Measurements of jet-related observables at the LHC
OOctober 22, 2018 4:43 WSPC/INSTRUCTION FILE kokkas-ijmpa
International Journal of Modern Physics Ac (cid:13)
World Scientific Publishing Company
Measurements of jet-related observables at the LHC
P. KOKKAS
Physics Department, University of Ioannina,45110 Ioannina, [email protected]
Received Day Month YearRevised Day Month YearDuring the first years of the LHC operation a large amount of jet data was recorded bythe ATLAS and CMS experiments. In this review several measurements of jet-relatedobservables are presented, such as multi-jet rates and cross sections, ratios of jet crosssections, jet shapes and event shape observables. All results presented here are basedon jet data collected at a center-of-mass energy of 7 TeV. Data are compared to vari-ous Monte Carlo generators, as well as to theoretical next-to-leading-order calculationsallowing a test of perturbative Quantum Chromodynamics in a previously unexploredenergy region.
Keywords : Jet and multi-jet rates and cross sections; Ratios of jet cross sections; Jetevent shapes; Jet shapes.PACS numbers:
1. Introduction
After three years of very successful operation of the Large Hadron Collider (LHC), alarge amount of jet data was recorded both by the ATLAS and CMS experiments.Up to now these collaborations published results on jet cross sections, ratios ofjet cross sections, multi-jet rates and other jet related observables using the datacollected during the first two years at a center-of-mass energy of 7 TeV. The goalsof these studies are to test perturbative Quantum Chromodynamics (pQCD) in apreviously unexplored energy region, check the Standard Model (SM) predictionsat high energy scales, measure and understand the main background to many newphysics searches, determine the strong coupling constant α s and its running, andprovide constraints on parton distribution functions (PDFs).At leading order (LO) in pQCD, jet production in proton-proton (pp) collisionsoccurs when two partons interact via the strong force to produce two final-statepartons. Each of the final state particles may subsequently lose energy by emittingother quarks and gluons in a process referred to as a parton shower (PS). Finally,the products of the parton shower undergo hadronisation and form hadron jets.Events with three or more jets in the final state originate from hard-gluon radiation a r X i v : . [ h e p - e x ] S e p ctober 22, 2018 4:43 WSPC/INSTRUCTION FILE kokkas-ijmpa P.Kokkas and other higher-order QCD processes.Classical measurements are those of the inclusive jet p T and dijet mass crosssection, which are presented in Refs. 3 to 9 and also discussed in a separate reviewin this volume . Here, a review of recent measurements on other jet-related ob-servables at the LHC is presented, based on the data collected during 2010 and 2011at a center-of-mass energy of 7 TeV. The review is organized as follows: Section 2presents results on multi-jet rates and cross sections. In section 3 measurements ofratios of jet cross sections are presented. Section 4 presents results on jet shapesobservables. In section 5 measurements of event shapes are presented, followed bythe conclusions in Section 6.
2. Multi-jet rates and cross sections
The goal of the studies with the very first LHC jet data was to test the performanceof the different LO Monte Carlo (MC) simulations, so that they can be used toestimate multi-jet backgrounds for new particle searches. For example the ATLAScollaboration, in Ref. 11, presents studies on inclusive multi-jet production, usingthe very first jet data collected during 2010 which correspond to an integratedluminosity of 2 . − . Figure 1 shows the p T -dependent differential cross sectionsfor the first four leading jets in multi-jet events. The results are compared to differentLO MC simulations based on the pythia , Alpgen and Sherpa generatorsusing various optimised sets of parameters (so-called tunes ). All MC simulationsagree reasonably well with the data.In Ref. 15 the ATLAS collaboration presents the measurement of double-differential three-jet production cross sections as a function of the three-jet mass m and the sum of absolute rapidity separation between the three leading jets | Y ∗ | = | y − y | + | y − y | + | y − y | . The measurement is done for two dif-ferent values of the jet radius parameter, R = 0 . R = 0 .
6, using a data samplecorresponding to an integrated luminosity of 4 .
