A Comprehensive Monte Carlo Framework for Jet-Quenching
NNuclear Physics A 00 (2020) 1–7
NuclearPhysics A / locate / procedia XXVIIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions(Quark Matter 2019)
A Comprehensive Monte Carlo Framework for Jet-Quenching
Ron Soltz
Wayne State University and Lawrence Livermore National Laboratory
Abstract
This article presents the motivation for developing a comprehensive modeling framework in which di ff erent models andparameter inputs can be compared and evaluated for a large range of jet-quenching observables measured in relativisticheavy-ion collisions at RHIC and the LHC. The concept of a framework us discussed within the context of recent e ff ortsby the JET Collaboration, the authors of JEWEL, and the JETSCAPE collaborations. The framework ingredients foreach of these approaches is presented with a sample of important results from each. The role of advanced statisticaltools in comparing models to data is also discussed, along with the need for a more detailed accounting of correlatederrors in experimental results. Keywords: quark-gluon plasma, jet-quenching, framework, modeling, statistics
1. Framework Motivation and Ingredients
The benefit of using a mutli-stage model with an advanced statistics package to study the properties andevolution of the quark-gluon plasma created in heavy ion collisions has been demonstrated in the soft physicssector by the work of the MADAI collaboration [1] and the Duke QCD theory group [2]. It stands to reasonthat hard physics sector may benefit from a similar approach. Whereas the methods for calculating soft ob-servables have converged around viscous hydrodynamics preceded by an initial glasma + hydrodynamizationand followed by Cooer-Frye hadronization into to a hadronic cascade, the methodology for jet-quenching ismore varied, and may itself require a multi-stage approach [3]. Thus, for hard sector, a framework is neededto provide the flexibility of testing the inherent assumptions within corresponding models, and for adding,removing, or modifying di ff erent stages or mechanisms of energy loss.Figure 1 shows the essential ingredients for such a framework. It includes the elements currently usedto calculate soft observables and adds in components for jet evolution and a jet-finder to calculate jet ob-servables. In the next section we will discuss how the work of the JET Collaboration, and the JEWEL, andJETSCAPE computational approaches map onto this framework. Email address: [email protected] (Ron Soltz) a r X i v : . [ phy s i c s . d a t a - a n ] M a r R. Soltz / Nuclear Physics A 00 (2020) 1–7
Ron Soltz (WSU/LLNL) Wuhan Quark Matter 2019
Comprehensive Framework Ingredients Initial State Medium
Jet Evolution Jet Observables R AA , v , A ij , X γ J , rho(r), D(z), … H a d r o n i z a t i o n H y d r od y n a m i z a t i o n Modular components to test physics assumptions Full events to calculate any observable that can be measured in data
Jet-FinderParticle Observables R AA , v , etc. Fig. 1. Essential ingredients for a jet-quenching framework.
2. Framework Examples
The first steps towards building a true framework for jet-quenching were taken by the JET Collaboration.Their goal was to develop a consistent approach for determining ˆ q = (cid:104) ( ∆ k T ) (cid:105) / L , the energy-loss metric formeasuring the transverse di ff usion per unit length for a jet or parton traversing a dense nuclear-medium [4].In this work, five di ff erent approaches were used to constrain ˆ q with the leading hadron nuclear modification, R AA . All approaches used a 2D + +
1D idealhydro) with central Glauber initial conditions (except for HT-M which used MC-KLN for initial conditions).Parameterizations for ˆ q / T were allow to di ff er for central collisions at RHIC and the LHC, but wereotherwise independent of temperature during the evolution of a single collision system. Chi-squared min-imizations were used to determine optimal values for the leading hardon nuclear-monification factor, R AA .The left panel of Figure 2 shows the general framework schematic, and the right panel shows the corre-sponding values of ˆ q / T for each approach. Although theses comparisons were not performed within singleframework, the ability to compare models and data under a consistent set of assumptions represents a sig-nificant step in this direction. Ron Soltz (WSU/LLNL) Wuhan Quark Matter 2019
Partial Framework Mostly Glauber Various Hydro
GLV-CUJET s i n g l e h a d r o n R AA HT-BW —> LBT
Consistent hydro profile given to each model practitioner Apples-to-apples determination of q-hat
HT-M —> MATTERMcGill-AMY / MARTINI
KAREN M. BURKE et al.
