Measurement of jet fragmentation in Pb+Pb and pp collisions at √sNN=5.02 TeV with the ATLAS detector

PHYSICAL REVIEW C 98, 024908 (2018) Measurement of jet fragmentation in Pb+Pb and pp collisions at √sNN =5.02 TeV with the ATLAS detector M. Aaboud et al.∗ (ATLAS Collaboration) (Received 16 May 2018; published 16 August 2018) This paper presents a measurement of jet fragmentation functions in 0.49 nb−1of Pb+Pb collisions and 25 pb−1 of pp collisions at √sNN =5.02 TeV collected in 2015 with the ATLAS detector at the LHC. These measurements provideinsightinto thejet quenchingprocess inthe quark-gluonplasma createdin theaftermath ofultrarelativistic collisions between two nuclei. The modifications to the jet fragmentation functions are quantified by dividing the measurements in Pb+Pb collisions by baseline measurements in pp collisions. This ratio is studied as a function of the transverse momentum of the jet, the jet rapidity, and the centrality of the collision. In both collision systems, the jet fragmentation functions are measured for jets with transverse momentum between 126 and 398 GeV and with an absolute value of jet rapidity less than 2.1. An enhancement of particles carrying a small fraction of the jet momentum is observed, which increases with centrality and with increasing jet transverse momentum. Yields of particles carrying a very large fraction of the jet momentum are also observed to be enhanced. Between these two enhancements of the fragmentation functions a suppression of particles carrying an intermediate fraction of the jet momentum is observed in Pb+Pb collisions. A small dependence of the modifications on jet rapidity is observed. DOI: 10.1103/PhysRevC.98.024908 I. INTRODUCTION Ultrarelativistic nuclear collisions at the Large Hadron Collider (LHC) produce hot dense matter called the quark-gluon plasma (QGP); recent reviews can be found in Refs. [1,2]. Hard-scattering processes occurring in these collisions producejetswhichtraverseandinteractwiththeQGP.Thestudyof modifications of jet rates and properties in heavy-ion collisions compared to pp collisions provides information about the properties of the QGP. The rates of jet production are observed to be reduced by approximately a factor of 2 in lead-lead (Pb+Pb) collisions at LHC energies compared to expectations from the jet production cross sections measured in pp interactions scaled by the nuclear overlap function of Pb+Pb collisions [3–5]. Similarly, back-to-back dijet [6–8] and photon-jet pairs [9]are observed to have unbalanced transverse momentum in Pb+Pb collisions compared to pp collisions. Related phenomena were first observed at the Relativistic Heavy Ion Collider where the measurements were made with hadrons rather than reconstructedjets[10–12].Theseobservationsimplythatsome of the energy of the parton showering process is transferred outside of the jet through its interaction with the QGP. This has been termed “jet quenching.” ∗Full author list given at the end of the article. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. The distribution of particles within the jet are affected by this mechanism of energy loss. Several related observables sensitive to the properties of the medium can be constructed. Measurements of the jet shape [13] and the fragmentation functions were made in 2.76 TeV Pb+Pb collisions [14–16]. In Ref. [16], jet fragmentation functions are measured as a function of both the charged-particle transverse momentum pTand the charged-particle longitudinal momentum fraction relative to the jet, z≡pTcos R/p jet T.(1) The fragmentation functions are defined as D(z)≡1 Njet dnch dz , and D(pT)≡1 Njet dnch dpT , where pjet Tis the transverse momentum of the jet, nch is the number of charged particles in the jet, Njet is the number of jets under consideration, and R=(η)2+(φ)2with ηand φdefined as the differences between the jet axis and the charged-particle direction in pseudorapidity and azimuth,1 1ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the center of the detector and the z axis along the beam pipe. The xaxis points from the IP to the center of the LHC ring, and the yaxis points upward. Cylindrical coordinates (r, φ) are used in the transverse plane, φbeing the azimuthal angle 2469-9985/2018/98(2)/024908(34) 024908-1 ©2018 CERN, for the ATLAS Collaboration M. AABOUD et al. PHYSICAL REVIEW C 98, 024908 (2018) respectively. In order to quantify differences between Pb+Pb and pp collisions at the same collision energy, the ratios of the fragmentation functions are measured: RD(z)≡D(z)PbPb D(z)pp , and RD(pT)≡D(pT)PbPb D(pT)pp . Relative to jets in pp collisions, it was found in Ref. [16] that jets in Pb+Pb collisions have an excess of particles with transverse momentum below 4 GeV and an excess of particles carrying a large fraction of the jet transverse momentum. At intermediate charged-particle pT, there is a suppression of the charged-particle yield. At the same time, an excess of low-pTparticles is observed for particles in a wide region around the jet cone [17,18]. These observations may indicate that the energy lost by jets through the jet quenching process is being transferred to soft particles within and around the jet [19,20]; measurements of these soft particles have the potential to constrain the models describing such processes. A possible explanation for the enhancement of particles carrying a large fraction of the jet momentum is that it is related to the gluon-initiated jets losing more energy than quarkinitiated jets. This leads to a higher quark-jet fraction in Pb+Pb collisions than in pp collisions. The change in flavor composition combined with the different shapes of the quark and gluon fragmentation functions [21] then lead to the observed excess. Proton-nucleus collisions, which do not generate a large amount of QGP, are used to differentiate between initialand final-state effects due to the QGP formed in Pb+Pb collisions. Fragmentation functions in p+Pb collisions show no evidence of modification when compared with those in pp collisions [22]. Thus, any modifications observed in Pb+Pb collisions can be attributed to the presence of the QGP rather than to effects arising from the presence of the large nucleus. The rapidity dependence of jet observables in Pb+Pb collisions is of great interest, in part because at fixed pjet Tthe fraction of quark jets increases with increasing |yjet|(see, for example,Refs.[21,23]).Thismakestherapiditydependenceof jetobservablespotentiallysensitivetothedifferentinteractions of quarks and gluons with the QGP. Previous measurements of the rapidity dependence of jet fragmentation functions at √sNN =2.76 TeV in Pb+Pb collisions found a rapidity dependence of the fragmentation function modification with limited significance [16]. In this paper, the fragmentation functions and the RD(z) and RD(pT)ratios are measured in Pb+Pb and pp collisions at 5.02 TeV using 0.49 nb−1of Pb+Pb collisions and 25 pb−1 of pp collisions collected in 2015. Jets are measured over a around the beam pipe. The pseudorapidity is defined in terms of the polar angle θas η=−ln tan(θ/2). The rapidity is defined as y= 0.5ln[(E+pz)/(E−pz)] where Eand pzare the energy and the component of the momentum along the beam direction. rapidityrangeof|yjet|<2.1usingtheanti-ktreconstructionalgorithm[24]withradiusparameterR=0.4.Themeasurement is presented in intervals of pjet T,yjet, and collision centrality. These data extend the previous studies at √sNN =2.76 TeV in two ways. First, an increase in the peak energy density of the medium is expected. Second, the Pb+Pb integrated luminosity in the current dataset is 3.5 times the integrated luminosity available at 2.76 TeV, and the increase in the collision energy also increases the jet cross sections. These two factors allow a measurement of the dependence of jet fragmentation functions on the transverse momentum of the jet over a wider range than was previously possible. II. EXPERIMENTAL SETUP The measurements presented in this paper were performed using the ATLAS inner detector, calorimeter, trigger, and data acquisition systems [25]. The calorimeter system consists of a sampling liquid argon (LAr) electromagnetic (EM) calorimeter covering |η|<3.2, a steel/scintillator sampling hadronic calorimeter covering |η|<1.7, LAr hadronic calorimeters covering 1.5<|η|<3.2, and two LAr forward calorimeters (FCal) covering 3.1<|η|<4.9[25]. The EM calorimeters are segmented longitudinally in shower depth into three layers withanadditional presamplerlayer.Theyhavesegmentation in φand ηthat varies with layer and pseudorapidity. The hadronic calorimeters have three sampling layers longitudinal in shower depth. The inner detector measures charged particles within the pseudorapidity interval |η|<2.5 using a combination of silicon pixel detectors, silicon microstrip detectors (SCTs), and a straw-tube transition radiation tracker (TRT), all immersed ina2Taxialmagnetic field [25]. Each of the three detectors is composed of a barrel and two symmetric endcap sections. The pixel detector is composed of four layers: the “insertableB layer” [26,27] and three layers with apixel size of 50 μm×400 μm. The SCT barrel section containsfourlayers of modules with 80 μm pitch sensors on both sides and each endcap consists of nine layers of double-sided modules with radial strips having a mean pitch of 80 μm. The two sides of eachSCTlayerinboththebarrelandtheendcapshavearelative stereo angle of 40 mrad. The TRT contains up to 73 (160) layers of staggered straws interleaved with fibers in the barrel (endcap). The zero-degree calorimeters (ZDCs) are located symmetrically at z=±140 m and cover |η|>8.3. They are constructed from tungsten absorber plates and ˇ Cerenkov light is transmitted via quartz fibers. In Pb+Pb collisions the ZDCs primarily measure “spectator” neutrons, i.e., neutrons that do not interact hadronically when the incident nuclei collide. A ZDCcoincidencetriggeris implemented by requiringthepulse height from each ZDC to be above a threshold set to accept the single-neutron peak. A two-level trigger system is used to select the Pb+Pb and pp collisions. The first trigger level (L1) is hardware-based and implemented with custom electronics. The second level is the software-based high-level trigger (HLT) and is used to further reduce the accepted event rate. Minimum-bias Pb+Pb events are recorded using a trigger defined by the logical OR 024908-2 MEASUREMENT OF JET FRAGMENTATION IN Pb+Pb AND … PHYSICAL REVIEW C 98, 024908 (2018) of a L1 total energy trigger and the ZDC coincidence trigger. The total energy trigger required the total transverse energy measured in the calorimeter system to be greater than 50 GeV in Pb+Pb collisions. Jet events are selected by the HLT, after requiring the identification of a jet by the L1 jet trigger in pp collisions or the total energy trigger with a threshold of 50 GeV in Pb+Pb collisions. The L1 jet trigger utilized in pp collisions required a jet with transverse momentum greater than 20 GeV. The HLT jet trigger used a jet reconstruction algorithm similar to that used in the offline analysis (the offline jet reconstruction is discussed in Sec. IV). It selected events containing jets with transverse energy of at least 75 GeV in Pb+Pb collisions and at least 85 GeV in pp collisions. In pp collisions, the 85 GeV threshold jet trigger sampled the full delivered luminosity. The 75 GeV threshold jet trigger used in Pb+Pb collisions was prescaled2in a small part of the Pb+Pb data-taking period; however, the trigger sampled more than 99% of the total integrated luminosity. The measurement is performed in the jet transverse momentum region where the triggers are fully efficient. III. DATA SETS AND EVENT SELECTION The Pb+Pb and pp data used in this analysis were recorded in2015.The datasamplesconsistof25 pb−1of√s=5.02TeV pp data and 0.49 nb−1of √sNN =5.02 TeV Pb+Pb data. In Pb+Pb and pp collisions, events are required to have a reconstructed vertex within 150 mm of the nominal interaction point along the beam axis. Only events taken during stable beam conditions and satisfying detector and data-quality requirements, which include the calorimeters and inner tracking detectors being in nominal operation, are considered. In Pb+Pb collisions, the event centrality reflects the overlap area of the two colliding nuclei and is characterized by EFCal T, the total transverse energy deposited in the FCal [28]. The centrality intervals used in this analysis are defined according to successive percentiles of the EFCal Tdistribution obtained from minimum-bias triggered Pb+Pb events ordered from the most central (highest EFCal T) to the most peripheral collisions (lowest EFCal T): 0–10%, 10–20%, 20–30%, 30–40%, 40– 60%, 60–80%. In addition to the jet-triggered sample, a separate Pb+Pb data sample was recorded with the minimum-bias trigger and two total transverse-energy triggers requiring 1.5 and 6.5 TeV to enhance the rate of more central Pb+Pb events. This data sample is used to produce a Pb+Pb Monte Carlo (MC) events with conditions that match those registered while the data were recorded. The performance of the detector and of the analysis procedure in Pb+Pb collisions is evaluated using 1.8×107 5.02 TeV MC events. These were produced from minimumbias Pb+Pb data events overlaid with hard-scattering dijet pp events generated with POWHEG+PYTHIA8[29,30]using a set of tuned parameters called the A14 tune [31] and the 2The prescale indicates which fraction of events that passed the trigger selection was selected for recording by the data acquisition system. NNPDF23LO parton distribution function (PDF) set [32]. The detector response was simulated using GEANT4[33,34] and the simulated hits were combined with those from the data event. A weight is assigned to each MC event such that the event sample obtained from the minimum-bias trigger has the same centrality distribution as the sample collected by the jet trigger. A separate sample of 1.8×107simulated 5.02 TeV PYTHIA8pp hard-scattering events, generated with the same tuneandPDFsas for thePb+PbMCsample,is usedtoevaluate the performance for measuring fragmentation functions in the pp data. The contribution from additional collisions in the same bunch crossing is not included in the MC simulation. A sample of Pb+Pb events generated with HIJING version 1.38b [35] is also used to evaluate the performance of the track reconstruction. IV. JET AND TRACK SELECTION The jet reconstruction, underlying event (UE) determination, and subtraction procedures closely follow those used by ATLAS for jet measurements in pp and Pb+Pb collisions at √sNN =2.76 TeV [4]. The anti-ktalgorithm is first run in fourmomentum recombination mode, on η×φ=0.1×0.1 calorimeter towers with the anti-ktradius parameter R=0.2 and R=0.4. The energies in the towers are obtained by summing the energies of calorimeter cells at the electromagnetic energy scale within the tower boundaries. Then, an iterative procedure is used to estimate the η-dependent UE transverse energy density on an event-by-event basis using the energy measurements in all calorimeter towers in the event while excluding the regions populated by jets. The resulting UE transverse energy density is modulated taking into account the presence of the azimuthal anisotropy of particle production [36]. The modulation includes contributions of the second-, third-, and fourth-order azimuthal anisotropy harmonics. Higher-order harmonics introduce negligible variation of the reconstructed jet energy. The UE transverse energy is subtracted from each calorimeter cell within the towers included in the reconstructed jet, and the four-momentum of the jet is updated accordingly. Then, a jet ηand pT-dependent correction factor to the pjet Tderived from the simulation samples is applied to correct for the calorimeter energy response [37]. An additional correction based on in situ studies of jets recoiling against photons, Zbosons, and jets in other regions of the calorimeter is applied [38,39]. The same jet reconstruction procedure without the azimuthal modulation of the UE is also applied to pp collisions. Jets are required to have a rapidity within |yjet|<2.1 so that all R=0.4 jet cones are contained within the inner detector’s acceptance. To prevent neighboring jets from distorting the measurementofthe fragmentationfunctions,jetsare rejectedif there is another jet with higher pjet Tanywhere within a distance R<1.0. A correction is applied to reduce the effects of the broadening of the jet direction measurement for R=0.4 jets due to the UE. The correction uses jets reconstructed with a smaller distance parameter R=0.2 since their angular resolution evaluated in MC studies is found to be less affected by the UE fluctuations than that of larger-Rjets. The jet direction is redefined as that of the closest R=0.2 jet with 024908-3 M. AABOUD et al. PHYSICAL REVIEW C 98, 024908 (2018) [GeV] truth T p 1 10 2 10 Tracking efficiency 0.7 0.75 0.8 0.85 0.9 0.95 1 ATLAS Simulation = 5.02 TeVs pp < 158 GeV jet T p126 GeV < < 200 GeV jet T p158 GeV < < 251 GeV jet T p200 GeV < < 316 GeV jet T p251 GeV < < 398 GeV jet T p316 GeV < | < 0.3 jet y| =0.4R t kanti- [GeV] truth T p 1 10 2 10 Tracking efficiency 0.7 0.75 0.8 0.85 0.9 0.95 1 < 158 GeV jet T p0-10%, 126 GeV < < 316 GeV jet T p0-10%, 251 GeV < < 158 GeV jet T p60-80%, 126 GeV < < 316 GeV jet T p60-80%, 251 GeV < ATLAS Simulation = 5.02 TeV NN s Pb+Pb | < 0.3 jet y| =0.4R t kantiFIG. 