51 fb − collected with the ATLASdetector during 2011. The goal of this study is to test the description of multi-jetevents in next-to-leading-order (NLO) QCD, and provide constraints on the protonPDFs beyond those from inclusive and dijet cross sections. Figure 2, on the top,shows the comparison of the three-jet double-differential cross section as a functionof m , binned in | Y ∗ | , to NLO predictions times non-perturbative (NP) correctionsusing the CT10
16, 17 -NLO PDF set. The same figure on the bottom shows the ratioof data to NLO predictions using different PDF sets, like CT10, MSTW2008
18, 19 ,and GJR08 . It is found that for a jet radius parameter R = 0 . R = 0 . m −| Y ∗ | plane. The discrepancy is covered by the experimentaland theoretical uncertainty bands and it has only a minor dependence on the PDFset used.The differential 3-jet production cross section as a function of the invariant mass m and the maximum rapidity | y | max of the 3-jet system has been published by thectober 22, 2018 4:43 WSPC/INSTRUCTION FILE kokkas-ijmpa Measurements of jet-related observables at the LHC
100 200 300 400 500 600 700 800 [ pb / G e V ] T / d p σ d -1
100 200 300 400 500 600 700 800 [ pb / G e V ] T / d p σ d -1 ATLAS -1 L dt=2.4 pb ∫ R=0.4, =7 TeV)+syst.sData ( 1.11 × ALPGEN+HERWIG AUET1 0.65 × PYTHIA AMBT1 1.22 × ALPGEN+PYTHIA MC09’ 1.06 × SHERPA 2 ≥ jets N (leading jet) [GeV] T p100 200 300 400 500 600 700 800 M C / D a t a T p100 200 300 400 500 600 700 800 M C / D a t a
100 200 300 400 500 600 700 800 [ pb / G e V ] T / d p σ d -1
100 200 300 400 500 600 700 800 [ pb / G e V ] T / d p σ d -1 ATLAS -1 L dt=2.4 pb ∫ R=0.4, =7 TeV)+syst.sData ( 1.11 × ALPGEN+HERWIG AUET1 0.65 × PYTHIA AMBT1 1.22 × ALPGEN+PYTHIA MC09’ 1.06 × SHERPA 2 ≥ jets N leading jet) [GeV] nd (2 T p100 200 300 400 500 600 700 800 M C / D a t a nd (2 T p100 200 300 400 500 600 700 800 M C / D a t a
100 150 200 250 300 350 400 [ pb / G e V ] T / d p σ d -1
100 150 200 250 300 350 400 [ pb / G e V ] T / d p σ d -1 ATLAS -1 L dt=2.4 pb ∫ R=0.4, =7 TeV)+syst.sData ( 1.11 × ALPGEN+HERWIG AUET1 0.65 × PYTHIA AMBT1 1.22 × ALPGEN+PYTHIA MC09’ 1.06 × SHERPA 3 ≥ jets N leading jet) [GeV] rd (3 T p100 150 200 250 300 350 400 M C / D a t a rd (3 T p100 150 200 250 300 350 400 M C / D a t a
60 80 100 120 140 160 180 200 [ pb / G e V ] T / d p σ d -1
60 80 100 120 140 160 180 200 [ pb / G e V ] T / d p σ d -1 ATLAS -1 L dt=2.4 pb ∫ R=0.4, =7 TeV)+syst.sData ( 1.11 × ALPGEN+HERWIG AUET1 0.65 × PYTHIA AMBT1 1.22 × ALPGEN+PYTHIA MC09’ 1.06 × SHERPA 4 ≥ jets N leading jet) [GeV] th (4 T p60 80 100 120 140 160 180 200 M C / D a t a th (4 T p60 80 100 120 140 160 180 200 M C / D a t a Fig. 1. The differential cross section of the four leading jets as a function of jet p T , measured bythe ATLAS collaboration. The results are compared to different LO MC simulations. CMS collaboration in Ref. 21. The measurement is done in two rapidity bins with | y | max < ≤ | y | max < − collectedwith the CMS detector during 2011. Figure 3, on the left, shows the comparisonof the 3-jet mass distribution to the NLO prediction employing the CT10 PDF settimes non-perturbative corrections. It is observed that pQCD is able to describethe cross section as a function of the 3-jet mass over five orders of magnitude andfor 3-jet masses up to 3 TeV. The same figure on the right presents the ratiosof the measured cross sections, for the lowest rapidity bin, to theoretical predic-tions including NP effects, using various PDF sets, such as CT10, NNPDF2.1
