrapolation high Total low Total high25 GeV 35 GeV 8.62 8.62 11.52 11.74 2.14 2.14 14.55 14.7235 GeV 45 GeV 6.33 6.33 7.97 7.97 2.22 2.22 10.42 10.4245 GeV 55 GeV 5.89 5.89 5.94 5.95 2.28 2.28 8.67 8.6855 GeV 65 GeV 5.53 5.53 4.69 4.74 2.33 2.33 7.61 7.6565 GeV 75 GeV 5.51 5.51 4.16 4.21 2.37 2.37 7.30 7.3375 GeV 85 GeV 5.67 5.67 3.87 3.89 2.40 2.40 7.27 7.2885 GeV 105 GeV 5.48 5.48 3.80 3.82 2.45 2.45 7.11 7.12105 GeV 125 GeV 5.55 5.55 3.83 3.83 2.50 2.50 7.19 7.20125 GeV 150 GeV 6.13 6.13 4.04 4.03 2.55 2.55 7.77 7.76150 GeV 175 GeV 7.52 7.52 4.83 4.83 2.59 2.59 9.30 9.30175 GeV 200 GeV 7.80 7.80 4.96 4.95 2.63 2.63 9.61 9.60200 GeV 250 GeV 8.39 8.39 5.51 5.49 2.68 2.68 10.39 10.38250 GeV 350 GeV 11.37 11.37 7.32 7.09 2.75 2.75 13.80 13.68350 GeV 550 GeV 12.89 12.89 10.95 10.36 2.86 2.86 17.15 16.78 Table A.24: Table of components of the total systematic uncertainty for the forward-to-backward R p Pb ratioshown as percents for each p T bin. E T low E T high E-scale low E-scale high Purity low Purity high Other low Other high Extrapolation low Extrapolation high Total low Total high20 GeV 25 GeV 3.43 5.01 1.72 1.67 1.07 1.07 2.56 2.56 4.74 5.9725 GeV 35 GeV 2.15 1.95 1.18 1.07 1.07 1.07 2.46 2.46 3.63 3.4835 GeV 45 GeV 1.62 1.64 1.37 1.21 1.07 1.07 2.39 2.39 3.37 3.3245 GeV 55 GeV 1.58 1.57 1.11 1.17 1.07 1.07 2.37 2.37 3.23 3.2655 GeV 65 GeV 1.59 1.63 1.07 1.12 1.06 1.06 2.37 2.37 3.23 3.2665 GeV 75 GeV 1.59 1.58 1.05 1.21 1.06 1.06 2.38 2.38 3.23 3.2875 GeV 85 GeV 1.59 1.59 1.11 1.47 1.06 1.06 2.41 2.41 3.27 3.4185 GeV 105 GeV 1.58 1.58 0.81 0.27 1.06 1.06 2.45 2.45 3.21 3.11105 GeV 125 GeV 1.60 1.59 1.02 1.31 1.05 1.05 2.51 2.51 3.32 3.42125 GeV 150 GeV 1.59 1.59 0.79 1.20 1.05 1.05 2.59 2.59 3.31 3.43150 GeV 175 GeV 1.73 1.73 1.57 2.40 1.05 1.05 2.67 2.67 3.70 4.12175 GeV 200 GeV 1.57 1.57 0.93 1.63 1.05 1.05 2.75 2.75 3.46 3.71200 GeV 250 GeV 1.58 1.58 3.90 1.67 1.05 1.05 2.86 2.86 5.20 3.82250 GeV 350 GeV 1.57 1.57 2.08 4.26 1.04 1.04 3.05 3.05 4.15 5.57350 GeV 550 GeV 1.72 1.66 4.72 2.39 1.04 1.04 3.36 3.36 6.13 4.57 A.6 P- S comparisons This section contains comparisons of efficiencies and leakages from P and Sherpa data overlay. A.6.1 Efficiencies [GeV] T E R e c o e ff i c i en cy PythiaSherpa * < 1.90 h [GeV] T E R e c o e ff i c i en cy * < 0.91 h -1.84 < Internal ATLAS [GeV] T E R e c o e ff i c i en cy * < -2.02 h -2.83 < [GeV] T E R e c o e ff i c i en cy PythiaSherpa * < 1.90 h [GeV] T E R e c o e ff i c i en cy * < 0.91 h -1.84 < Internal ATLAS [GeV] T E R e c o e ff i c i en cy * < -2.02 h -2.83 < Figure A.1: Reconstruction efficiency comparison for period A (top) and period B (bottom). A.6.2 Leakages [GeV] T E T i gh t e ff i c i en cy PythiaSherpa * < 1.90 h [GeV] T E T i gh t e ff i c i en cy * < 0.91 h -1.84 < Internal ATLAS [GeV] T E T i gh t e ff i c i en cy * < -2.02 h -2.83 < [GeV] T E T i gh t e ff i c i en cy PythiaSherpa * < 1.90 h [GeV] T E T i gh t e ff i c i en cy * < 0.91 h -1.84 < Internal ATLAS [GeV] T E T i gh t e ff i c i en cy * < -2.02 h -2.83 < Figure A.2: Tight ID efficiency comparison for period A (top) and period B (bottom). [GeV] T E I s o e ff i c i en cy PythiaSherpa * < 1.90 h [GeV] T E I s o e ff i c i en cy * < 0.91 h -1.84 < Internal ATLAS [GeV] T E I s o e ff i c i en cy * < -2.02 h -2.83 < [GeV] T E I s o e ff i c i en cy PythiaSherpa * < 1.90 h [GeV] T E I s o e ff i c i en cy * < 0.91 h -1.84 < Internal ATLAS [GeV] T E I s o e ff i c i en cy * < -2.02 h -2.83 < Figure A.3: Isolation efficiency comparison for period A (top) and period B (bottom).10 [GeV] T E Lea k age f r a c t i on B PythiaSherpa * < 1.90 h [GeV] T E Lea k age f r a c t i on B * < 0.91 h -1.84 < Internal ATLAS [GeV] T E Lea k age f r a c t i on B * < -2.02 h -2.83 < Figure A.4: Sideband B leakage fraction [GeV] T E Lea k age f r a c t i on C PythiaSherpa * < 1.90 h [GeV] T E Lea k age f r a c t i on C * < 0.91 h -1.84 < Internal ATLAS [GeV] T E Lea k age f r a c t i on C * < -2.02 h -2.83 < Figure A.5: Sideband C leakage fraction [GeV] T E Lea k age f r a c t i on D PythiaSherpa * < 1.90 h [GeV] T E - · Lea k age f r a c t i on D * < 0.91 h -1.84 < Internal ATLAS [GeV] T E Lea k age f r a c t i on D * < -2.02 h -2.83 < Figure A.6: Sideband D leakage fraction11 A.7 Shower shape comparisons The following section contains comparisons for all ten shower shape variables. We show the distributions,compared to MC before and after applying fudge factors, in each η slice and, for brevity, two representative E T bins: GeV < E T < GeV and GeV < E T < GeV.12 h R - - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging h R - - - - < 0.60 Lab h T p h R - - - - < -0.60 Lab h -1.37 < h R - - - - < 1.37 Lab h h R - - - < -1.56 Lab h -1.81 < h R - - - < 1.81 Lab h h R - - - - < -1.81 Lab h -2.37 < h R - - - - < 2.37 Lab h h R - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging h R - - - < 0.60 Lab h T p h R - - - < -0.60 Lab h -1.37 < h R - - - < 1.37 Lab h h R - - - < -1.56 Lab h -1.81 < h R - - - < 1.81 Lab h h R - - - < -1.81 Lab h -2.37 < h R - - - < 2.37 Lab h Figure A.7: Shower shape parameter, R η , in each pseudorapidity slice from E T bins GeV < E T < GeV(above) and GeV < E T < GeV (below). Reconstructed data plotted as black points overlaid with MCbefore (blue histogram) and after (red histogram) fudging.13 f R - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging f R - - - < 0.60 Lab h T p f R - - - - < -0.60 Lab h -1.37 < f R - - - - < 1.37 Lab h f R - - - < -1.56 Lab h -1.81 < f R - - - < 1.81 Lab h f R - - - - < -1.81 Lab h -2.37 < f R - - - - < 2.37 Lab h f R - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging f R - - - < 0.60 Lab h T p f R - - - < -0.60 Lab h -1.37 < f R - - - < 1.37 Lab h f R - - - < -1.56 Lab h -1.81 < f R - - - < 1.81 Lab h f R - - - < -1.81 Lab h -2.37 < f R - - - < 2.37 Lab h Figure A.8: Shower shape parameter, R φ , in each pseudorapidity slice from E T bins GeV < E T < GeV(above) and GeV < E T < GeV (below). Reconstructed data plotted as black points overlaid with MCbefore (blue histogram) and after (red histogram) fudging.14 - - - - had R - - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging - - - - had R - - - - < 0.60 Lab h T p - - - - had R - - - - < -0.60 Lab h -1.37 < - - - - had R - - - - < 1.37 Lab h - - - - had R - - - < -1.56 Lab h -1.81 < - - - - had R - - - < 1.81 Lab h - - - - had R - - - - < -1.81 Lab h -2.37 < - - - - had R - - - - < 2.37 Lab h - - - - had R - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging - - - - had R - - - < 0.60 Lab h T p - - - - had R - - - < -0.60 Lab h -1.37 < - - - - had R - - - < 1.37 Lab h - - - - had R - - - < -1.56 Lab h -1.81 < - - - - had R - - - < 1.81 Lab h - - - - had R - - - < -1.81 Lab h -2.37 < - - - - had R - - - < 2.37 Lab h Figure A.9: Shower shape parameter, R had , in each pseudorapidity slice from E T bins GeV < E T < GeV(above) and GeV < E T < GeV (below). Reconstructed data plotted as black points overlaid with MCbefore (blue histogram) and after (red histogram) fudging.15 - - - - - had1 R - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging - - - - - had1 R - - - < 0.60 Lab h T p - - - - - had1 R - - - - < -0.60 Lab h -1.37 < - - - - - had1 R - - - - < 1.37 Lab h - - - - - had1 R - - - < -1.56 Lab h -1.81 < - - - - - had1 R - - - < 1.81 Lab h - - - - - had1 R - - - - < -1.81 Lab h -2.37 < - - - - - had1 R - - - < 2.37 Lab h - - - - - had1 R - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging - - - - - had1 R - - - < 0.60 Lab h T p - - - - - had1 R - - - < -0.60 Lab h -1.37 < - - - - - had1 R - - - < 1.37 Lab h - - - - - had1 R - - - < -1.56 Lab h -1.81 < - - - - - had1 R - - < 1.81 Lab h - - - - - had1 R - - - < -1.81 Lab h -2.37 < - - - - - had1 R - - - < 2.37 Lab h Figure A.10: Shower shape parameter, R had , in each pseudorapidity slice from E T bins GeV < E T < GeV (above) and GeV < E T < GeV (below). Reconstructed data plotted as black points overlaidwith MC before (blue histogram) and after (red histogram) fudging.16 h W - - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging h W - - - - < 0.60 Lab h T p h W - - - - < -0.60 Lab h -1.37 < h W - - - - < 1.37 Lab h h W - - - < -1.56 Lab h -1.81 < h W - - - < 1.81 Lab h h W - - - < -1.81 Lab h -2.37 < h W - - - - < 2.37 Lab h h W - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging h W - - - < 0.60 Lab h T p h W - - - < -0.60 Lab h -1.37 < h W - - - < 1.37 Lab h h W - - - < -1.56 Lab h -1.81 < h W - - - < 1.81 Lab h h W - - - < -1.81 Lab h -2.37 < h W - - - < 2.37 Lab h Figure A.11: Shower shape parameter, W η , in each pseudorapidity slice from E T bins GeV < E T < GeV(above) and GeV < E T < GeV (below). Reconstructed data plotted as black points overlaid with MCbefore (blue histogram) and after (red histogram) fudging.17 h W - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging h W - - - < 0.60 Lab h T p h W - - - - < -0.60 Lab h -1.37 < h W - - - - < 1.37 Lab h h W - - - < -1.56 Lab h -1.81 < h W - - - < 1.81 Lab h h W - - - - < -1.81 Lab h -2.37 < h W - - - - < 2.37 Lab h h W - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging h W - - - < 0.60 Lab h T p h W - - - < -0.60 Lab h -1.37 < h W - - - < 1.37 Lab h h W - - - < -1.56 Lab h -1.81 < h W - - - < 1.81 Lab h h W - - - < -1.81 Lab h -2.37 < h W - - - < 2.37 Lab h Figure A.12: Shower shape parameter, W η , in each pseudorapidity slice from E T bins GeV < E T < GeV(above) and GeV < E T < GeV (below). Reconstructed data plotted as black points overlaid with MCbefore (blue histogram) and after (red histogram) fudging.18 - tots1 W - - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging - tots1 W - - - - < 0.60 Lab h T p - tots1 W - - - - < -0.60 Lab h -1.37 < - tots1 W - - - - < 1.37 Lab h - tots1 W - - - < -1.56 Lab h -1.81 < - tots1 W - - - < 1.81 Lab h - tots1 W - - - - < -1.81 Lab h -2.37 < - tots1 W - - - - < 2.37 Lab h - tots1 W - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging - tots1 W - - - < 0.60 Lab h T p - tots1 W - - - < -0.60 Lab h -1.37 < - tots1 W - - - < 1.37 Lab h - tots1 W - - - < -1.56 Lab h -1.81 < - tots1 W - - - < 1.81 Lab h - tots1 W - - - < -1.81 Lab h -2.37 < - tots1 W - - - < 2.37 Lab h Figure A.13: Shower shape parameter, W totes , in each pseudorapidity slice from E T bins GeV < E T < GeV (above) and GeV < E T < GeV (below). Reconstructed data plotted as black points overlaidwith MC before (blue histogram) and after (red histogram) fudging.19 E D - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging E D - - - - < 0.60 Lab h T p E D - - - - < -0.60 Lab h -1.37 < E D - - - < 1.37 Lab h E D - - - < -1.56 Lab h -1.81 < E D - - - < 1.81 Lab h E D - - - - < -1.81 Lab h -2.37 < E D - - - - < 2.37 Lab h E D - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging E D - - - < 0.60 Lab h T p E D - - - < -0.60 Lab h -1.37 < E D - - - < 1.37 Lab h E D - - - < -1.56 Lab h -1.81 < E D - - - < 1.81 Lab h E D - - - < -1.81 Lab h -2.37 < E D - - - < 2.37 Lab h Figure A.14: Shower shape parameter, ∆ E , in each pseudorapidity slice from E T bins GeV < E T < GeV(above) and GeV < E T < GeV (below). Reconstructed data plotted as black points overlaid with MCbefore (blue histogram) and after (red histogram) fudging.20 ratio E - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging ratio E - - - < 0.60 Lab h T p ratio E - - - - < -0.60 Lab h -1.37 < ratio E - - - < 1.37 Lab h ratio E - - - < -1.56 Lab h -1.81 < ratio E - - - < 1.81 Lab h ratio E - - - - < -1.81 Lab h -2.37 < ratio E - - - - < 2.37 Lab h ratio E - - - < 0.00 Lab h -0.60 < Internal ATLAS DataMC after fudgingMC before fudging ratio E - - - < 0.60 Lab h T p ratio E - - - < -0.60 Lab h -1.37 < ratio E - - - < 1.37 Lab h ratio E - - - < -1.56 Lab h -1.81 < ratio E - - - < 1.81 Lab h ratio E - - - < -1.81 Lab h -2.37 < ratio E - - - < 2.37 Lab h Figure A.15: Shower shape parameter, E ratio , in each pseudorapidity slice from E T bins GeV < E T < GeV (above) and GeV < E T < GeV (below). Reconstructed data plotted as black points overlaidwith MC before (blue histogram) and after (red histogram) fudging.21 - - < 0.00 Lab h -0.60 < DataMC after fudgingMC before fudging - - < 0.60 Lab h T p Internal ATLAS - < -0.60 Lab h -1.37 < - < 1.37 Lab h - < -1.56 Lab h -1.81 < - < 1.81 Lab h - - < -1.81 Lab h -2.37 < - - < 2.37 Lab h - - < 0.00 Lab h -0.60 < DataMC after fudgingMC before fudging - - < 0.60 Lab h T p Internal ATLAS - < -0.60 Lab h -1.37 < - < 1.37 Lab h - < -1.56 Lab h -1.81 < - < 1.81 Lab h - - < -1.81 Lab h -2.37 < - - < 2.37 Lab h Figure A.16: Shower shape parameter, fracs1, in each pseudorapidity slice from E T bins GeV < E T < GeV (above) and GeV < E T < GeV (below). Reconstructed data plotted as black points overlaidwith MC before (blue histogram) and after (red histogram) fudging.22 A.8 Photon Isolation This section contains the full set of isolation energy distributions for ”Tight” identified photons in data(black histogram) overlaid with ”Non-tight” designated photons (blue histogram) which are selected to increasebackgrounds. The Non-tight histograms are scaled to match the integral of the tight histogram above 7 GeV.Additionally, the distribution of tight and truth-isolated reconstructed photons from MC are overlaid (red brokenhistogram). The second panel on each page compares the MC to the data isolation energy with the ”Non-Tight”subtracted from the ”Tight”. The distributions are plotted in their usual η slices for each E T bin.23 - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < TightNon-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < - cone40 [GeV] T E topo < 1.37 Lab h - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < - cone40 [GeV] T E topo < 1.81 Lab h - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < - cone40 [GeV] T E topo < 2.37 Lab h - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < = 5.48 s = 0.41, m = 5.54 s = 0.41, m Tight - Non-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h = 5.42 s = 0.38, m = 5.57 s = 0.36, m < 35.00 T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < = 5.32 s = 0.41, m = 5.55 s = 0.39, m - cone40 [GeV] T E topo < 1.37 Lab h = 5.52 s = 0.66, m = 5.37 s = 0.65, m - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < = 6.31 s = 0.17, m = 6.08 s = 0.17, m - cone40 [GeV] T E topo < 1.81 Lab h = 6.04 s = 0.56, m = 6.02 s = 0.57, m - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < = 5.81 s = 0.29, m = 5.98 s = 0.28, m - cone40 [GeV] T E topo < 2.37 Lab h = 5.34 s = 0.76, m = 5.80 s = 0.74, m - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < TightNon-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < - cone40 [GeV] T E topo < 1.37 Lab h - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < - cone40 [GeV] T E topo < 1.81 Lab h - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < - cone40 [GeV] T E topo < 2.37 Lab h - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < = 5.62 s = 0.37, m = 5.53 s = 0.38, m Tight - Non-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h = 5.55 s = 0.42, m = 5.49 s = 0.41, m < 45.00 T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < = 5.55 s = 0.48, m = 5.43 s = 0.48, m - cone40 [GeV] T E topo < 1.37 Lab h = 5.58 s = 0.66, m = 5.26 s = 0.68, m - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < = 6.51 s = 0.09, m = 6.01 s = 0.08, m - cone40 [GeV] T E topo < 1.81 Lab h = 6.23 s = 0.52, m = 5.94 s = 0.53, m - cone40 [GeV] T E topo - < -1.81 Lab h -2.37 < = 6.04 s = 0.37, m = 5.99 s = 0.38, m - cone40 [GeV] T E topo - < 2.37 Lab h = 5.56 s = 0.86, m = 5.73 s = 0.85, m - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < TightNon-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < - cone40 [GeV] T E topo < 1.37 Lab h - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < - cone40 [GeV] T E topo < 1.81 Lab h - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < - cone40 [GeV] T E topo < 2.37 Lab h - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < = 5.62 s = 0.37, m = 5.53 s = 0.38, m Tight - Non-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h = 5.55 s = 0.42, m = 5.49 s = 0.41, m < 45.00 T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < = 5.55 s = 0.48, m = 5.43 s = 0.48, m - cone40 [GeV] T E topo < 1.37 Lab h = 5.58 s = 0.66, m = 5.26 s = 0.68, m - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < = 6.51 s = 0.09, m = 6.01 s = 0.08, m - cone40 [GeV] T E topo < 1.81 Lab h = 6.23 s = 0.52, m = 5.94 s = 0.53, m - cone40 [GeV] T E topo - < -1.81 Lab h -2.37 < = 6.04 s = 0.37, m = 5.99 s = 0.38, m - cone40 [GeV] T E topo - < 2.37 Lab h = 5.56 s = 0.86, m = 5.73 s = 0.85, m - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < TightNon-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < - cone40 [GeV] T E topo < 1.37 Lab h - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < - cone40 [GeV] T E topo < 1.81 Lab h - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < - cone40 [GeV] T E topo < 2.37 Lab h - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < = 5.62 s = 0.38, m = 5.52 s = 0.39, m Tight - Non-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h = 5.52 s = 0.38, m = 5.50 s = 0.38, m < 65.00 T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < = 5.66 s = 0.62, m = 5.36 s = 0.62, m - cone40 [GeV] T E topo < 1.37 Lab h = 5.55 s = 0.74, m = 5.30 s = 0.76, m - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < = 6.40 s = 0.22, m = 6.03 s = 0.23, m - cone40 [GeV] T E topo < 1.81 Lab h = 6.26 s = 0.54, m = 6.07 s = 0.54, m - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < = 6.11 s = 0.52, m = 5.98 s = 0.52, m - cone40 [GeV] T E topo < 2.37 Lab h = 5.66 s = 0.96, m = 5.73 s = 0.94, m - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < TightNon-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < - cone40 [GeV] T E topo < 1.37 Lab h - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < - cone40 [GeV] T E topo < 1.81 Lab h - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < - cone40 [GeV] T E topo < 2.37 Lab h - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < = 5.56 s = 0.31, m = 5.59 s = 0.31, m Tight - Non-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h = 5.62 s = 0.41, m = 5.52 s = 0.41, m < 75.00 T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < = 5.83 s = 0.63, m = 5.45 s = 0.62, m - cone40 [GeV] T E topo < 1.37 Lab h = 5.60 s = 0.80, m = 5.28 s = 0.81, m - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < = 6.85 s = 0.32, m = 6.11 s = 0.32, m - cone40 [GeV] T E topo < 1.81 Lab h = 6.18 s = 0.60, m = 6.10 s = 0.60, m - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < = 5.72 s = 0.46, m = 6.03 s = 0.44, m - cone40 [GeV] T E topo - < 2.37 Lab h = 5.62 s = 0.97, m = 5.84 s = 0.93, m - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < TightNon-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < - cone40 [GeV] T E topo < 1.37 Lab h - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < - cone40 [GeV] T E topo < 1.81 Lab h - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < - cone40 [GeV] T E topo < 2.37 Lab h - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < = 5.64 s = 0.29, m = 5.67 s = 0.29, m Tight - Non-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h = 5.80 s = 0.44, m = 5.54 s = 0.44, m < 85.00 T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < = 5.70 s = 0.72, m = 5.39 s = 0.73, m - cone40 [GeV] T E topo < 1.37 Lab h = 5.56 s = 0.87, m = 5.29 s = 0.89, m - cone40 [GeV] T E topo - < -1.56 Lab h -1.81 < = 6.57 s = 0.24, m = 6.16 s = 0.23, m - cone40 [GeV] T E topo - < 1.81 Lab h = 6.39 s = 0.51, m = 6.11 s = 0.49, m - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < = 6.00 s = 0.59, m = 6.10 s = 0.56, m - cone40 [GeV] T E topo < 2.37 Lab h = 5.61 s = 1.10, m = 5.75 s = 1.08, m - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < TightNon-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < - cone40 [GeV] T E topo < 1.37 Lab h - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < - cone40 [GeV] T E topo < 1.81 Lab h - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < - cone40 [GeV] T E topo < 2.37 Lab h - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < = 5.63 s = 0.33, m = 5.60 s = 0.33, m Tight - Non-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h = 5.66 s = 0.32, m = 5.62 s = 0.32, m < 105.00 T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < = 5.64 s = 0.69, m = 5.47 s = 0.68, m - cone40 [GeV] T E topo < 1.37 Lab h = 5.64 s = 0.90, m = 5.34 s = 0.90, m - cone40 [GeV] T E topo - < -1.56 Lab h -1.81 < = 6.23 s = 0.19, m = 6.24 s = 0.18, m - cone40 [GeV] T E topo - < 1.81 Lab h = 6.06 s = 0.57, m = 6.08 s = 0.57, m - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < = 6.10 s = 0.56, m = 6.09 s = 0.55, m - cone40 [GeV] T E topo - < 2.37 Lab h = 5.59 s = 1.00, m = 5.91 s = 0.97, m - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < TightNon-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < - cone40 [GeV] T E topo < 1.37 Lab h - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < - cone40 [GeV] T E topo < 1.81 Lab h - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < - cone40 [GeV] T E topo < 2.37 Lab h - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < = 5.45 s = 0.35, m = 5.73 s = 0.34, m Tight - Non-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h = 5.55 s = 0.38, m = 5.69 s = 0.38, m < 150.00 T p ATLAS - cone40 [GeV] T E topo - < -0.60 Lab h -1.37 < = 5.41 s = 0.81, m = 5.57 s = 0.80, m - cone40 [GeV] T E topo < 1.37 Lab h = 5.63 s = 0.98, m = 5.45 s = 0.99, m - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < = 6.46 s = 0.44, m = 6.36 s = 0.53, m - cone40 [GeV] T E topo - < 1.81 Lab h = 6.75 s = 0.71, m = 6.35 s = 0.73, m - cone40 [GeV] T E topo - < -1.81 Lab h -2.37 < = 6.07 s = 1.02, m = 6.26 s = 0.66, m - cone40 [GeV] T E topo - - < 2.37 Lab h = 5.97 s = 0.92, m = 6.15 s = 1.00, m - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < TightNon-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < - cone40 [GeV] T E topo < 1.37 Lab h - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < - cone40 [GeV] T E topo < 1.81 Lab h - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < - cone40 [GeV] T E topo < 2.37 Lab h - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < = 5.45 s = 0.35, m = 5.73 s = 0.34, m Tight - Non-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h = 5.55 s = 0.38, m = 5.69 s = 0.38, m < 150.00 T p ATLAS - cone40 [GeV] T E topo - < -0.60 Lab h -1.37 < = 5.41 s = 0.81, m = 5.57 s = 0.80, m - cone40 [GeV] T E topo < 1.37 Lab h = 5.63 s = 0.98, m = 5.45 s = 0.99, m - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < = 6.46 s = 0.44, m = 6.36 s = 0.53, m - cone40 [GeV] T E topo - < 1.81 Lab h = 6.75 s = 0.71, m = 6.35 s = 0.73, m - cone40 [GeV] T E topo - < -1.81 Lab h -2.37 < = 6.07 s = 1.02, m = 6.26 s = 0.66, m - cone40 [GeV] T E topo - - < 2.37 Lab h = 5.97 s = 0.92, m = 6.15 s = 1.00, m - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < TightNon-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < - cone40 [GeV] T E topo < 1.37 Lab h - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < - cone40 [GeV] T E topo < 1.81 Lab h - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < - cone40 [GeV] T E topo < 2.37 Lab h - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < = 5.85 s = 0.40, m = 5.79 s = 0.26, m Tight - Non-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h = 5.88 s = 0.31, m = 5.73 s = 0.28, m < 175.00 T p ATLAS - cone40 [GeV] T E topo - < -0.60 Lab h -1.37 < = 5.75 s = 1.09, m = 5.69 s = 0.65, m - cone40 [GeV] T E topo - < 1.37 Lab h = 5.73 s = 1.20, m = 5.46 s = 0.99, m - cone40 [GeV] T E topo - < -1.56 Lab h -1.81 < = 6.29 s = 0.05, m = 6.41 s = 0.53, m - cone40 [GeV] T E topo - < 1.81 Lab h = 7.63 s = 0.94, m = 6.35 s = 0.73, m - cone40 [GeV] T E topo - < -1.81 Lab h -2.37 < = 6.45 s = 0.78, m = 6.34 s = 0.66, m - cone40 [GeV] T E topo - - - < 2.37 Lab h = 5.89 s = 1.24, m = 6.23 s = 1.02, m - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < TightNon-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < - cone40 [GeV] T E topo < 1.37 Lab h - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < - cone40 [GeV] T E topo < 1.81 Lab h - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < - cone40 [GeV] T E topo < 2.37 Lab h - cone40 [GeV] T E topo - < 0.00 Lab h -0.60 < = 5.63 s = 0.41, m = 5.86 s = 0.32, m Tight - Non-tightPYTHIA8 - cone40 [GeV] T E topo - < 0.60 Lab h = 5.94 s = 0.34, m = 5.83 s = 0.32, m < 200.00 T p ATLAS - cone40 [GeV] T E topo - < -0.60 Lab h -1.37 < = 5.34 s = 1.24, m = 5.73 s = 0.69, m - cone40 [GeV] T E topo - < 1.37 Lab h = 5.62 s = 1.25, m = 5.53 s = 1.01, m - cone40 [GeV] T E topo - < -1.56 Lab h -1.81 < = 7.62 s = 0.56, m = 6.41 s = 0.56, m - cone40 [GeV] T E topo - < 1.81 Lab h = 6.44 s = 0.44, m = 6.55 s = 0.76, m - cone40 [GeV] T E topo - < -1.81 Lab h -2.37 < = 6.91 s = 0.76, m = 6.44 s = 0.68, m - cone40 [GeV] T E topo - < 2.37 Lab h = 4.81 s = 1.06, m = 6.39 s = 1.08, m - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < TightNon-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < - cone40 [GeV] T E topo < 1.37 Lab h - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < - cone40 [GeV] T E topo < 1.81 Lab h - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < - cone40 [GeV] T E topo < 2.37 Lab h - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < = 5.53 s = 0.40, m = 5.80 s = 0.35, m Tight - Non-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h = 5.51 s = 0.38, m = 5.92 s = 0.35, m < 250.00 T p ATLAS - cone40 [GeV] T E topo - < -0.60 Lab h -1.37 < = 4.82 s = 1.16, m = 5.85 s = 0.71, m - cone40 [GeV] T E topo - < 1.37 Lab h = 6.66 s = 1.39, m = 5.59 s = 1.04, m - cone40 [GeV] T E topo - - < -1.56 Lab h -1.81 < = 6.41 s = 0.42, m = 6.69 s = 0.62, m - cone40 [GeV] T E topo - - < 1.81 Lab h = 6.36 s = 0.71, m = 6.57 s = 0.81, m - cone40 [GeV] T E topo - < -1.81 Lab h -2.37 < = 5.87 s = 1.07, m = 6.64 s = 0.78, m - cone40 [GeV] T E topo - < 2.37 Lab h = 6.47 s = 2.11, m = 6.50 s = 1.10, m - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < TightNon-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < - cone40 [GeV] T E topo < 1.37 Lab h - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < - cone40 [GeV] T E topo < 1.81 Lab h - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < - cone40 [GeV] T E topo < 2.37 Lab h - cone40 [GeV] T E topo - < 0.00 Lab h -0.60 < = 4.99 s = 0.47, m = 6.04 s = 0.43, m Tight - Non-tightPYTHIA8 - cone40 [GeV] T E topo - < 0.60 Lab h = 5.17 s = 0.48, m = 6.02 s = 0.42, m < 300.00 T p ATLAS - cone40 [GeV] T E topo - < -0.60 Lab h -1.37 < = 6.19 s = 1.23, m = 6.02 s = 0.74, m - cone40 [GeV] T E topo - - < 1.37 Lab h = 5.72 s = 1.14, m = 5.78 s = 1.05, m - cone40 [GeV] T E topo - < -1.56 Lab h -1.81 < = 5.72 s = -0.32, m = 7.02 s = 0.69, m - cone40 [GeV] T E topo - - < 1.81 Lab h = 5.00 s = 0.58, m = 6.97 s = 0.87, m - cone40 [GeV] T E topo - < -1.81 Lab h -2.37 < = 6.74 s = 0.52, m = 6.92 s = 0.78, m - cone40 [GeV] T E topo < 2.37 Lab h = 0.00 s = 2.25, m = 6.79 s = 1.12, m - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < TightNon-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < - cone40 [GeV] T E topo < 1.37 Lab h - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < - cone40 [GeV] T E topo < 1.81 Lab h - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < - cone40 [GeV] T E topo < 2.37 Lab h - cone40 [GeV] T E topo - - - < 0.00 Lab h -0.60 < = 6.03 s = 1.30, m = 6.11 s = 0.44, m Tight - Non-tightPYTHIA8 - cone40 [GeV] T E topo - - < 0.60 Lab h = 5.91 s = 1.00, m = 6.09 s = 0.45, m < 350.00 T p ATLAS - cone40 [GeV] T E topo - - < -0.60 Lab h -1.37 < = 6.09 s = 1.93, m = 6.12 s = 0.74, m - cone40 [GeV] T E topo - - - < 1.37 Lab h = 4.79 s = 1.89, m = 5.84 s = 1.07, m - cone40 [GeV] T E topo - - < -1.56 Lab h -1.81 < = 5.30 s = 0.55, m = 7.15 s = 0.66, m - cone40 [GeV] T E topo < 1.81 Lab h = 3.61 s = 1.92, m = 7.16 s = 0.84, m - cone40 [GeV] T E topo - < -1.81 Lab h -2.37 < = 8.74 s = 1.19, m = 7.08 s = 0.76, m - cone40 [GeV] T E topo < 2.37 Lab h = nan s = nan, m = nan s = nan, m - cone40 [GeV] T E topo < 0.00 Lab h -0.60 < TightNon-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h T p ATLAS - cone40 [GeV] T E topo < -0.60 Lab h -1.37 < - cone40 [GeV] T E topo < 1.37 Lab h - cone40 [GeV] T E topo < -1.56 Lab h -1.81 < - cone40 [GeV] T E topo < 1.81 Lab h - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < - cone40 [GeV] T E topo < 2.37 Lab h - cone40 [GeV] T E topo - < 0.00 Lab h -0.60 < = 5.00 s = 0.42, m = 6.19 s = 0.50, m Tight - Non-tightPYTHIA8 - cone40 [GeV] T E topo < 0.60 Lab h = 1.06 s = -1.50, m = 6.19 s = 0.47, m < 400.00 T p ATLAS - cone40 [GeV] T E topo - - < -0.60 Lab h -1.37 < = 5.01 s = 1.97, m = 6.26 s = 0.76, m - cone40 [GeV] T E topo - < 1.37 Lab h = 2.12 s = 2.75, m = 6.05 s = 1.07, m - cone40 [GeV] T E topo - < -1.56 Lab h -1.81 < = 6.94 s = -0.75, m = 7.37 s = 0.67, m - cone40 [GeV] T E topo < 1.81 Lab h = nan s = nan, m = nan s = nan, m - cone40 [GeV] T E topo < -1.81 Lab h -2.37 < = 11.67 s = -0.50, m = 7.34 s = 0.76, m - cone40 [GeV] T E topo < 2.37 Lab h = nan s = nan, m = nan s = nan, m ppendix BMeasurement of Azimuthal AnisotropyB.1 Multiplicity Distributions Figures B.1 and B.2 show the run-by-run multiplicity distributions for each trigger used to construct theminimum bias selection. The histograms contain raw counts and are not prescale corrected.Figures B.3 and B.4 show the run-by-run multiplicity distributions summed over each trigger used toconstruct the minimum bias selection. The histograms contain raw counts and are not prescale corrected.39 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313063 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313067 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313100 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313107 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313136 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313187 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313259 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313285 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313295 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313333 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313435 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313574 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313575 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313603 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313629 Figure B.1: Run-by-run multiplicity distributions for each trigger used to construct the minimum bias selection.Vertical lines are drawn to indicate the thresholds partitioning the N trk range. In each region, only the triggeroffering the largest number of events is used.40 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313630 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313688 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313695 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313833 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313878 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313929 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313935 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 313984 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 314014 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 314077 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 314105 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 314112 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 314157 50 100 150 200 250 300 350 400 450 trk N c oun t s HLT_mb_sptrk_L1MBTS_1HLT_mb_sp2400_pusup500_trk120_hmt_L1TE20HLT_mb_sp2800_pusup600_trk140_hmt_L1TE50HLT_mb_sp4100_pusup900_trk200_hmt_L1TE120HLT_mb_sp4800_pusup1100_trk240_hmt_L1TE120 Internal ATLAS Run 314170 Figure B.2: Run-by-run multiplicity distributions for each trigger used to construct the minimum bias selection.Vertical lines are drawn to indicate the thresholds partitioning the N trk range. In each region, only the triggeroffering the largest number of events is used.41 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313063 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313067 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313100 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313107 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313136 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313187 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313259 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313285 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313295 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313333 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313435 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313574 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313575 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313603 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313629 Figure B.3: Total run-by-run multiplicity distributions composing the minimum bias selection. Vertical lines aredrawn to indicate the thresholds partitioning the N trk range. In each region, only the trigger offering the largestnumber of events is used.42 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313630 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313688 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313695 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313833 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313878 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313929 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313935 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 313984 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 314014 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 314077 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 314105 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 314112 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 314157 50 100 150 200 250 300 350 400 450 trk N c oun t s Internal ATLAS Run 314170 Figure B.4: Total run-by-run multiplicity distributions composing the minimum bias selection. Vertical lines aredrawn to indicate the thresholds partitioning the N trk range. In each region, only the trigger offering the largestnumber of events is used.43 B.2 Systematic uncertainties in v B.2.1 PerformanceB.2.1.1 MinBias tracking efficiency - · 10 [GeV] T p - - v With efficiency correctionWithout efficiency correction Internal ATLAS MB [GeV] A T p - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v With efficiency correctionWithout efficiency correction Internal ATLAS > 75 GeV JetT p [GeV] A T p - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v With efficiency correctionWithout efficiency correction Internal ATLAS > 100 GeV JetT p [GeV] A T p - - - R e l a t i v e d i ff e r en c e Figure B.5: v versus p T for MB (left), 75 GeV jet (center), and 100 GeV jet (right) events with and withouttrigger and