1. Tracking efficiency ε, smoothed using a third-order polynomial in ln(ptruth T) as a function of ptruth Tin pp collisions in five different jet-pTintervals (left) and in Pb+Pb collisions (right) in two different jet-pTintervals and for 0–10% and 60–80% centrality intervals. In both plots the efficiency is evaluated for tracks within jets with |yjet|<0.3. pjet T>35 GeV and matching the original jet direction within R=0.3oftheR=0.4 jet, when such a matching jet is found. If no matching R=0.2 jet is found the axis remains unchanged. Charged-particle tracks are reconstructed from hits in the inner detector using the track reconstruction algorithm with settings optimized for the high hit density in heavy-ion collisions [40]. Tracks used in this analysis are required to have a total of at least 9 (11) hits in the silicon pixel and microstrip detectors for charged particles with pseudorapidity |ηch|⩽ 1.65(|ηch|>1.65). At least one hit is required in one of the two innermost pixel layers. If the track trajectory passed through an active module in the innermost layer, then a hit in this layer is required. Furthermore, a track must have no more than two holes in the Pixel and SCT detectors together, where a hole is defined by the absence of a hit predicted by the track trajectory. All charged-particle tracks used in this analysis are required to have reconstructed transverse momentum pch T>1GeV.In ordertosuppress the contributionfrom secondary particles,the distance of closest approach of the track to the primary vertex in the transverse plane is required to be less than a value which varies from 0.45 mm at pch T=4GeVto0.2mmatpch T=20 GeV, and at that point the track must be less than 1.0 mm from the primary vertex in the longitudinal direction. The efficiency, ε(ptruth T,p jet T,yjet), for reconstructing charged particles within jets in Pb+Pb and pp collisions is evaluated from the matching of reconstructed tracks to generator-levelprimaryparticles3usingMCsamplesdescribed above. The matching is based on contributions of generatorlevel particles to the hits in the detector layers. A reconstructed track is matched to a generator-level particle if it contains hits produced primarily by this particle [34]. The efficiency is evaluated separately in four |yjet|intervals and each interval of reconstructed pjet Tused in the measurement. Furthermore, the efficiency is evaluated separately for each centrality interval in the case of Pb+Pb collisions. The charged-particle 3Primary particles are defined as particles with a mean lifetime τ>0.3×10−10 s either directly produced in pp interactions or from subsequent decays of particles with a shorter lifetime. All other particles are considered to be secondary. reconstruction efficiencies as a function of the generator-level primary particle transverse momentum, ptruth T,areshownin Fig. 1for jets with |yjet|<0.3inpp and Pb+Pb collisions. In order to remove fluctuations in the efficiency due to the limited MC sample size, the ptruth Tdependence of the efficiencies is parametrized and smoothed using a third-order polynomial in ln(ptruth T) that gives a good description of the efficiency in the full range of ptruth T. The efficiencies shown in Fig. 1exhibit only a modest variation with ptruth T, centrality, and pjet T.Asmall almostcontinuousincreaseoftheefficiencywiththeincreasing ptruth Tis observed. The efficiency over the 20–100 GeV ptruth T range is smaller for high pjet Tcompared to low pjet Tby about 2% and 5% in pp and Pb+Pb collisions, respectively. This behavior is attributed to the higher probability to lose tracks in the dense core of high-pTjets than to lose tracks that are more isolated [41]. The efficiency is lower in more central Pb+Pb collisions due to the higher hit density. The efficiency exhibits only a small variation with yjet in the region |yjet|<1.2, and it decreases by approximately 10% in the most forward yjet interval. The contribution of reconstructed tracks which are not be matched to a generated primary particle in the MC samples of pp collision events produced without data overlay, along with the residual contribution of tracks matched to secondary particles, are together considered “fake” tracks. The fraction of fake tracks is less than 2% over the full kinematic range of this measurement. A possible degradation of the tracking performance at high occupancy is checked in the sample of Pb+Pb collision events simulated with the HIJING MC. No significant dependence of the rate of fake tracks on centrality is observed. The correction for the fake contribution is discussed in Sec. V. V. ANALYSIS PROCEDURE The analysis procedure closely follows the one used in the measurement of jet fragmentation at √sNN =2.76 TeV [16]. Reconstructed tracks are associated with a reconstructed jet if they fall within R=0.4 of the jet axis and for each of these particles the longitudinal momentum fraction zis calculated. The measured track yields, dnmeas ch /dz or dnmeas ch /dpch T,are 024908-4 MEASUREMENT OF JET FRAGMENTATION IN Pb+Pb AND … PHYSICAL REVIEW C 98, 024908 (2018) FIG. 2. Ratio of the measured charged-particle distributions before and after the subtraction of the UE and fake tracks as a function of pch T for pjet Tin the range 126–158 GeV for 0–10% (left), 30–40% (middle), and 60–80% (right) centrality. The uncertainties are smaller than the marker size in all cases for which there is a significant UE. constructed as dnmeas ch dz = Nchz, yjet,p jet T z and dnmeas ch dpch T= Nchpch T,yjet,p jet T pch T , where the quantities Nch(z) and Nch(pch T) represent the number of associated tracks within the given zor pch Trange, respectively corrected for the track reconstruction efficiency. The efficiency correction is applied as a 1/ε(pch T,p jet T,yjet) weight on a track-by-track basis, assuming pch T=ptruth T. While that assumption is not strictly valid, the efficiency varies sufficiently slowly with ptruth Tthat the error introduced by this assumption is less than 1%. Tracks which are not correlated with the jet need to be subtracted from the measured distributions; these tracks come from both fake tracks and the UE. In Pb+Pb collisions, contributions to the fragmentation functions from the charged particles originating from the UE in Pb+Pb collisions are subtracted. This contribution is evaluated as a function of charge particle zor pch T,yjet,pjet T, and the collision centrality. Additionally, the measured track yields in pp and Pb+Pb collisions are corrected for the presence of fake tracks. The UE contribution is determined for each measured jet usingagridofR=0.4 cones spanning the full coverage of the inner detector and following the method introduced in Ref. [14]. The method is applied to events containing jets included in the analysis. The cones have a fixed distance between their centers chosen such that the inner detector acceptance is uniformly covered while avoiding overlaps. z 2− 10 1− 10 1 )z(D / sub )z(D 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 , 0-10% -1 = 5.02 TeV, 0.49 nb NN sPb+Pb, -1 = 5.02 TeV, 25 pbs,pp < 158 GeV jet T p126 < ATLAS |<2.1 jet y=0.4 jets, |R t kanti- [GeV] T p 1 10 ) T p(D / sub ) ch T p(D 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 , 0-10% -1 = 5.02 TeV, 0.49 nb NN sPb+Pb, -1 = 5.02 TeV, 25 pbs,pp < 158 GeV jet T p126 < ATLAS |<2.1 jet y=0.4 jets, |R t kantiz 2− 10 1− 10 1 )z(D / sub )z(D 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 , 0-10% -1 = 5.02 TeV, 0.49 nb NN sPb+Pb, -1 = 5.02 TeV, 25 pbs,pp < 316 GeV jet T p251 < ATLAS |<2.1 jet y=0.4 jets, |R t kanti- [GeV] T p 1 10 2 10 ) T p(D / sub ) ch T p(D 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 , 0-10% -1 = 5.02 TeV, 0.49 nb NN sPb+Pb, -1 = 5.02 TeV, 25 pbs,pp < 316 GeV jet T p251 < ATLAS |<2.1 jet y=0.4 jets, |R t kantiFIG. 