22, 23 ,MSTW2008, HERAPDF1.5 and ABM11 . Within uncertainties most PDF setsare able to describe the data. This measurement is used by the CMS collaborationfor the determination of the strong coupling constant, α s , see Ref. 26.Considering a final state of higher complexity, the differential cross section forthe production of exactly four jets is interesting to study. This measurement hasbeen performed by the CMS collaboration as a function of the jet transverse mo-mentum p T and rapidity | y | , c.f. Ref. 27. Events with four jets can be produced viaa single hard parton scattering (SPS) process, where two or more partons at highctober 22, 2018 4:43 WSPC/INSTRUCTION FILE kokkas-ijmpa P.Kokkas [GeV] jjj m400 1000 2000 3000 / d | Y * | [ pb / G e V ] jjj / d m s d -6 -4 -2
10 1 ATLAS -1 L dt = 4.5 fb (cid:242) = 7 TeVs R = 0.4 t k anti- non-pert. corr · CT 10 ˜ NLO QCD ) |Y*|<2 (x10 ) [GeV] jjj m · · P r ed i c t i on / D a t a |Y*|<2 [GeV] jjj m · · [GeV] jjj m · · [GeV] jjj m · · [GeV] jjj m · · ATLAS -1 L dt = 4.5 fb (cid:242) = 7 TeVs R = 0.4 t k anti- DATA Uncert.TotalStatistical non-pert. corr. · PDF ˜ NLO QCD
CT 10MSTW 2008GJR 08
Fig. 2. Top: the three-jet double-differential cross section, measured by the ATLAS collaboration,compared to the NLO prediction times NP corrections using the CT10-NLO PDF set. Bottom:the ratio of data to NLO theoretical predictions using various PDF sets. p T are produced, with the initial- and final-state QCD radiation resulting in addi-tional jets at lower p T . Multiparton interactions (MPI) can lead to the productionof events, where more than one partonic interaction has occured in the same ppcollision. In this case a pair of hard jets and a pair of softer jets can be produced viadouble parton scattering (DPS) leading to events with four jets. The SPS and DPSprocesses result in different distributions of angular correlations in observables suchas the azimuthal angle ∆S between the two dijet pairs. The analysis is based on adata sample collected in 2010, with an integrated luminosity of 36 pb − . Figure 4shows the cross sections for the production of exactly four jets as a function of thejet transverse momenta p T (left), and the azimuthal angle ∆S between the two dijetpairs (right), compared to predictions of various MC generators, like powheg
28, 29 , MadGraph , Sherpa , pythia8 and herwig++ . It is found that thectober 22, 2018 4:43 WSPC/INSTRUCTION FILE kokkas-ijmpa Measurements of jet-related observables at the LHC
500 1000 2000 m [GeV]10 − − − − − − d σ / d m d y m a x [ pb / G e V ] CMS − (7 TeV) Anti- k t R = 0.7CT10-NLONLO × NP | y | max ≤ < | y | max ≤
500 1000 2000 m [GeV]0.00.20.40.60.81.01.21.41.61.8 R a t i o t o N L O ( C T - N L O ) CMS − (7 TeV) Anti- k t R = 0.7, | y | max < ∆ PDF CL68MSTW2008-NLONNPDF2.1-NLOHERAPDF1.5-NLOABM11-NLO
Fig. 3. Left: the comparison of the 3-jet mass cross section with the NLO prediction times NPcorrections, for the two considered regions in | y | max , using the CT10-NLO PDF set. Right: ratioof the measured 3-jet mass distribution to theoretical predictions using various PDF sets withNLO PDF evolution. models considered are able to describe the differential cross sections only in someregions of the phase space. Especially, the ∆S distribution is not described by anyof the predictions and this may be taken as an indication for the need of includingDPS in the investigated models. h Jet -4 -3 -2 -1 0 1 2 3 4 ( pb ) h / d s d fi , pp -1 = 7 TeV, L = 36 pbsCMS, | < 4.7 h | jet: nd , 2 st
1 > 50 GeV T p jet: th , 4 rd