PHYSICAL REVIEW C , 014909 (2014) N /T (DIS) eff ˆ T (GeV) q / T ˆ FIG. 10. (Color online) Theassumedtemperaturedependenceofthe scaled jet transport parameter ˆ q/T in different jet quenchingmodels for an initial quark jet with energy E =
10 GeV. Values ofˆ q at the center of the most central A + A collisions at an initialtime τ = . /c in HT - BW and HT - M models are extracted fromfitting to experimental data on hadron suppression factor R AA at bothRHIC and LHC. In GLV - CUJET , MARTINI , and
MCGILL - AMY models,it is calculated within the corresponding model with parametersconstrained by experimental data at RHIC and LHC. Errors fromthe fits are indicated by filled boxes at three separate temperaturesat RHIC and LHC, respectively. The arrows indicate the range oftemperatures at the center of the most central A + A collisions.The triangle indicates the value of ˆ q N /T in cold nuclei from DISexperiments. agaugeofmediumpropertiesatitsmaximumdensityachievedin heavy-ion collisions, we will consider the value of ˆ q for aquark jet at the center of the most central A + A collisionsat an initial time τ when hydrodynamic models are appliedfor the bulk evolution. For all the hydrodynamic models usedin this paper with different approaches of parton energy loss,the initial time is set at τ = . /c with initial temperature T = + Au collisions at √ s =
200 GeV / n at RHIC andPb + Pb collisions at √ s = .
76 TeV / n at LHC, respectively.Shown in Fig. 10 are the extracted or calculated valuesfor ˆ q as a function of the initial temperature for a quark jetwith initial energy E =
10 GeV. For the
GLV - CUJET model, ˆ q is calculated from one set of parameters with HTL screeningmassandthemaximumvalueofrunningcoupling α max = . T =
378 MeV, and for another set with α max = .
24 for 378 ! T !
486 MeV. The difference in α max and the corresponding ˆ q in these two temperature regions canbe considered part of the theoretical uncertainties.Similarly, the values of ˆ q from the MARTINI and
MCGILL - AMY models are calculated according to the leading orderpQCD HTL formula in Eq. (18) with the two values of α s extracted from comparisons to the experimental data on R AA at RHIC and LHC, respectively. The GLV , MARTINI , and
MCGILL - AMY models all assume zero parton energy loss andtherefore zero ˆ q in the hadronic phase. In the HT - BW model,the fit to the experimental data gives ˆ q = . ± . / fm at temperatures reached in the most central Au + Au collisionsat RHIC, and 2 . ± . / fm at temperatures reached inthe most central Pb + Pb collisions at LHC. Values of ˆ q inthe hadronic phase are assumed to be proportional to thehadron density in a hadron resonance gas model with thenormalization in a cold nuclear matter determined by DISdata [81]. Values of ˆ q in the QGP phase are consideredproportional to T and the coefficient is determined by fittingto the experimental data on R AA at RHIC and LHC separately.In the HT - M model the procedure is similar except that ˆ q isassumed to be proportional to the local entropy density andits initial value is ˆ q = . ± .