3. Ratios Dsub(z)/D(z)(left)andDsub(pch T)/D(pT) (right) for pp and 0–10% central Pb+Pb collisions for 126 <p jet T<158 GeV (top) and 251 <p jet T<316 GeV (bottom) for |yjet|<2.1. The error bars show the statistical uncertainties and the boxes show the systematic uncertainties in the unfolding procedure. 024908-5 M. AABOUD et al. PHYSICAL REVIEW C 98, 024908 (2018) z 2− 10 1− 10 1 [%] D(z)δ 20− 15− 10− 5− 0 5 10 15 20 25 JES JER Unfolding MC non-closure Tracking UE subtraction Total =0.4R t kanti- |<2.1 jet y| ATLAS = 5.02 TeV NN s -1 Pb+Pb 2015, 0.49 nb < 158 GeV jet T p126 < 0-10% z 2− 10 1− 10 1 [%] D(z)δ 20− 15− 10− 5− 0 5 10 15 20 25 JES JER Unfolding MC non-closure Tracking Total =0.4R t kanti- |<2.1 jet y| ATLAS = 5.02 TeVs -1 2015, 25 pbpp < 158 GeV jet T p126 < [GeV] T p 1 10 ) [%] T p(Dδ 20− 15− 10− 5− 0 5 10 15 20 25 JES JER Unfolding MC non-closure Tracking UE subtraction Total =0.4R t kanti- |<2.1 jet y| ATLAS = 5.02 TeV NN s -1 Pb+Pb 2015, 0.49 nb < 158 GeV jet T p126 < 0-10% [GeV] T p 1 10 ) [%] T p(Dδ 20− 15− 10− 5− 0 5 10 15 20 25 JES JER Unfolding MC non-closure Tracking Total =0.4R t kanti- |<2.1 jet y| ATLAS = 5.02 TeVs -1 2015, 25 pbpp < 158 GeV jet T p126 < FIG. 4. Summary of the systematic uncertainties of the D(z) (top) and D(pT) (bottom) distributions in 0–10% central Pb+Pb collisions (left) and pp collisions (right) for jets in the 126–158 GeV pjet Tinterval. The systematic uncertainties due to JES, JER, unfolding, UE contribution, MC nonclosure and tracking are shown along with the total systematic uncertainty from all sources. Any cone having a charged particle with pch T>10 GeV or overlapping with a reconstructed jet with pjet T>90 GeV is assumed to be associated with a hard process and is excluded from the UE estimation to avoid biasing it. The parameters defining the exclusion regions are evaluated in MC studies and are subjected to variations as part of the estimation of systematic uncertainties. The resulting UE charged particle yields, dnUE ch /dz or dnUE ch /dpch T, are evaluated over 1 <p ch T< 10 GeV according to dnUE ch dz =1 Ncone 1 εpch T,ηch Ncone ch z,pjet T,yjet zz=pch Tcos R/pjet T , dnUE ch dpch T=1 Ncone 1 εpch T,η ch Ncone ch pch T,p jet T,yjet pch T . Here Ncone is the number of background cones used in the UE determination of a given jet, Ncone ch represents the number of charged particles summed over all background cones, and R represents the distance between the center of a cone and the directionofa givenchargedparticle. Thetermε(pch T,η ch)isthe efficiency for reconstructing charged particles, estimated as a functionofpch Tandηch withoutrequiringtrack-to-jetmatching. The estimated contribution from the UE in each cone is corrected for the difference in the average yield of UE charged particles at a given pch Tbetween the ηposition of the cone and ηposition of the jet. This correction is based on the centrality-, pch T-, and η-dependent distribution of charged-particle yields in minimum-bias data events. An additional correction is applied to the charged-particle UE estimate to account for the difference in the azimuthal particle density, due to elliptic flow, between the φangle of the cone and the φangle of the jet. This utilizes a centralityand pch T-dependent parametrization of the measured elliptic flow coefficients [36]. The UE contribution is further corrected for the correlation between the actual UE charged particle yield underneath the jet and the jet energy resolution [14]; in regions where the UE has an upward fluctuation, the jet energy resolution is worse. The smearing due to jet energy resolution leads to a net migration of jets from lower pjet Tto higher pjet Tvalues. The effect of the migration causes the actual UE contribution underneath the jet to be larger than that estimated from the procedure described above. This effect is corrected for by applying multiplicative correction factors, depending on pch Tor z,yjet,pjet T, and collision centrality. The correction is estimated as a ratio of the UE charged particle yield evaluated by two different methods using the Pb+Pb MC samples. The first estimate uses the cone method discussed above. The second method calculates the UE contribution in the data overlay MC samples from tracks, within the area of a jet, that do not have an associated generated primary particle. The size of the correction is less than 2% at low zor pch Twhere the UE has the largest impact, and has only a small dependence on pjet T. The contribution from fake tracks to the fragmentation functionsisestimatedfromtheMCsampleswithoutminimumbias interactions overlaid. The fraction of these tracks is found to be below 2% of the tracks that pass the selection in all track and jet kinematic regions in this analysis. 024908-6 MEASUREMENT OF JET FRAGMENTATION IN Pb+Pb AND … PHYSICAL REVIEW C 98, 024908 (2018) z 2− 10 1− 10 1 [%] D(z) Rδ 20− 15− 10− 5− 0 5 10 15 20 25 JES JER Unfolding MC non-closure Tracking UE subtraction Total =0.4R t kanti- |<2.1 jet y| ATLAS -1 = 5.02 TeV, 0.49 nb NN sPb+Pb, -1 = 5.02 TeV, 25 pbs,pp < 158 GeV jet T p126 < 0-10% [GeV] T p 110 [%] ) T D(p Rδ 20− 15− 10− 5− 0 5 10 15 20 25 JES JER Unfolding MC non-closure Tracking UE subtraction Total =0.4R t kanti- |<2.1 jet y| ATLAS -1 = 5.02 TeV, 0.49 nb NN sPb+Pb, -1 = 5.02 TeV, 25 pbs,pp < 158 GeV jet T p126 < 0-10% FIG. 5. Summary of the systematic uncertainties for 0–10% central RD(z)(left) and RD(pT)(right) ratios, for jets in the 126–158 GeV pjet T interval. The systematic uncertainties due to JES, JER, unfolding, UE contribution, MC nonclosure, and tracking are shown along with the total systematic uncertainty from all sources. The UE distributions corrected for the additive contribution of fake tracks, d˜ nUE+fake ch /dpch Tand d˜ nUE+fake ch /dz, are then subtracted from the measured distributions, and the subtracted charged-particle yields and fragmentation functions are evaluated: dnsub ch dz =dnmeas ch dz −d˜ nUE+fake ch dz , Dsub(z)=1 Nmeas jet dnsub ch dz , and dnsub ch dpch T=dnmeas ch dpch T−d˜ nUE+fake ch dpch T , Dsubpch T=1 Nmeas jet dnsub ch dpch T , where Nmeas jet is the total number of measured jets in a given pjet T interval. The signal-to-background ratio, nsub ch /nUE ch , strongly depends on the collision centrality and pch T. Figure 2shows the distributions prior to the UE and fake-track subtraction, dnmeas ch dpch T ,divided by the distributionsafterthesubtraction, dnsub ch dpch T , as a function of pch Tfor three centrality selections. In 0–10% central collisions, the distributions prior to subtraction are over ten times larger than the subtracted distributions for the most extreme case of 1 GeV charged particles. This ratio is reduced to approximately 2 in peripheral collisions at the same charged particle pT. The fake-track contribution to the fragmentation functions is subtracted from the measured fragmentation functions in both the pp and Pb+Pb collisions; the UE subtraction is performed only for the Pb+Pb measurement as the UE contribution is negligible in the pp collisions (less than 2% over the entire kinematic range measured). To remove the effects of bin migration due to the jet energy and track momentum resolution, the subtracted dnsub ch /dz and dnsub ch /dpch Tdistributions are corrected by using a twodimensional Bayesian unfolding procedure [42]inzor pT and pjet Tas implemented in the RooUnfold package [43]. Two-dimensionalunfoldingisusedbecausethecalorimetricjet energyresponsedependsonthefragmentationpatternofthejet [44]. Using MC samples, four-dimensional response matrices are created using the generator-level and reconstructed pjet T, and the generator-level and reconstructed charged-particle z or pT. Separate unfolding matrices are constructed for pp data and each centrality interval in Pb+Pb collisions. A separate one-dimensional Bayesian