3 > 20 GeV T p SHERPAPOWHEG+P6 Z2'MADGRAPH+P6 Z2*PYTHIA8 4C) jet (x 10 st jet (x 10 nd jet (x 10 rd
3 jet th (GeV) T Jet p50 100150200250300350400450500 ( pb / G e V ) T / dp s d -2
10 1 fi , pp -1 = 7 TeV, L = 36 pbsCMS, | < 4.7 h | jet: nd , 2 st
1 > 50 GeV T p jet: th , 4 rd
3 > 20 GeV T p SHERPAPOWHEG+P6 Z2'MADGRAPH+P6 Z2*PYTHIA8 4C) jet (x 10 st jet (x 10 nd jet (x 10 rd
3 jet th T p softrel D M C / D a t a SHERPAPOWHEG+P6 Z2'MADGRAPH+P6 Z2*PYTHIA8 4CHERWIG++ UE-EE-3POWHEG+P6 Z2' MPI offTotal Uncertainty T p s o ft r e l D / d s ) d s ( / fi , pp -1 = 7 TeV, L = 36 pbsCMS, | < 4.7 h | jet: nd , 2 st
1 > 50 GeV T p jet: th , 4 rd
3 > 20 GeV T p SHERPAPOWHEG+P6 Z2'MADGRAPH+P6 Z2*PYTHIA8 4CHERWIG++ UE-EE-3POWHEG+P6 Z2' MPI offDataTotal Uncertainty
S (rad) D M C / D a t a SHERPAPOWHEG+P6 Z2'MADGRAPH+P6 Z2*PYTHIA8 4CHERWIG++ UE-EE-3POWHEG+P6 Z2' MPI offTotal Uncertainty S ( / r ad ) D / d s ) d s ( / -1 fi , pp -1 = 7 TeV, L = 36 pbsCMS, | < 4.7 h | jet: nd , 2 st
1 > 50 GeV T p jet: th , 4 rd
3 > 20 GeV T p SHERPAPOWHEG+P6 Z2'MADGRAPH+P6 Z2*PYTHIA8 4CHERWIG++ UE-EE-3POWHEG+P6 Z2' MPI offDataTotal Uncertainty
Fig. 4. The differential cross sections for the production of exactly four jets, measured by theCMS collaboration, as a function of the jet transverse momenta p T (left) and the azimuthal angle∆S between the pair of the two leading and the pair of the two subleading jets(right), comparedto predictions of powheg , MadGraph , Sherpa , pythia8 , and herwig++ . ctober 22, 2018 4:43 WSPC/INSTRUCTION FILE kokkas-ijmpa P.Kokkas
In Ref. 33, the CMS collaboration presents studies of inclusive topological dis-tributions of three- and four-jet events using a data sample corresponding to anintegrated luminosity of 5 . − collected during 2011. These studies of three-jetevents include the invariant mass of the system and the scaled energy distributionsof the first and second jet. The scaled energy of the jet is defined as twice it’s en-ergy divided by the mass of the three-jet system. In the case of four-jet events, thefour-jet mass and two event plane angles, namely the Nachtmann-Reiter and theBengtsson-Zerwas angle, are presented. For example, in Fig. 5 the three-jet mass,the scaled energy of the leading jet in the three-jet system, and the four-jet mass arepresented. Data are compared to predictions of various LO MC models, with thosefrom MadGraph + pythia6 being closest to the data for most of the observables.The multi-jet observables presented in this study are sensitive to higher-order pro-cesses and the approximations used in their treatment. Furthermore, they providea good test of various LO MC models widely used at the LHC. d m d N . N -5 -4 -3 -2 Herwig++ Tune23Madgraph + Pythia6 TuneZ2Pythia8 Tune4CPythia6 TuneZ2Data
CMS
Three-Jet Mass (GeV) D a t a P y t h i a6 Three-Jet Mass (GeV)1000 1500 2000 2500 3000 3500 D a t a P y t h i a8 Three-Jet Mass (GeV)1000 1500 2000 2500 3000 3500 D a t a M adg r aph Three-Jet Mass (GeV)1000 1500 2000 2500 3000 3500 D a t a H e r w i g ++ (7 TeV) -1 (b) d x d N . N Herwig++ Tune23Madgraph + Pythia6 TuneZ2Pythia8 Tune4CPythia6 TuneZ2Data
CMS x D a t a P y t h i a6 D a t a P y t h i a8 D a t a M adg r aph D a t a H e r w i g ++ (7 TeV) -1 (b) d m d N . N -5 -4 -3 -2 Herwig++ Tune23Madgraph + Pythia6 TuneZ2Pythia8 Tune4CPythia6 TuneZ2Data
CMS