11 GeV / fm in the center ofthe most central Au + Au collisions at RHIC, and ˆ q = . ± .
27 GeV / fm in the most central Pb + Pb collisions at LHC(note that the values of ˆ q extracted in Sec. IV are for gluon jetsand therefore 9/4 times the corresponding values for quarkjets). For temperatures close to and below the QCD phasetransition, ˆ q isassumedtofollowtheentropydensity,and ˆ q/T shown in Fig. 10 is calculated according to the parameterizedequation of state [97] that is used in the hydrodynamicevolution of the bulk medium. In both HT approaches, nojet energy dependence of ˆ q is considered.Considering the variation of the ˆ q values between the fivedifferent models studied here as theoretical uncertainties, onecan extract its range of values as constrained by the measuredsuppression factors of single hadron spectra at RHIC and LHCas follows: ˆ qT ≈ ! . ± . , . ± . , at the highest temperatures reached in the most centralAu + Au collisions at RHIC and Pb + Pb collisions at LHC.The corresponding absolute values for ˆ q for a 10 GeV quarkjet areˆ q ≈ ! . ± . . ± . / fm at T =
370 MeV ,T =
470 MeV , at an initial time τ = . /c . These values are very closeto an early estimate [6] and are consistent with leading order(LO) pQCD estimates, albeit with a somewhat surprisinglysmall value of the strong coupling constant as obtained in CUJET , MARTINI , and
MCGILL - AMY models. The HT modelsassume that ˆ q is independent of jet energy in this study. CUJET , MARTINI , and
MCGILL - AMY models, on the other hand, shouldhave a logarithmic energy dependence on the calculated ˆ q from the kinematic limit on the transverse momentum transferin each elastic scattering, which also gives the logarithmictemperature dependence as seen in Fig. 10.As a comparison, we also show in Fig. 10 the value ofˆ q N /T in cold nuclei as extracted from jet quenching inDIS [81,89]. The value of ˆ q N = . − .
06 GeV / fm and aneffective temperature of an ideal quark gas with three quarkswithin each nucleon at the nucleon density in a large nucleusare used. It is an order of magnitude smaller than that in A + A collisions at RHIC and LHC.There have been recent attempts [92,98] to calculate the jettransport parameter in lattice gauge theories. A recent latticecalculation [98] found that the nonperturbative contribution Fig. 2. (Left) JET collaboration approach as a jet-quenching framework and (right) ˆ q evaluations obtained using this approach. The first genuine Monte Carlo jet-quenching framework to match the criteria shown in Figure 1 isJEWEL [5–9], which includes both collisional and radiative energy-loss with formation time-ordering. Thisframework can be implemented with any medium description specifying the space-time and momentumdistribution of scattering centers. The current implementation of JEWEL uses PYTHIA6 [10] for both the . Soltz / Nuclear Physics A 00 (2020) 1–7 initial hard-scattering and final hadronization. Jet observables are calculated in FastJet [11] and RIVET [12]for comparison to experimental, and the medium description is calculated with an ideal 1 +
1D Bjorken hy-drodynamics with Glauber initial conditions. Figure 3 shows this implementation of the JEWEL framework.
Ron Soltz (WSU/LLNL) Wuhan Quark Matter 2019
Framework ingredients Glauber Ideal 1+1D Bjorken hydro τ f FastJet + RIVET
JEWEL PY T H I A h a d r o n i z a t i o n PY T H I A h a r d s ca tt e r i n g Jet Observables R AA , v , A ij , X γ J , rho(r), D(z), … Any medium profile can be inserted
Fig. 3. JEWEL representation as jet-quenching framework.