unfolding is used to correct the measuredpjet Tspectrawhichareusedtonormalizetheunfolded unnormalized fragmentation functions, dnunfolded ch /dpTand dnunfolded ch /dz. To achieve better agreement with the data, the MC jet spectra and fragmentation functions are reweighted to match the shapes in the reconstructed data. The Bayesian procedure requires a choice in the number of iterations. Additional iterations reduce the sensitivity to the choice of prior, but may amplify statistical fluctuations in the distributions. After four iterations for both the one-dimensional and two-dimensional unfoldings the fragmentation functions are stable for both the Pb+Pb and pp data. The final, particle-level corrected distributions are defined as D(z)=1 Nunfolded jet dnunfolded ch dz , D(pT)=1 Nunfolded jet dnunfolded ch dpT , where Nunfolded jet is the unfolded number of jets in a given pjet T interval. The performance of the analysis procedure is tested by dividing the MC events in half and using one half to generate response matrices with which the other half is unfolded and the ratio of unfolded to generator-level fragmentation functions4is evaluated. This procedure tests all the analysis corrections and the unfolding procedure. Good recovery of the generator-level (truth) MC distributions is observed for the unfolded events. The deviations from the exact recovery of the generatorlevel MC distributions, the nonclosure, are included in the systematic uncertainties. The ratios of Dsub(z) and Dsub(pch T) distributions to the unfolded D(z) and D(pT) distributions are 4The generator-level fragmentation functions are constructed using generator-level jets and primary charged particles. 024908-7 M. AABOUD et al. PHYSICAL REVIEW C 98, 024908 (2018) z −2 10 −1 10 1 )z(D −4 10 −2 10 1 2 10 4 10 6 10 8 10 | <2.1 jet y| ATLAS = 5.02 TeVs ,pp -1 25 pb =0.4R t kanti- < 158 GeV x10p126 < < 200 GeV x10p158 < < 251 GeV x10p200 < < 316 GeV x10p251 < < 398 GeV x10p316 < [GeV] T p 110 2 10 ] -1 ) [GeV T p(D −6 10 −3 10 1 3 10 6 10 | <2.1 jet y| ATLAS = 5.02 TeVs ,pp -1 25 pb =0.4R t kanti- < 158 GeV x10p126 < < 200 GeV x10p158 < < 251 GeV x10p200 < < 316 GeV x10p251 < < 398 GeV x10p316 < FIG. 6. Fragmentation functions, D(z)(left)andD(pT) (right), in pp collisions measured in five pjet Tranges from 126 to 398 GeV. The vertical bars on the data points indicate statistical uncertainties, while the shaded bands indicate systematic uncertainties. In most cases, the statistical uncertainties are smaller than the marker size. shown in Fig. 3for pp collisions and 0–10% central Pb+Pb collisions. The magnitude of the unfolding effect varies as a function of pjet T,pch T, and centrality. The effect of the unfolding is similar in pp and Pb+Pb collisions at low zand pT,but for higher-momentum particles within the jet, the effect of the unfolding in pp and Pb+Pb collisions differs by up to 25% between the two collision systems for 126 <p jet T<158 GeV. This difference is due to UE fluctuations, which lead to poorer jet energy resolution in Pb+Pb collisions than in pp collisions. With increasing pjet T, the effect of UE fluctuations decreases; for 251 <p jet T<316 GeV the effect of the unfolding is similar in Pb+Pb and pp collisions at all value of zand pT. The effect of the unfolding is larger at high zand pTdue to the steepness of the fragmentation function near z=1. The shaded boxes in Fig. 3show the size of systematic uncertainties associated with the unfolding which originate from the sensitivity of the unfolding to the shape of input MC distributions, as described in the next section. z −2 10 1− 10 1 )z(D 4− 10 1− 10 2 10 5 10 8 10 | <2.1 jet y| ATLAS -1 = 5.02 TeV, 0.49 nb NN sPb+Pb, =0.4 jetsR t kanti- < 158 GeV jet T p 126 < 3 0 - 10% x 10 2 10 - 20% x 10 1 20 - 30% x 10 0 30 - 40% x 10 -1 40 - 60% x 10 -2 60 - 80% x 10 [GeV] T p 1 10 ] -1 ) [GeV T p(D 6− 10 3− 10 1 3 10 6 10 | <2.1 jet y| ATLAS -1 = 5.02 TeV, 0.49 nb NN sPb+Pb, =0.4 jetsR t kanti- < 158 GeV jet T p 126 < 3 0 - 10% x 10 2 10 - 20% x 10 1 20 - 30% x 10 0 30 - 40% x 10 -1 40 - 60% x 10 -2 60 - 80% x 10 FIG. 7. Fragmentation functions, D(z)(left)andD(pT) (right), in Pb+Pb collisions measured in six different centrality classes for pjet Tof 126 to 158 GeV. The vertical bars on the data points indicate statistical uncertainties, while the shaded bands indicate systematic uncertainties. In most cases, the statistical uncertainties are smaller than the marker size. 024908-8 MEASUREMENT OF JET FRAGMENTATION IN Pb+Pb AND … PHYSICAL REVIEW C 98, 024908 (2018) z 2− 10 1− 10 1 )z(D 4− 10 1− 10 2 10 5 10 8 10 | <2.1 jet y| ATLAS -1 = 5.02 TeV, 0.49 nb NN sPb+Pb, =0.4 jetsR t kanti- < 200 GeV jet T p 158 < 3 0 - 10% x 10 2 10 - 20% x 10 1 20 - 30% x 10 0 30 - 40% x 10 -1 40 - 60% x 10 -2 60 - 80% x 10 [GeV] T p 1 10 2 10 ] -1 ) [GeV T p(D 6− 10 3− 10 1 3 10 6 10 | <2.1 jet y| ATLAS -1 = 5.02 TeV, 0.49 nb NN sPb+Pb, =0.4 jetsR t kanti- < 200 GeV jet T p 158 < 3 0 - 10% x 10 2 10 - 20% x 10 1 20 - 30% x 10 0 30 - 40% x 10 -1 40 - 60% x 10 -2 60 - 80% x 10 FIG. 8. Fragmentation functions, D(z)(left)andD(pT) (right), in Pb+Pb collisions measured in six different centrality classes for pjet Tof 158 to 200 GeV. The vertical bars on the data points indicate statistical uncertainties, while the shaded bands indicate systematic uncertainties. In most cases, the statistical uncertainties are smaller than the marker size. VI. SYSTEMATIC UNCERTAINTIES The following sources of systematic uncertainty are considered: the jet energy scale (JES), the jet energy resolution (JER), the sensitivity of the unfolding to the prior, the residual nonclosure of the analysis procedure, UE contribution, and tracking-related uncertainties. For each variation accounting for a source of systematic uncertainty, the fragmentation functions and ratios of D(z) and D(pT) distributions in Pb+Pb and pp collisions are re-evaluated. The difference between the varied and nominal distributions is used as an estimate of the resulting uncertainty. The systematic uncertainty due to the JES in Pb+Pb collisions is composed of two parts: a centrality-independent baseline component and a centrality-dependent component. Only the centrality-independent baseline component is used in pp collisions; it is determined from in situ studies of the calorimeter response [37,45,46], and studies of the relative z 2− 10 1− 10 1 )z(D 4− 10 1− 10 2 10 5 10 8 10 | <2.1 jet y| ATLAS -1 = 5.02 TeV, 0.49 nb NN sPb+Pb, =0.4 jetsR t kanti- < 251 GeV jet T p 200 < 3 0 - 10% x 10 2 10 - 20% x 10 1 20 - 30% x 10 0 30 - 40% x 10 -1 40 - 60% x 10 -2 60 - 80% x 10 [GeV] T p 1 10 2 10 ] -1 ) [GeV T p(D 6− 10 3− 10 1 3 10 6 10 | <2.1 jet y| ATLAS -1 = 5.02 TeV, 0.49 nb NN sPb+Pb, =0.4 jetsR t kanti- < 251 GeV jet T p 200 < 3 0 - 10% x 10 2 10 - 20% x 10 1 20 - 30% x 10 0 30 - 40% x 10 -1 40 - 60% x 10 -2 60 - 80% x 10 FIG. 9. Fragmentation functions, D(z)(left)andD(pT) (right), in Pb+Pb collisions measured in six different centrality classes for pjet Tof 200 to 251 GeV. The vertical bars on the data points indicate statistical uncertainties, while the shaded bands indicate systematic uncertainties. In most cases, the statistical uncertainties are smaller than the marker size. 024908-9 M. AABOUD et al. PHYSICAL REVIEW C 98, 024908 (2018) FIG. 17. Ratios of D(pT) distributions in six centrality intervals of Pb+Pb collisions to pp collisions evaluated in four pjet Tranges for jets with 1.2<|yjet|<2.1. The vertical bars on the data points indicate statistical uncertainties, while the shaded bands indicate systematic uncertainties. Centrality decreases from top to bottom panels and pjet Tincreases from left to right panels. VII. RESULTS In this section, results are presented of the measurement of the D(z) and D(pT) distributions for jet pTbetween 126 and 398 GeV and six centrality intervals in Pb+Pb collisions; the same distributions are presented in pp collisions for the same pjet Tranges. In order to study the effects of hot dense matter on the jet fragmentation process, ratios of Pb+Pb fragmentation functions to pp fragmentation functions are evaluated. The D(z) and D(pT) distributions in pp collisions are shown in Fig. 6. The corresponding distributions in Pb+Pb collisions are shown in Figs. 7–11. In order to quantify the difference in the fragmentation functions between Pb+Pb and pp collisions, the ratios of D(z) andD(pT)distributions measuredinPb+Pbcollisionstothose measured in pp collisions, RD(z)and RD(pT), are shown in Figs. 12 and 13, respectively. In each figure, the shaded boxes indicate systematic uncertainties and the vertical bars show the statistical uncertainties. 