Four-Jet Mass (GeV) D a t a P y t h i a6 Four-Jet Mass (GeV)1000 1500 2000 2500 3000 3500 D a t a P y t h i a8 Four-Jet Mass (GeV)1000 1500 2000 2500 3000 3500 D a t a M adg r aph Four-Jet Mass (GeV)1000 1500 2000 2500 3000 3500 D a t a H e r w i g ++ (7 TeV) -1 (b) Fig. 5. The three-jet mass (left), the scaled energy of the leading jet in the three-jet system(middle) and the four-jet mass (right) measured by the CMS collaboration. Data are compared topredictions from four MC models: pythia6 , pythia8 , MadGraph + pythia6 , and herwig++ .
3. Ratios of jet cross sections
The advantages of measuring ratios of jet cross sections are the reduction of severalexperimental uncertainties, such as uncertainties in the jet energy scale and in theluminosity determination, as well as of several theoretical systematic uncertaintiesrelated to the choice of the renormalisation and factorisation scales, µ r and µ f , andto NP effects. For these reasons ratios of jet cross sections provide a nice tool fortesting pQCD, tuning MC models, constraining PDFs or determining the strongcoupling constant.ctober 22, 2018 4:43 WSPC/INSTRUCTION FILE kokkas-ijmpa Measurements of jet-related observables at the LHC A measurement with particular sensitivity to limitations in the LO MC sim-ulations and NLO pQCD calculations is the ratio R of the inclusive 3-jet crosssection to the inclusive 2-jet cross section. In Ref. 11, the ATLAS collaborationpresents the measurement of R as a function of the leading jet p T and the to-tal jet transverse momentum of the event, H T . The results are compared to LOMC simulations, as well as to NLO theoretical predictions corrected for NP effects.For example, Fig. 6 (left) shows the measured R distribution together with theNLO prediction. Within uncertainties a nice agreement between data and theory isobserved.
100 200 300 400 500 600 700 800 ≥ ] T l ead / d p σ /[ d ≥ ] T l ead / d p σ [ d ATLAS -1 L dt=2.4 pb ∫ R=0.6, =7 TeV)+syst.sData (NLO+non.pert.+syst (leading jet) [GeV] T p100 200 300 400 500 600 700 800 T heo r y / D a t a (GeV) æ T1,2 p Æ
200 400 600 800 1000 1200 1400 R ) -1 Data (Int. Lumi. = 5.0 fb ) = 0.119 Z (M s a NNPDF2.1-NNLO NPC ˜ NLO Scale uncertaintyPDF uncertainty
CMS = 7 TeVs R = 0.7 T anti-k (GeV) æ T1,2 p Æ
200 400 600 800 1000 1200 1400 D a t a / T heo r y Fig. 6. The ratio R together with the NLO theoretical prediction, corrected for NP effects, mea-sured by ATLAS (left) and CMS (right). In the bottom panels the ratio of data to the theoreticalpredictions is shown. The CMS collaboration has presented measurements of R in two publications,see Refs. 36 and 37. In the first publication, R is measured versus H T , using anintegrated luminosity of 36 pb − collected during 2010. The measurement is used totest the validity of various MC generators such as pythia6 , pythia8 , herwig++ , MadGraph , and
Alpgen , at multi-TeV scales. All MC generators describe thedata within 20%, with
MadGraph giving the best results.In a second publication, CMS presented a measurement of R as a function ofthe average transverse momentum of the two jets leading in p T , using an integratedluminosity of 5 fb − collected during 2011. Data are compared to NLO theoreticalpredictions using various PDF sets. For example, Fig. 6 (right) shows the measuredratio R together with the NLO prediction using the NNPDF2.1 PDF set. Withinuncertainties most PDF sets are able to describe the data. This R measurement,due to its sensitivity to the strong coupling constant, has been used by the CMScollaboration for the first determination of α s in the TeV region, see Ref. 26.ctober 22, 2018 4:43 WSPC/INSTRUCTION FILE kokkas-ijmpa P.Kokkas
A three-jet observable which is sensitive to the pattern of QCD radiation atNLO (including terms up to α s ), is the ratio R (0 . , .