A large set jet observables for Pb + Pb at √ s NN = R CP nuclear modification factor in the peripheral region, which is problematic for many models. Theratio of MC to data shows that the JEWEL results are within the systematic error band (yellow bars) forthe asymmetry. The role of systematic errors in model-to-data comparisons will be discussed further inSection 3. Ron Soltz (WSU/LLNL) Wuhan Quark Matter 2019
JEWEL Results (Zapp,Krauss,Wiedemann:1312.5536) ! (0-10)%0.20.40.60.81 R C P (10-20)%0.20.40.60.81 R C P (20-30)%0.20.40.60.81 R C P (30-40)%0.20.40.60.81 R C P (40-50)%0.20.40.60.81 R C P (50-60)% ATLASdataJEWEL+PYTHIA40 60 80 100 120 140 160 180 20000.20.40.60.81 p ⊥ [ GeV ] R C P ( - )%( - )% × − ( - )% × − ( - )% × − ( - )% × − ( - )% × − ( - )% × − JEWEL+PYTHIAATLASpreliminarydata . . . . . . . . . . − − − − − − − R= . z D ( z ) CMSdataJEWEL+PYTHIA . . . . . . . ( - )%, p ⊥ ,1 > e v e n t f r a c t i o n . . . . . . . . . . . . A J M C / d a t a CMSdataJEWEL+PYTHIA . . . . . . . . . ( - )%, p ⊥ ,1 > e v e n t f r a c t i o n . . . . . . . . . . . A J M C / d a t a ATLASdataJEWEL+PYTHIA . . . . . . ( - )%,45GeV < p ⊥ < / N j e t d N j e t / d p ⊥ d ∆ φ !!! c o rr [ G e V − ] . . . . . . . . . . ∆ φ M C / d a t a ATLASdataJEWEL+PYTHIA . . . . . . ( - )%,45GeV < p ⊥ < / N j e t d N j e t / d p ⊥ d ∆ φ !!! c o rr [ G e V − ] . . . . . . . . . . ∆ φ M C / d a t a Jet R CP Fragmentation Delta-Phi Asymmetry
Broad agreement, larger differences for peripheral
Fig. 4. JEWEL results [7] for Jet nuclear modification, fragmentation, reaction-plane angle, and asymmetry for Pb + Pb at √ s NN = The Jet Energy-loss Tomography with a Statistically and Computationally Advanced Program Envelope(JETSCAPE) framework expands upon previous e ff orts by applying the concept of multi-stage modularity toa virtuality and energy ordered evolution of the jet partons. As shown in Figure 5, the TRENTO model [17]is used to calculate the initial state nuclear geometry. This model was chosen for its ability to approximate R. Soltz / Nuclear Physics A 00 (2020) 1–7 a number of physically motivated distributions as well as interpolate between them. The hard-scatteringcross-sections are calculated with PYTHIA8 [18], and evolution of the medium can be calculated with theviscous 2 +
1D hydrodynamic code, VISHNU [19], or the viscous 3 +
1D codes, MUSIC [20] or CLVisc [21].For the jet evolution, the initial splitting functions can be calculated within MATTER [22]. Below a vir-tuality denoted by Q , the jet evolution may be passed to the Linear Boltzmann Transport (LBT) [23] orMARTINI [24] models. Initial comparisons in a static medium have shown both LBT and MARTINI toyield consistent results. A separate module may also be employed at lower virtuality and energy to calculatethe parton drag based on the AdS / CFT duality. The Cooper-Frye formula [25] is used for soft particlization,and hard particle hadronization proceeds through PYTHIA8 routines, modified to provide both a coloredor colorless option. Recent benchmarks with p + p data indicate that the colorless option, developed for theparton-rich heavy-ion environment, may also be preferred for proton collisions [26]. All subsequent soft-hadronic interactions are calculated within SMASH [27] and final outputs are saved in the HEPMC format.See [28] for a detailed description of JETSCAPE code and use. Ron Soltz (WSU/LLNL) Wuhan Quark Matter 2019 ! Event Generator Ingredients
Introduce virtuality/energy ordered jet-quenching Any component is replaceable I n i t i a l g e o m e t r y T R E N T O H a r d P a r t i c l e P r o du c t i o n P Y T H I A I n i t i a l S o ft D e n s i t y d i s t r i bu t i o n H a d r o n i c C a s c a d e S M A S H H a d o r o n i z a t i o n P Y T H I A C oo p e r - F r y e S a m p li ng Viscous Fluid Dynamics for Medium VISHNU / MUSIC
Energy-momentum Deposition
Large- Q ( > Q ) Small- Q ( < Q ) MATTER LBT MARTINI AdS/CFT