024908-16 MEASUREMENT OF JET FRAGMENTATION IN Pb+Pb AND … PHYSICAL REVIEW C 98, 024908 (2018) FIG. 18. RD(z)(left) and RD(pT)(right) for 126–158 GeV jets for collision energies of 5.02 TeV (this analysis) and 2.76 TeV [16]. The vertical bars on the data points indicate statistical uncertainties while the boxes indicate systematic uncertainties. The shapes of the RD(z)and RD(pT)distributions are similar for all centralities: inside the jets; the yields of particles with low pTor zare enhanced; there is a reduction for particles with intermediate pTor z; and the yields of particles with high pTor zare enhanced. This is qualitatively consistent with previous measurements of jet fragmentation at √sNN = 2.76 TeV [14–16]; a quantitative comparison is provided in Sec. VIII. The magnitudes of the deviations of the ratios from unity decrease with decreasing collision centrality. In the most central collisions, the size of the enhancement is as large as 70% at low pTor zand 30% at high pTor z. The depletion of charged-particle yields at intermediate pTand zis as large as 20%.Insomecentralityandpjet Trangesthereisadecreaseofthe fragmentation functions at the highest zvalues. In this region the statistical and systematic uncertainties are the largest; more precise measurements are needed to determine if a significant decrease exists. Figures 14 and 15 show the RD(z)distributions for jets in the most central and most forward rapidity intervals, 0.0–0.3 and 1.2–2.1, respectively, for the six centrality intervals used in this analysis and for four pjet Tintervals: 126–158, 158– 200, 200–251, and 251–316 GeV. Figures 16 and 17 show RD(pT)distributions for the same jet rapidity, centrality, and pjet Tranges. In all rapidity ranges, the RD(z)and RD(pT) distributions have the same qualitative shape and centrality dependence as the rapidity-inclusive results presented above. VIII. DISCUSSION In this section, the results from the previous section are further discussed and compared to theoretical models. In order to make a direct comparison with measurements at 2.76 TeV, Fig. 18 overlays the RD(z)and RD(pT)distributions measured in 2.76 TeV collisions [16] on those obtained in this FIG. 19. RD(z)(left) and RD(pT)(right) ratios for three pjet Tranges: 126–158 GeV (circles), 200–251 GeV (diamonds), and 316–398 GeV (crosses). The statistical uncertainties are shown as bars and the systematic uncertainties as outlined boxes. 024908-17 M. AABOUD et al. PHYSICAL REVIEW C 98, 024908 (2018) FIG. 20. RD(z)forjetswith126 <p jet T<158GeVcomparedwith calculations from Ref. [51] (hybrid model) for Rres =0 (dot-dashed curve), Rres =3 (dashed curve), and to calculations from Ref. [21] (EQ model). analysisat5.02TeV.Thetwomeasurementsatthetwocollision energies quantitatively agree over the entire zand chargedparticle pTrange of the measurement; no significant collision energy dependence is observed [the lowest point in the D(pT) ratios differs by less than two standard deviations when the statistical and systematic uncertainties are combined]. In order to determine how the fragmentation functions depend on pjet T, the fragmentation functions from three pjet T intervals are compared in Fig. 19.TheD(pT) and D(z) distributions are closely related to each other, differing, primarily, in the normalization by pjet Tin the definition of z[see Eq. (1)]. Therefore, a comparison of the modifications of the fragmentation functions as a function of pjet Tcan show whether the size of modifications scales with charged-particle zor with pT. The former would be expected for fragmentation effects, and the latter might indicate some scale in the QGP. The large pjet Trange available in this measurement allows these two scenarios to be distinguished. Figure 19 shows that the excess of soft particles observed in central Pb+Pb collisions exhibits a much smaller pjet Tdependence for the D(pT) ratios than for the D(z) ratios; the transition from enhancement to suppressionforsoftfragmentsoccursatpTaround4GeVforall pjet Tvalues investigated in this analysis. The same comparison can be made for the hard particles. In this case, Fig. 19 shows that the enhancement of hard fragments with z0.3 is nearly independent of pjet T. The fragmentation functions have been calculated within a hybrid model of jet quenching, which uses perturbative techniques for the high-Q2processes in jet evolution and strong coupling for the low momentum scales associated with the QGP [50,51]. Within this model, there is a length scale Lreswhich can be interpreted as the minimum distance required to resolve a parton as separate from the others in the showering process when it occurs in the QGP medium. The scale Lres can be expressed in terms of the temperature of QGP, T, FIG. 21. RD(pT)ratios for three pjet Tranges: 126–158 GeV (circles), 200–251 GeV (diamonds), and 316–398 GeV (crosses) compared with calculations from the hybrid model [51] with Rres =3. as Lres =Rres/πT where Rres is a parameter of the model. The fragmentation functions measured here are compared with calculations from this model in Fig. 20 for two values of Rres. ThecalculationswithRres =3arequalitatively consistent with the measurement at high zand pT.Atlowzand pT, the results of the calculations are below the data, in agreement with prior observations in comparisons to related observables [52]. Also shown in Fig. 20 is a calculation from Ref. [21] which is a phenomenological model, the effective quenching (EQ) model, incorporating energy-loss effects through two downward shifts in the pjet Tspectrum: one for quark-initiated jets and a larger one for gluon-initiated jets. In this case, the jets fragment as in vacuum, but RD(z)differs from unity due to an increase in the fraction of quark jets in Pb+Pb collisions relative to pp collisions at a fixed pjet T. Since quark jets are more likely to produce high-zparticles than gluon jets [53,54] this causes RD(z)>1athighzin the model predictions. The EQ model does not have a description of the soft processes from soft gluon radiation or the response of the hot QCD matter to the jet passing through it, so the comparison with data is only appropriate at z>0.1. Figure 21 shows a comparison between measured RD(pT) andthehybridmodelcalculationwith Rres =3forthreepjet Tintervals.Themagnitudeoftheenhancementofhigh-pTparticles in the calculation agrees with the observations for pjet Tin the ranges 126–158 and 200–251 GeV. The RD(z)values are also compared in Fig. 22 with a third model which uses calculations based on soft collinear effective theory (SCET) [55,56]. This model well describes RD(z)in the low and intermediate z regions, but does not reproduce the enhancement in the high-z region observed in the data. In order to quantify the magnitude of the low-pTenhancement in the D(pT) distributions in Pb+Pb collisions compared to pp collisions, the difference between the two distributions is evaluated for the pjet Tand centrality intervals used in this 024908-18 MEASUREMENT OF JET FRAGMENTATION IN Pb+Pb AND … PHYSICAL REVIEW C 98, 024908 (2018) FIG. 22. RD(z)for three pjet Tranges: 126–158 GeV (circles), 200– 251 GeV (diamonds), and 316–398 GeV (crosses) compared with calculations from the SCET model [55,56]. analysis: Nch|cent ≡pT,max pT,min [D(pT)|cent −D(pT)|pp ]dpT, where “cent” represents one of the six centrality intervals, and the values of pT,min and pT,max are boundaries of the low pTenhancement region, chosen to be 1.0 and 4.2 GeV, respectively. In addition, the pT-weighted difference between the same quantities is also computed: Pch Tcent ≡pT,max pT,min [D(pT)|cent −D(pT)|pp ]pTdpT. The Pch T|cent represents the total transverse momentum carried byparticlesinthelowpTenhancementregion.Thedependence of Nch|cent and Pch T|cent on pjet Tand centrality is presented in Fig. 23. Overall, both quantities are found to increase as a function of pjet Tand collision centrality. In the most central