7) of the inclusive jet crosssections using the anti- k T clustering algorithm with two radius parameters, R = 0 . .
7. The CMS collaboration has presented the measurement of R (0 . , .
7) inRef. 38. Figure 7 shows R (0 . , .
7) in the central rapidity bin | y | < .
5, compared toLO and NLO predictions with and without NP corrections (left), as well as to NLOcalculations corrected for NP effects and to MC predictions (right). The study of thisobservable shows that models using LO ( pythia6 , herwig++ ) or NLO matrixelement calculations matched to the parton showers ( powheg + pythia6 ), give abetter description than the fixed order calculations corrected for NP effects. The bestdescription for R (0 . , .
7) is obtained by powheg + pythia6 . This demonstratesthat jet radius dependent effects, measurable in data, require pQCD predictionswith at least one order higher than NLO or a combination of NLO matrix elementsand parton showers. (GeV) T Jet p
60 100 200 1000 ( . , . ) ´ DataLONLONP ˜ LO NP ˜ NLO|y| < 0.5 = 7 TeVs -1 CMS (unpublished), L = 5 fb (GeV) T Jet p
60 100 200 1000 ( . , . ) ´ Data NP ˜ NLOPYTHIA6 Z2HERWIG++POWHEG+PYTHIA6|y| < 0.5 = 7 TeVs -1 CMS (unpublished), L = 5 fb
Fig. 7. The jet radius ratio R (0 . , . | y | < . ⊗ NP) and to MC predictions (right).The bands represent the total correlated systematic uncertainty, while the error bars indicate thetotal uncorrelated uncertainty.
4. Jet Shapes
Jet shapes, the normalised transverse momentum flow as a function of the distanceto the jet axis, provide information about the details of the parton-to-jet fragmen-tation process, see e.g. Ref. 39. The ATLAS and CMS collaborations have providedthe first measurements of jet shapes in proton-proton collisions at the LHC, seeRefs. 40 and 41.Traditionally, the internal structure of a jet is studied in terms of the differentialctober 22, 2018 4:43 WSPC/INSTRUCTION FILE kokkas-ijmpa
Measurements of jet-related observables at the LHC and integrated jet shapes. The differential jet shape ρ ( r ), with r = (cid:112) ∆ y + ∆ φ being the distance to the jet axis, is defined as the average fraction of the transversemomentum contained inside an annulus of inner and outer radius r − δr/ r + δr/ r ) is definedas the average fraction of the transverse momentum of particles inside a cone ofradius r around the jet axis. (r) ρ -1 ATLAS jets R = 0.6 t anti-k < 40 GeV T
30 GeV < p| y | < 2.8 (a) -1 - 3 pb -1 dt = 0.7 nb L ∫ Data PYTHIA-Perugia2010HERWIG++ALPGENPYTHIA-MC09 r D A T A / M C (r) r -1 =7 TeV )spp Data ( Pythia Tune Z2Pythia Perugia2010Pythia Tune D6TPythia8Herwig++ CMS |y| < 1 < 40 GeV jetT
30 GeV < P , -1 L dt = 36 pb (cid:242) radius (r) M C / D a t a (r) ρ -1 ATLAS jets R = 0.6 t anti-k < 600 GeV T
500 GeV < p| y | < 2.8 (c) -1 - 3 pb -1 dt = 0.7 nb L ∫ Data PYTHIA-Perugia2010HERWIG++ALPGENPYTHIA-MC09 r D A T A / M C (r) r -1 =7 TeV )spp Data ( Pythia Tune Z2Pythia Perugia2010Pythia Tune D6TPythia8Herwig++ CMS |y| < 1 < 600 GeV jetT
500 GeV < P , -1 L dt = 36 pb (cid:242) radius (r) M C / D a t a Fig. 8. The measured differential jet shape ρ ( r ) from ATLAS for | y | < . | y | < p T , 30 GeV < p T <
40 GeV (top) and500 GeV < p T <
600 GeV (bottom). The ATLAS data are compared to predictions of PYTHIA-Perugia2010 (solid lines), HERWIG++ (dashed lines), ALPGEN interfaced with HERWIG andJIMMY (dotted lines), and PYTHIA-MC09 (dash-dotted lines). The CMS data are compared toHERWIG++, PYTHIA8, and PYTHIA6 predictions with various tunes.