tracking efficiency corrections. B.2.1.2 Total - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS MB Efficiency correctionsTotal - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p Efficiency correctionsTotal - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p Efficiency correctionsTotal Figure B.6: Combined performance uncertainty, plotted as the absolute difference in v between the varied andnominal selections, for MB (left), 75 GeV jet (center), and 100 GeV jet (right) events. B.2.2 Signal extractionB.2.2.1 Event Mixing - · 10 [GeV] T p - - v No mixed event correctionWith mixed event correction Internal ATLAS MB [GeV] A T p - - - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v With mixed event correctionNo mixed event correction Internal ATLAS > 75 GeV JetT p [GeV] A T p - - - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v With mixed event correctionNo mixed event correction Internal ATLAS > 100 GeV JetT p [GeV] A T p - - - - - R e l a t i v e d i ff e r en c e Figure B.7: v versus p T for both MB (left), 75 GeV jet (center), and 100 GeV jet (right) events with the nominalvalues using the mixed event correction, and variation without the correction.45 B.2.2.2 Template fitting reference selection - · 10 [GeV] T p - - v ATLAS MB Reference selection [GeV] A T p - - - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v ATLAS > 75 GeV JetT p Reference selection [GeV] A T p - - - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v ATLAS > 100 GeV JetT p Reference selection [GeV] A T p - - - - - R e l a t i v e d i ff e r en c e Figure B.8: v versus p T for both MB (left), 75 GeV jet (center), and 100 GeV jet (right) events with the nominaland two varied P reference selections. B.2.2.3 Total - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS MB Event mixingReference selectionTotal - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p Event mixingReference selectionTotal - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p Event mixingReference selectionTotal Figure B.9: Combined signal extraction uncertainty, plotted as the absolute difference in v between the variedand nominal selections, for MB (left), 75 GeV jet (center), and 100 GeV jet (right) events. B.2.3 Jet selectionB.2.3.1 Jet p T threshold - · - - > 75 [GeV] (nominal) jetT p > 80 [GeV] jetT p Internal ATLAS > 75 GeV JetT p [GeV] A T p - - - R e l a t i v e d i ff e r en c e - · - - > 100 [GeV] (nominal) jetT p > 105 [GeV] jetT p Internal ATLAS > 100 GeV JetT p [GeV] A T p - - - R e l a t i v e d i ff e r en c e Figure B.10: v versus p T for 75 GeV (left) and 100 GeV (right) jet events with offline jet p T thresholds variationsof +5 GeV.47 B.2.3.2 Associated particle jet rejection min jet p T - · 10 [GeV] T p - - v Reject jets > 15 GeV (nominal)Reject jets > 20 GeV Internal ATLAS > 75 GeV JetT p [GeV] A T p - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v Reject jets > 15 GeV (nominal)Reject jets > 20 GeV Internal ATLAS > 100 GeV JetT p [GeV] A T p - - - R e l a t i v e d i ff e r en c e Figure B.11: v versus p T for 75 GeV (left) and 100 GeV (right) jet events with the nominal and varied ∆ η jet p T selection. - · 10 [GeV] T p - - v Reject jets > 15 GeV (nominal) > 2 jet trk N && Internal ATLAS > 75 GeV JetT p [GeV] A T p - - - R e l a t i v e d i ff e r en c e - · 10 [GeV] T p - - v Reject jets > 15 GeV (nominal) > 2 jet trk N && Internal ATLAS > 100 GeV JetT p [GeV] A T p - - - R e l a t i v e d i ff e r en c e Figure B.12: v versus p T for 75 GeV (left) and 100 GeV (right) jet events with the nominal and varied associatedparticle rejection jet multiplicity selection. B.2.3.3 Total - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p cut T p Jet cut T p Jet rejection low Jet multiplicity > 2 < 1.56 LabTrack B h Total - · AT p - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p cut T p Jet cut T p Jet rejection low Jet multiplicity > 2 < 1.56 LabTrack B h Total Figure B.13: Combined jet selection uncertainty for MB (left), 75 GeV jet (center), and 100 GeV jet (right)events. B.3 Systematic uncertainties in v vs. centrality B.3.1 Performance - - - - A b s o l u t e d i ff e r en c e Internal ATLAS MB+HMT Efficiency correctionsTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p Efficiency correctionsTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p Efficiency correctionsTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS MB+HMT Efficiency correctionsTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p Efficiency correctionsTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p Efficiency correctionsTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS MB+HMT Efficiency correctionsTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p Efficiency correctionsTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p Efficiency correctionsTotal Figure B.14: Combined performance uncertainty in v as a function of centrality, plotted as the absolute dif-ference between the varied and nominal selections, for MB (left), 75 GeV jet (center), and 100 GeV jet (right)events. The uncertainties are determined separately for . < p A T < GeV (top row), < p A T < GeV (middlerow), and < p A T < GeV (bottom row).50 B.3.2 Signal extraction - - - - A b s o l u t e d i ff e r en c e Internal ATLAS MB+HMT Event mixingReference selectionTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p Event mixingReference selectionTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p Event mixingReference selectionTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS MB+HMT Event mixingReference selectionTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p Event mixingReference selectionTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p Event mixingReference selectionTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS MB+HMT Event mixingReference selectionTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p Event mixingReference selectionTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p Event mixingReference selectionTotal Figure B.15: Combined signal extraction uncertainty in v as a function of centrality, plotted as the absolutedifference between the varied and nominal selections, for MB (left), 75 GeV jet (center), and 100 GeV jet (right)events. The uncertainties are determined separately for . < p A T < GeV (top row), < p A T < GeV (middlerow), and < p A T < GeV (bottom row). B.3.3 Jet selection - - - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p cut T p Jet cut T p Jet rejection low Jet multiplicity > 2 < 1.56 LabTrack B h Jet UE biasTotal - - - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p cut T p Jet cut T p Jet rejection low Jet multiplicity > 2 < 1.56 LabTrack B h Jet UE biasTotal - - - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p cut T p Jet cut T p Jet rejection low Jet multiplicity > 2 < 1.56 LabTrack B h Jet UE biasTotal - - - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p cut T p Jet cut T p Jet rejection low Jet multiplicity > 2 < 1.56 