collisions, Nch increases from approximately 1.5 to 2.0 particles over the pjet Trange of this measurement. The amount of transverse momentum carried by these particles increases from approximately 2.5 to 4 GeV over the same pjet Trange. In peripheral collisions, the number of particles contributing to the enhancement is much smaller, approximately 0.2 particles carrying less than 0.5 GeV of transverse momentum in the lowest pjet Trange. These results are in qualitative agreement with measurements of the same quantities in √sNN =2.76 TeV Pb+Pb collisions [16]; however, the pjet Tranges are not the same as used in this analysis and the pjet Tdependence is not reported in that measurement. In order to quantify the rapidity dependence, the ratio of RD(z)in the rapidity intervals 0.3–0.8, 0.8–1.2, and 1.2–2.1 to the RD(z)in |yjet|<0.3 is shown in Fig. 24 for pjet Tintervals of 126–158, 158–200, and 200–251 GeV and for 0–10%, 10–20%, and 20–30% central collisions. A similar quantity was reported in Ref. [16] for 100–398 GeV jets at 2.76 TeV. In that measurement, a small rapidity dependence for RD(z)is observed at high zfor jets with |yjet|<0.8; however, no strong conclusion could be drawn due to the size of the uncertainties. The pjet Tintervals used in the measurement presented here are selected to be similar to those used in the measurement of fragmentation functions at 2.76 TeV. Furthermore, jets populating the 200–251 GeV pjet Tinterval in collisions at 5.02 TeV have similar fractions of quarkand gluon-initiated jets as jets having pTbetween 126 and 158 GeV in 2.76 TeV collisions. The ratiosofRD(z)evaluatedinvariousrapidityintervalstothemost central rapidity RD(z)in different pjet Tintervals suggest with a FIG. 23. Difference between Pb +Pb collisions and pp collisions in the total yield of charged particles Nch|cent (left), and difference in the total transverse momentum carried by charged particles Pch T|cent (right) for particles with pTfrom 1 <p T<4.2 GeV evaluated as a function of pjet Tfor six centrality intervals. The vertical bars on the data points indicate statistical uncertainties while the boxes indicate systematic uncertainties. 024908-19 M. AABOUD et al. PHYSICAL REVIEW C 98, 024908 (2018) FIG. 24. Ratio of the rapidity-selected RD(z)distributions to the RD(z)distributions measured in |yjet|<0.3 for three pjet Tranges and three centrality intervals. The vertical bars on the data points indicate statistical uncertainties while the shaded bands indicate systematic uncertainties. FIG. 25. Comparison of the measured ratio of the rapidity-selected RD(z)distributions to the RD(z)distributions measured in |yjet|<0.3 and the same quantity evaluated in the hybrid model [51]forRres =3 and in the EQ model [21]. The comparison with the hybrid model is done for three pjet Tranges in 0–10% central collisions. The comparison with the EQ model is shown for 126–158 GeV pjet Tinterval. The vertical bars on the data points indicate statistical uncertainties while the shaded bars indicate systematic uncertainties. The band represents the statistical uncertainty of the calculations. 024908-20 MEASUREMENT OF JET FRAGMENTATION IN Pb+Pb AND … PHYSICAL REVIEW C 98, 024908 (2018) low significance a small enhancement of yields of fragments with low and intermediate zand reduction of yields of high-z fragments for more forward jets in the most central Pb +Pb collisions. However, the observation for high-zfragments is of limited significance due to the limited size of the available data sample. Figure 25 shows the same ratios for the 0–10% centrality interval compared with calculations from the hybrid model [51] and the effective quenching model [21]. Both calculations are consistent with the data for jets with |yjet|<1.2 with larger deviations in rapidity interval 1.2<|yjet|<2.1. IX. SUMMARY This paper presents an analysis of 0.49 nb−1of Pb+Pb and 25 pb−1of pp collisions at √sNN =5.02 TeV using data collected with the ATLAS detector at the LHC in 2015. The analysis measures the fragmentation functions of jets into charged particles and the distributions of charged-particle transverse momenta within R=0.4 anti-ktjets with |yjet|< 2.1 and with pjet Tfrom 126 to 398 GeV. The studies are performed as a function of the event centrality, jet rapidity, and jet transverse momentum for charged particles with transverse momentum greater than 1 GeV. Centrality-dependent modifications to these fragmentation functions in Pb+Pb collisions are observed when compared with those measured in pp collisions. The magnitude of these modifications increases with increasing collision centrality. The ratios of fragmentation functions evaluated in Pb+Pb collisions to those in pp collisions exhibit enhancements both for transverse momentum less than 4 GeV and for z0.3. Between these two enhancements there is a suppression of the fragmentation functions in Pb+Pb collisions compared to pp collisions. The enhancement of yields of low and high transverse momentum fragments is as large as 70% and 30%, respectively, in central collisions. The depletion of fragment yields with intermediate pTand zis as large as 20%. The difference in charged-particle multiplicity and total transverse momentum in Pb+Pb compared to pp collisions for 1.0< pT<4.2 GeV range increases with increasing centrality and jet transverse momentum. No significant dependence of the high-zenhancement on the transverse momentum of the jet is observed. The SCET model describes the low pTexcess and the EQ and hybrid models describe the high-zexcess, but none of the models describes the modification of the full fragmentation functions. A small increase in the modification of yields of fragments with low and intermediate zis observed in forward jets compared to those at central rapidity. These measurementsprovidenewinformationaboutthejettransverse momentum and rapidity dependence of the modifications to jet fragmentation in Pb+Pb collisions and, together with other jet measurements in heavy-ion collisions, will constrain models of jet quenching in the QGP created in heavy-ion collisions. ACKNOWLEDGMENTS We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOSTandNSFC, China;COLCIENCIAS,Colombia;MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS, CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF, and MPG, Germany; GSRT, Greece; RGC, Hong Kong SAR, China; ISF, I-CORE and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT, Portugal; MNE/IFA, Romania; MES of Russia and NRC KI, Russian Federation; JINR; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, South Africa; MINECO, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom; DOE and NSF, United States of America. In addition, individual groups and members have received support from BCKDF, the Canada Council, CANARIE, CRC, Compute Canada, FQRNT, and the Ontario Innovation Trust, Canada; EPLANET, ERC, ERDF, FP7, Horizon 2020 and Marie Skłodowska-Curie Actions, European Union; Investissements d’Avenir Labex and Idex, ANR, Région Auvergne and Fondation Partager le Savoir, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF; BSF, GIF and Minerva, Israel; BRF, Norway; CERCA Programme Generalitat de Catalunya, Generalitat Valenciana, Spain; the Royal Society and Leverhulme Trust, United Kingdom. 