Figure 8 shows the differential jet shape ρ ( r ) measured by ATLAS, for | y | < . | y | < p T ,ctober 22, 2018 4:43 WSPC/INSTRUCTION FILE kokkas-ijmpa P.Kokkas
30 GeV < p T <
40 GeV (top) and 500 GeV < p T <
600 GeV (bottom). The peakat small r indicates that the majority of the jet momentum is concentrated closeto the jet axis. At high jet p T the peak is higher, indicating that jets are highlycollimated with most of their p T close to the jet axis. About 95% of the transversemomentum is contained within a cone of radius r = 0 .
3. This fraction decreasesdown to 80% at low jet p T , where jets become wider. This is also demonstrated inFig. 9, where the measured integrated jet shape 1 − Ψ( r = 0 .
3) from ATLAS (left)and CMS (right) is shown as a function of jet p T . Data from ATLAS and CMS arecompared to predictions of various MC generators such as PYTHIA6, PYTHIA8,HERWIG++, and ALPGEN in various tunes, thus giving interesting sensitivity toa variety of perturbative and non-perturbative effects. (GeV) T p0 100 200 300 400 500 600 (r = . ) Ψ - jets R = 0.6 t anti-k| y | < 2.8 (a) ATLAS -1 - 3 pb -1 dt = 0.7 nb L ∫ Data PYTHIA-Perugia2010HERWIG++ALPGENPYTHIA-MC09 (r = . ) y - CMS -1 L dt = 36 pb (cid:242) = 7 TeV )spp Data ( Pythia Tune Z2Pythia Perugia2010Pythia Tune D6TPythia8Herwig++
Jets D = 0.7 T Anti k |y| < 1 (GeV/c) T Jet P M C / D a t a Fig. 9. The integrated jet shape 1 − Ψ( r = 0 .
3) measured by ATLAS for | y | < . | y | < p T . The ATLAS data are compared to the pre-dictions of PYTHIA-Perugia2010 (solid lines), HERWIG++ (dashed lines), ALPGEN interfacedwith HERWIG and JIMMY (dotted lines), and PYTHIA-MC09 (dash-dotted lines). The CMSdata are compared to HERWIG++, PYTHIA8, and PYTHIA6 predictions with various tunes. In Ref. 42 ATLAS also presented the first measurement of b-jet shapes in toppair events. This measurement allows the study of the differences between the b-quark and light-quark jets, using the differential and integrated jet shapes. Figure 10shows the differential ( (cid:104) ρ ( r ) (cid:105) , left) and the integrated ( (cid:104) Ψ( r ) (cid:105) , right) jet shapes,as a function of the radius r for b-jets (squares) and light jets (triangles) in arepresentative bin of jet p T , 100 GeV < p T <
150 GeV . The analysis shows thatb-jets are broader than light jets, with the cores of light jets having a larger energydensity than those of b-jets. The measurement of the integrated jet shape, (cid:104) Ψ( r ) (cid:105) ,shows that for low values of r it is possible to distinguish b-jets from light jets. TheMC event generators MC@NLO +HERWIG and POWHEG+PYTHIA reproducewell the jet shapes for both light and b-jets.ctober 22, 2018 4:43 WSPC/INSTRUCTION FILE kokkas-ijmpa Measurements of jet-related observables at the LHC (r) > ρ < b jets sys) ⊕ Data (stat MC@NLO+HerwigPowHeg+Pythialight jets sys) ⊕ Data (stat MC@NLO+HerwigPowHeg+Pythia < 70 GeV T
50 GeV < p = 7 TeVs
ATLAS L dt = 1.8 fb ∫ M C @ N L O / D a t a r P o wH eg / D a t a (r) > Ψ < b jets sys) ⊕ Data (stat MC@NLO+HerwigPowHeg+Pythialight jets sys) ⊕ Data (stat MC@NLO+HerwigPowHeg+Pythia < 70 GeV T
50 GeV < p = 7 TeVs
ATLAS L dt = 1.8 fb ∫ M C @ N L O / D a t a r P o wH eg / D a t a Fig. 10. The differential ( (cid:104) ρ ( r ) (cid:105) , left) and the integrated ( (cid:104) Ψ( r ) (cid:105) , right) jet shapes, measuredby ATLAS, as a function of the radius r for b-jets (squares) and light jets (triangles) in theinterval 100 GeV < p T <