LabTrack B h Jet UE biasTotal - - - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p cut T p Jet cut T p Jet rejection low Jet multiplicity > 2 < 1.56 LabTrack B h Jet UE biasTotal - - - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p cut T p Jet cut T p Jet rejection low Jet multiplicity > 2 < 1.56 LabTrack B h Jet UE biasTotal Figure B.16: Combined jet selection uncertainty in v as a function of centrality, plotted as the absolute differencebetween the varied and nominal selections, for 75 GeV (left) and 100 GeV jet (right) events. The uncertaintiesare determined separately for . < p A T < GeV (top row), < p A T < GeV (middle row), and < p A T < GeV (bottom row).52 B.3.4 Signal extraction - - - - A b s o l u t e d i ff e r en c e Internal ATLAS MB+HMT PerformanceSignal extractionTotal - - - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p PerformanceSignal extractionJet selectionTotal - - - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p PerformanceSignal extractionJet selectionTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS MB+HMT PerformanceSignal extractionTotal - - - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p PerformanceSignal extractionJet selectionTotal - - - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p PerformanceSignal extractionJet selectionTotal - - - - A b s o l u t e d i ff e r en c e Internal ATLAS MB+HMT PerformanceSignal extractionTotal - - - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 75 GeV jetT p PerformanceSignal extractionJet selectionTotal - - - - - - A b s o l u t e d i ff e r en c e Internal ATLAS > 100 GeV jetT p PerformanceSignal extractionJet selectionTotal Figure B.17: Total combined uncertainty in v as a function of centrality, plotted as the absolute differencebetween the varied and nominal selections, for MB (left), 75 GeV jet (center), and 100 GeV jet (right) events.The uncertainties are determined separately for . < p A T < GeV (top row), < p A T < GeV (middle row),and < p A T < GeV (bottom row). B.4 Template fits - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 0.75 A T p – = 0.004271 v 0.000010 – = 0.000399 v /NDF = 1.225628 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 1.00 A T p – = 0.005652 v 0.000012 – = 0.000620 v /NDF = 1.126702 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 1.25 A T p – = 0.006850 v 0.000015 – = 0.000825 v /NDF = 1.276321 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 1.50 A T p – = 0.007867 v 0.000019 – = 0.000991 v /NDF = 1.100041 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 1.75 A T p – = 0.008786 v 0.000024 – = 0.001216 v /NDF = 1.372319 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 2.00 A T p – = 0.009493 v 0.000030 – = 0.001307 v /NDF = 1.188716 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 2.50 A T p – = 0.010250 v 0.000028 – = 0.001532 v /NDF = 1.661627 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 3.00 A T p – = 0.010877 v 0.000041 – = 0.001761 v /NDF = 1.012848 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 3.50 A T p – = 0.010870 v 0.000059 – = 0.001899 v /NDF = 0.853721 c - fD - ) f D ( L M Y F - G ) - f D ( Y Figure B.18: Template fits to correlation functions from 0-5% central events using 60-90% central events asperipheral reference from the MB dataset. Each figure shows a different p T range.54 - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 4.00 A T p – = 0.010583 v 0.000081 – = 0.001908 v /NDF = 1.029387 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 4.50 A T p – = 0.010071 v 0.000110 – = 0.001801 v /NDF = 1.241782 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 5.00 A T p – = 0.008912 v 0.000145 – = 0.001803 v /NDF = 0.894907 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 6.00 A T p – = 0.007664 v 0.000147 – = 0.001839 v /NDF = 1.094411 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 7.00 A T p – = 0.005968 v 0.000227 – = 0.001228 v /NDF = 0.602993 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 8.00 A T p – = 0.004289 v 0.000332 – = 0.000506 v /NDF = 1.218758 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 9.00 A T p – = 0.003721 v 0.000462 – = 0.002064 v /NDF = 0.878213 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 11.00 A T p – = 0.002325 v 0.000493 – = 0.002162 v /NDF = 1.070892 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 16.00 A T p – = 0.001852 v 0.000638 – = 0.001368 v /NDF = 1.044818 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 100.00 A T p – = 0.002001 v 0.001189 – = -0.000508 v /NDF = 1.146815 c - fD - ) f D ( L M Y F - G ) - f D ( Y Figure B.19: Template fits to correlation functions from 0-5% central events using 60-90% central events asperipheral reference from the MB dataset. Each figure shows a different p T range.55 - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 0.75 A T p – = 0.003659 v 0.000086 – = 0.000504 v /NDF = 1.036258 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 1.00 A T p – = 0.004844 v 0.000113 – = 0.000705 v /NDF = 1.389332 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 1.25 A T p – = 0.005774 v 0.000127 – = 0.000953 v /NDF = 0.872688 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 1.50 A T p – = 0.007166 v 0.000172 – = 0.000963 v /NDF = 0.817942 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 1.75 A T p – = 0.007787 v 0.000195 – = 0.001276 v /NDF = 0.969068 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 2.00 A T p – = 0.008089 v 0.000242 – = 0.001571 v /NDF = 0.856636 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 2.50 A T p – = 0.009122 v 0.000234 – = 0.001470 v /NDF = 1.501075 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 3.00 A T p – = 0.008517 v 0.000301 – = 0.001912 v /NDF = 1.639594 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 3.50 A T p – = 0.008034 v 0.000433 – = 0.001795 v /NDF = 0.975533 c - fD - ) f D ( L M Y F - G ) - f D ( Y Figure B.20: Template fits to correlation functions from 0-5% central events using 60-90% central events asperipheral reference from the 75 GeV jet dataset. Each figure shows a different p T range.56 - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 4.00 A T p – = 0.006474 v 0.000423 – = 0.001342 v /NDF = 1.354681 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 4.50 A T p – = 0.006086 v 0.000448 – = 0.000832 v /NDF = 1.379151 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 5.00 A T p – = 0.005576 v 0.000430 – = 0.001130 v /NDF = 0.914653 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 6.00 A T p – = 0.004890 v 0.000366 – = 0.000829 v /NDF = 1.873486 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 7.00 A T p – = 0.003570 v 0.000423 – = 0.000601 v /NDF = 1.330052 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 8.00 A T p – = 0.002590 v 0.000490 – = 0.001152 v /NDF = 1.636573 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 9.00 A T p – = 0.002481 v 0.000505 – = 0.000559 v /NDF = 1.102625 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 11.00 A T p – = 0.002431 v 