Higher Twist formalism Higher Twist formalism AMY formalism = 4 super Yang-Mills 𝒩 Scattering dominated On-shell parton transportRadiation dominated Virtuality ordered splitting Diffusion into medium Large- E Small - E H E P M C O u t p u t Fig. 5. Example of Jet-quenching ingredients JETSCAPE Framework
Figure 6 shows a sample of results shown at Quark Matter 2019 for JETSCAPE run with MATTER + LBTwith a virtuality switching parameter Q = Q , using temperaturedependent parameterization of ˆ q / T [33] Ron Soltz (WSU/LLNL) Wuhan Quark Matter 2019 (GeV) T p
20 40 60 80 100 AA ± h R CMS [JHEP 1704 039 (2017)] =2GeV Q =0.25, s α JS (MATTER+LBT), =5.02 TeV s |<1.0 η |PbPb (30-50%) (GeV) T p
20 40 60 80 100 AA ± h R CMS [EPJ C72, 1945 (2012)] =2GeV Q =0.25, s α JS (MATTER+LBT), =2.76 TeV s |<1.0 η |PbPb (0-5%) PbPb MATTER+LBT (MLQ ! (GeV) Tjet p
50 100 150 200 250 300 AA j e t R − CMS [PRC 96, 015202 (2017)] =2GeV Q =0.25, s α JS (MATTER+LBT), =2.76 TeV, PbPb (0-5%) s =0.4 R T k anti- |<2.0 jet η | Charged hadron R AA Inclusive jet R AA (GeV) Tjet p AA j e t R ATLAS [PLB 790 108 (2019)] =2GeV Q =0.25, s α JS (MATTER+LBT), =5.02 TeV, PbPb (30-40%) s =0.4 R T k anti- |<2.8 jet y | ce n t r a l R AA n o n - ce n t r a l R AA (GeV) Tch p v − ATLAS [EPJ C78 997 (2018)] =2GeV =0.25,Q s α JS (MATTER+LBT), =5.02 TeV s |<2.5 η |PbPb (30-40%) hadron v D R AA . . . . . . r P ( r )( G e V ) PbPb 5.02 TeV, 0-10% p jet T > , | ⌘ jet | < . p trk T > . − −
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ATLAS (0-10%) =2 GeV) Q MATTER+AdS/CFT ( =1 GeV) Q MATTER+AdS/CFT ( − −
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ATLAS (0-10%)MATTER+MARTINIMATTER(vacuum)+MARTINI − −
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ATLAS (0-10%)MATTER+LBTMATTER(vacuum)+LBT D P b P b ( z ) / D pp ( z ) z z z JETSCAPE,2.76TeV,PbPb:0 - - k T R = 0.4,100< p jetT < 398GeV,0< | Y jet | < 2.1, p trkT > 1GeV − −
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ATLAS (0-10%)MATTER+LBTMATTER(vacuum)+LBT
JETSCAPE PRELIMINARY − −
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ATLAS (0-10%)MATTER+LBTMATTER(vacuum)+LBT
JETSCAPE PRELIMINARY (a) (b) (c)
Preliminary Preliminary Preliminary anti - k t , R = 0.4 p jetT :100 - | Y jet | < 2.1 p trkT > 1GeVPbPb(0 - − −
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ATLAS (0-10%) =2 GeV) Q MATTER+AdS/CFT ( =1 GeV) Q MATTER+AdS/CFT ( − −
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ATLAS (0-10%)MATTER+MARTINIMATTER(vacuum)+MARTINI − −
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ATLAS (0-10%)MATTER+LBTMATTER(vacuum)+LBT D P b P b ( z ) / D pp ( z ) z z z JETSCAPE,2.76TeV,PbPb : 0 - - k T R = 0.4,100 < p jetT < 398GeV,0 < | Y jet | < 2.1, p trkT > 1GeV − −
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ATLAS (0-10%)MATTER+LBTMATTER(vacuum)+LBT
JETSCAPE PRELIMINARY − −
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ATLAS (0-10%)MATTER+LBTMATTER(vacuum)+LBT
JETSCAPE PRELIMINARY (a) (b) (c)
Preliminary Preliminary Preliminary
ATLAS[EPJC77(2017)379]JETSCAPE (MATTER[vacuum]+ LBT) ρ (r) Broad agreement, larger differences for peripheral
Charged hadron R AA Inclusive jet R AA D PbPb ( z )/ D pp ( z ) Fig. 6. Overview of JETSCAPE results presented at Quark Matter 2019. . Soltz / Nuclear Physics A 00 (2020) 1–7
3. Framework Usage, Statistics, and Correlated Errors
As described earlier, the purpose of a framework is to provide a consistent basis for testing di ff erentmodels and comparing to wide range of experimental observables. The fact that each model within theframework may have one or more parameters adds another layer of complication to the comparison. Fora limited set of observables and for models with few parameters, a frequentist statistical approach can beused [34], but for a larger numbers of parameters and observables Bayesian approaches are optimal. Toprove this point, note that a chi-squared analysis of soft physics signatures by this author [35] took longer,produced fewer physics insights, and accumulated a smaller number of citations than a concurrent Bayesiananalysis by the MADAI Collaboration [1].If used properly, the Bayesian approach can be used to determine