150 GeV . Data are compared to the MC@NLO+HERWIG andPOWHEG+PYTHIA event generators.
5. Jet Event Shapes
Event shape variables are geometric properties of the energy flow in hadronic finalstates. They are sensitive to QCD radiation, as gluon emission changes the shapeof the energy flow, providing an indirect probe of multi-jet topologies.ATLAS (in Ref. 44) and CMS (in Refs. 45 and 46) presented the first eventshapes measurements at LHC, for testing the validity of various MC generators.These include: the event thrust τ ⊥ and its minor component T m, ⊥ ; the sphericity S and its transverse component S ⊥ ; the aplanarity A; the jet broadening B tot ; thetotal jet mass ρ tot and its transverse component ρ T tot ; and the third-jet resolutionparameter Υ . Phenomenological discussions and definitions of event shapes athadron colliders can be found in Refs. 47 and 48.Figure 11 shows the event thrust (left) and the sphericity (right), measured bythe ATLAS collaboration, using an integrated luminosity of 35 pb − collected during2010. Data are compared to predictions of herwig++ , Alpgen and pythia
MCsimulations, showing reasonable agreement. In Fig. 12, the measurements of theevent thrust (top left), the jet broadening (bottom left) and the total jet mass(bottom right) distributions, measured by the CMS collaboration, are presented.This analysis uses an integrated luminosity of 5 fb − collected during 2011. Data arecompared to the pythia6 , pythia8 , herwig++ , and MadGraph
MC generators.For the event thrust, all generators show an overall agreement with data within 10%,with pythia8 and herwig++ exhibiting a better agreement than the others. Forthe jet broadening and the total jet mass the agreement of the various MC generatorsctober 22, 2018 4:43 WSPC/INSTRUCTION FILE kokkas-ijmpa P.Kokkas with data is poor, except for
MadGraph , which provides a good description of themeasurements.
Fig. 11. The event thrust (left) and the sphericity (right) measured by the ATLAS collaboration.The results are compared to different MC simulations.
6. Conclusions
A review has been presented on recent measurements of jet-related observables atthe LHC, such as multi-jet rates and cross sections, ratios of jet cross sections,jet shapes and event shape observables. The measurements are based on the datacollected during the first two years of the LHC operation in proton-proton collisionsat the center-of-mass energy of 7 TeV.These observables are compared to predictions of various widely used LO andsome recent higher-order MC generators, providing valuable information regardingtheir usage at LHC energies. Furthermore, data are compared to predictions of NLOcalculations, thus providing a test of pQCD in a previously unexplored energy regionand constraining our knowledge of the Standard Model and its phenomenology.QCD is the main background in many searches of new physics and in this sense theoverall good agreement between data and theoretical predictions provides a solidfoundation for searches beyond the Standard Model.In the coming years the continuation of the analyses, by ATLAS and CMS, onthe 8 TeV data will provide more information on these jet-observables, completingthe QCD physics program based on the data of the first three-years operation periodof LHC. And of course, even more data are anticipated in the near future, from the13 TeV LHC run.
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