0.000418 – = 0.000287 v /NDF = 1.061336 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 16.00 A T p – = 0.001797 v 0.000360 – = -0.000406 v /NDF = 1.215329 c - fD - ) f D ( L M Y F - G ) - f D ( Y Figure B.21: Template fits to correlation functions from 0-5% central events using 60-90% central events asperipheral reference from the 75 GeV jet dataset. Each figure shows a different p T range.57 - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 26.00 A T p – = 0.001284 v 0.000423 – = 0.000887 v /NDF = 1.986117 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 100.00 A T p – = 0.001716 v 0.000517 – = 0.000388 v /NDF = 1.408975 c - fD - - ) f D ( L M Y F - G ) - f D ( Y Figure B.22: Template fits to correlation functions from 0-5% central events using 60-90% central events asperipheral reference from the 75 GeV jet dataset. Each figure shows a different p T range.58 - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 0.75 A T p – = 0.003755 v 0.000079 – = 0.000321 v /NDF = 1.693043 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 1.00 A T p – = 0.005228 v 0.000107 – = 0.000654 v /NDF = 0.809292 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 1.25 A T p – = 0.006219 v 0.000137 – = 0.000853 v /NDF = 0.949381 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 1.50 A T p – = 0.007105 v 0.000168 – = 0.000933 v /NDF = 1.069356 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 1.75 A T p – = 0.007981 v 0.000195 – = 0.001145 v /NDF = 0.742131 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 2.00 A T p – = 0.008073 v 0.000231 – = 0.001804 v /NDF = 0.932747 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 2.50 A T p – = 0.008886 v 0.000244 – = 0.001616 v /NDF = 0.893471 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 3.00 A T p – = 0.008586 v 0.000342 – = 0.001520 v /NDF = 1.520966 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 3.50 A T p – = 0.007607 v 0.000349 – = 0.001076 v /NDF = 1.175174 c - fD - - ) f D ( L M Y F - G ) - f D ( Y Figure B.23: Template fits to correlation functions from 0-5% central events using 60-90% central events asperipheral reference from the 100 GeV jet dataset. Each figure shows a different p T range.59 - fD ) f D ( Y cent Y Fit peri YF + G (0) peri YF + ridge2 Y (0) peri YF + ridge3 Y ATLAS -1 = 8.16 TeV, 165 nb NN s+Pb p < 4.0 GeV A T p – = 5.33 · v 0.47 – = 1.82 · v /NDF = 1.27 c | > 1 Bj hD | - fD - - ) f D ( pe r i Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 4.50 A T p – = 0.004879 v 0.000385 – = 0.000365 v /NDF = 1.269584 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 5.00 A T p – = 0.004199 v 0.000568 – = 0.001868 v /NDF = 1.586150 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 6.00 A T p – = 0.003481 v 0.000343 – = 0.000194 v /NDF = 0.944991 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 7.00 A T p – = 0.002603 v 0.000338 – = 0.000077 v /NDF = 1.506372 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 8.00 A T p – = 0.002131 v 0.000378 – = 0.000476 v /NDF = 1.255232 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 9.00 A T p – = 0.002215 v 0.000418 – = 0.000720 v /NDF = 1.371558 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 11.00 A T p – = 0.002088 v 0.000349 – = 0.000643 v /NDF = 1.146154 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 13.00 A T p – = 0.001587 v 0.000382 – = 0.000462 v /NDF = 0.774556 c - fD - ) f D ( L M Y F - G ) - f D ( Y Figure B.24: Template fits to correlation functions from 0-5% central events using 60-90% central events asperipheral reference from the 100 GeV jet dataset. Each figure shows a different p T range.60 - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 16.00 A T p – = 0.002056 v 0.000394 – = 0.000463 v /NDF = 0.641885 c - fD - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 20.00 A T p – = 0.002166 v 0.000430 – = -0.001209 v /NDF = 1.437285 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 26.00 A T p – = 0.001586 v 0.000437 – = -0.000233 v /NDF = 1.005143 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 45.00 A T p – = 0.001939 v 0.000393 – = 0.000172 v /NDF = 1.915499 c - fD - - ) f D ( L M Y F - G ) - f D ( Y - fD ) f D ( Y HM DataFit LM YF + G (0) LM YF + ridge2 Y (0) LM YF + ridge3 Y Internal ATLAS < 100.00 A T p – = 0.001749 v 0.000660 – = 0.001476 v /NDF = 0.826421 c - fD - - ) f D ( L M Y F - G ) - f D ( Y Figure B.25: Template fits to correlation functions from 0-5% central events using 60-90% central events asperipheral reference from the 100 GeV jet dataset. Each figure shows a different p T range.61 B.5 Track φ flattening maps Track φ flattening corrections are derived by normalizing track φ distributions in ∆ η = 0 . slices fortracks within a given p T range. These correction maps are generated for MB and jet events independently.62 - - - - - trk h - - - t r k f Internal ATLAS MB+HMT < 0.75 trk T p - - - - - trk h - - - t r k f Internal ATLAS > 100 GeV jet T p < 0.75 trk T p - - - - - trk h - - - t r k f Internal ATLAS MB+HMT < 1.00 trk T p - - - - - trk h - - - t r k f Internal ATLAS > 100 GeV jet T p < 1.00 trk T p - - - - - trk h - - - t r k f Internal ATLAS MB+HMT < 1.25 trk T p - - - - - trk h - - - t r k f Internal ATLAS > 100 GeV jet T p < 1.25 trk T p - - - - - trk h - - - t r k f Internal ATLAS MB+HMT < 1.50 trk T p - - - - - trk h - - - t r k f Internal ATLAS > 100 GeV jet T p < 1.50 trk T p Figure B.26: Track φ flattening corrections for MB (left) and jet (right) events for tracks in various p T ranges.63 - - - - - trk h - - - t r k f Internal ATLAS MB+HMT < 1.75 trk T p - - - - - trk h - - - t r k f Internal ATLAS > 100 GeV jet T p < 1.75 trk T p - - - - - trk h - - - t r k f Internal ATLAS MB+HMT < 2.00 trk T p - - - - - trk h - - - t r k f Internal ATLAS > 100 GeV jet T p < 2.00 trk T p - - - - - trk h - - - t r k f Internal ATLAS MB+HMT < 2.50 trk T p - - - - - trk h - - - t r k f Internal ATLAS > 100 GeV jet T p < 2.50 trk T p - - - - - trk h - - - t r k f Internal ATLAS MB+HMT < 3.00 trk T p - - - - - trk h - - - t r k f Internal ATLAS > 100 GeV jet T p < 3.00 trk T p Figure B.27: Track φ flattening corrections for MB (left) and jet (right) events for tracks in various p T ranges.64 - - - - - trk h - - - t r k f Internal ATLAS MB+HMT < 3.50 trk T p - - - - - trk h - - - t r k f Internal ATLAS > 100 GeV jet T p < 3.50 trk T p - - - - - trk h - - - t r k f Internal ATLAS MB+HMT < 4.50 trk T p - - - - - trk h - - - t r k f Internal ATLAS > 100 GeV jet T p < 4.50 trk T p - - - - - trk h - - - t r k f Internal ATLAS MB+HMT < 7.00 trk T p - - - - - trk h - - - t r k f Internal ATLAS > 100 GeV jet T p < 7.00 trk T p - - - - - trk h - - - t r k f Internal ATLAS MB+HMT < 100.00 trk T p - - - - - trk h - - - t r k f Internal ATLAS > 100 GeV jet T p < 100.00 trk T p Figure B.28: Track φ flattening corrections for MB (left) and jet (right) events for tracks in various p T ranges. ibliography [1] Particle Data Group. “Review of Particle Physics”. 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