the most likely range of values forinput parameters for an assumed set of prior distributions. The final results should not be overly sensitive toa particular choice of the prior distribution, and the posterior distributions are not meaningful if the modeldoes not give a reasonable description of all experimental observables. Models that do not describe thedata should eventually be discarded or modified once the underlying reasons for failure are understood,and prior distributions for input parameters should not extend beyond their physically admissible values.The phrase reasonable description refers to the probability that a given implementation of the frameworkdescribes the data within errors. The topic of model error is left for future discussion and future conferences,and the treatment of independent statistical and systematic errors is well understood. However, the propertreatment of correlated errors requires additional information than what is currently being released by mostexperimental collaborations.As an example, consider a hypothetical ratio measurement with two sources of errors, each with aGaussian profile, at low and high regions of the abscissa. The errors within each Gaussian region arecorrelated, but the errors in the separate regions are uncorrelated. Figure 7 shows a characteristic unitarymeasurement with this error profile. The top panel shows the data and error band for each region in the leftpanels, and the quadrature sum of errors on the right. The lower panel shows the corresponding co-varianceerror matrices, along with the sum. the top right panel shows two fits to the data, the solid-green curvesare draws from a distribution that reflects the uncorrelated nature of the two sources of errors, whereasthe dashed-magenta curves are drawn from distributions that assume all errors to be fully correlated. Notethat the dashed-magenta curves associated with fully correlated errors do not account for the full range ofvariation permitted by the data. Ron Soltz (WSU/LLNL) Wuhan Quark Matter 2019
A Tale of Two Systematic Errors ! + =+Sys. Error 1 fully correlated =Sys. Error 2 fully correlated quadrature sum of errors E rr o r C o v a r i a n ce σ ij = σ i σ j a r b i t r a r y m ea s u r e m e n t Fig. 7. Example of two uncorrelated Gaussian-errors and the di ff erence between summing in quadrature (above) vs. summing covari-ances (below). The curves are double-Gaussian fits assuming the two sets of errors to be fully correlated (dashed magenta) and fullyuncorrelated (solid green) R. Soltz / Nuclear Physics A 00 (2020) 1–7
A more realistic example for jet-quenching may be the one shown in Figure 8, which shows two sourcesof errors that increase in magnitude with the square-root of distance along the abscissa towards the lowand high regions, such that the quadrature sum shown on the right displays a constant error band. Themagenta-curves drawn from a fully correlated distributions are all lines of zero slope, whereas the solid-green draws from the true error distributions allow for a monotonic increase or decrease along the abscissa.To achieve a proper assessment of errors for model comparisons, experimentalists will need to start releasingfull covariances for the errors, or at least publish the separate, p T dependent contributions of errors in caseswhere the errors are assumed to be fully correlated. Note that this may also require new methods for plottingdata to visualize goodness-of-fit criteria when the systematic error correlations vary significantly with p T .Ultimate, a proper treatment of both experimental and model errors will be needed to realize the full potentialof the jet-quenching framework. Fig. 8. Example of two uncorrelated squre-root-errors peaking at low and high values abscissa.
Acknowledgements
This work was supported in part by the National Science Foundation within the framework of theJETSCAPE collaboration, Cooperative Agreement ACI-1550300, and the U.S. Department of Energy undercontract DE-AC52-07NA27344.
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