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PHYSICAL REVIEW C 98, 024908 (2018) 76Department of Physics and Astronomy, Iowa State University, Ames, Iowa, USA 77Joint Institute for Nuclear Research, Dubna, Russia 78aDepartamento de Engenharia Elétrica, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil 78bUniversidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil 78cUniversidade Federal de São João del Rei (UFSJ), São João del Rei, Brazil 78dInstituto de Física, Universidade de São Paulo, São Paulo, Brazil 79KEK, High Energy Accelerator Research Organization, Tsukuba, Japan 80Graduate School of Science, Kobe University, Kobe, Japan 81aAGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Krakow 81bMarian Smoluchowski Institute of Physics, Jagiellonian University, Krakow, Poland 82Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland 83Faculty of Science, Kyoto University, Kyoto, Japan 84Kyoto University of Education, Kyoto, Japan 85Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka, Japan 86Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina 87Physics Department, Lancaster University, Lancaster, United Kingdom 88Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom 89Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics, University of Ljubljana, Ljubljana, Slovenia 90School of Physics and Astronomy, Queen Mary University of London, London, United Kingdom 91Department of Physics, Royal Holloway University of London, Egham, United Kingdom 92Department of Physics and Astronomy, University College London, London, United Kingdom 93Louisiana Tech University, Ruston, Louisiana, USA 94Fysiska institutionen, Lunds Universitet, Lund, Sweden 95Centre de Calcul de l’Institut National de Physique Nucléaire et de Physique des Particules (IN2P3), Villeurbanne, France 96Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid, Spain 97Institut für Physik, Universität Mainz, Mainz, Germany 98School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom 99CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France 100Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA 101Department of Physics, McGill University, Montreal, Quebec, Canada 102School of Physics, University of Melbourne, Victoria, Australia 103Department of Physics, University of Michigan, Ann Arbor, Michigan, USA 104Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan, USA 105B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, Belarus 106Research Institute for Nuclear Problems of Byelorussian State University, Minsk, Belarus 107Group of Particle Physics, University of Montreal, Montreal, Quebec, Canada 108P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia 109Institute for Theoretical and Experimental Physics (ITEP), Moscow, Russia 110National Research Nuclear University MEPhI, Moscow, Russia 111D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow, Russia 112Fakultät für Physik, Ludwig-Maximilians-Universität München, München, Germany 113Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München, Germany 114Nagasaki Institute of Applied Science, Nagasaki, Japan 115Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan 116Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico, USA 117Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, Netherlands 118Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, Netherlands 119Department of Physics, Northern Illinois University, DeKalb, Illinois, USA 120aBudker Institute of Nuclear Physics, SB RAS, Novosibirsk 120bNovosibirsk State University Novosibirsk, Russia 121Department of Physics, New York University, New York, New York, USA 122Ohio State University, Columbus, Ohio, USA 123Faculty of Science, Okayama University, Okayama, Japan 124Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma, USA 125Department of Physics, Oklahoma State University, Stillwater, Oklahoma, USA 126Palacký University, RCPTM, Joint Laboratory of Optics, Olomouc, Czech Republic 127Center for High Energy Physics, University of Oregon, Eugene, Oregon, USA 128LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France 024908-32 MEASUREMENT OF JET FRAGMENTATION IN Pb+Pb AND … PHYSICAL REVIEW C 98, 024908 (2018) 129Graduate School of Science, Osaka University, Osaka, Japan 130Department of Physics, University of Oslo, Oslo, Norway 131Department of Physics, Oxford University, Oxford, United Kingdom 132LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3, Paris, France 133Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania, USA 134Konstantinov Nuclear Physics Institute of National Research Centre “Kurchatov Institute,” PNPI, St. Petersburg, Russia 135Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania, USA 136aLaboratório de Instrumentação e Física Experimental de Partículas - LIP, Lisboa, Portugal 136bDepartamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal 136cDepartamento de Física, Universidade de Coimbra, Coimbra, Portugal 136dCentro de Física Nuclear da Universidade de Lisboa, Lisboa, Portugal 136eDepartamento de Física, Universidade do Minho, Braga, Portugal 136fDepartamento de Física Teorica y del Cosmos, Universidad de Granada, Granada, Spain 136gDep Física and CEFITEC of Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal 137Institute of Physics, Academy of Sciences of the Czech Republic, Prague,Czech Republic 138Czech Technical University in Prague, Prague, Czech Republic 139Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic 140State Research Center Institute for High Energy Physics, NRC KI, Protvino, Russia 141Particle Physics Department, Rutherford Appleton Laboratory, Didcot, United Kingdom 142IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France 143Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, California, USA 144aDepartamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile 144bDepartamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile 145Department of Physics, University of Washington, Seattle, Washington, USA 146Department of Physics and Astronomy, University of Sheffield, Sheffield, United Kingdom 147Department of Physics, Shinshu University, Nagano, Japan 148Department Physik, Universität Siegen, Siegen, Germany 149Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada 150SLAC National Accelerator Laboratory, Stanford, California, USA 151Physics Department, Royal Institute of Technology, Stockholm, Sweden 152Departments of Physics and Astronomy, Stony Brook University, Stony Brook, New York, USA 153Department of Physics and Astronomy, University of Sussex, Brighton, United Kingdom 154School of Physics, University of Sydney, Sydney, Australia 155Institute of Physics, Academia Sinica, Taipei, Taiwan 156aE. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia 156bHigh Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia 157Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel 158Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel 159Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece 160International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo, Japan 161Graduate School of Science and Technology, Tokyo Metropolitan University, Tokyo, Japan 162Department of Physics, Tokyo Institute of Technology, Tokyo, Japan 163Tomsk State University, Tomsk, Russia 164Department of Physics, University of Toronto, Toronto, Ontario, Canada 165aTRIUMF, Vancouver BC 165bDepartment of Physics and Astronomy, York University, Toronto, Ontario, Canada 166Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba Japan 167Department of Physics and Astronomy, Tufts University, Medford, Massachusetts, USA 168Department of Physics and Astronomy, University of California Irvine, Irvine, California, USA 169Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden 170Department of Physics, University of Illinois, Urbana, Illinois, USA 171Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia - CSIC, Valencia, Spain 172Department of Physics, University of British Columbia, Vancouver, British Columbia, Canada 173Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia, Canada 174Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg, Germany 175Department of Physics, University of Warwick, Coventry, United Kingdom 176Waseda University, Tokyo, Japan 177Department of Particle Physics, Weizmann Institute of Science, Rehovot, Israel 024908-33 M. AABOUD et al. PHYSICAL REVIEW C 98, 024908 (2018) 178Department of Physics, University of Wisconsin, Madison, Wisconsin, USA 179Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal, Germany 180Department of Physics, Yale University, New Haven, Connecticut, USA 181Yerevan Physics Institute, Yerevan, Armenia aDeceased. bAlso at Department of Physics, King’s College London, London, United Kingdom. cAlso at Istanbul University, Dept. of Physics, Istanbul, Turkey. dAlso at Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan. eAlso at TRIUMF, Vancouver, BC, Canada. fAlso at Department of Physics and Astronomy, University of Louisville, Louisville, KY, USA. gAlso at Department of Physics, California State University, Fresno, CA, USA. hAlso at Department of Physics, University of Fribourg, Fribourg, Switzerland. iAlso at II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany. jAlso at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spain. kAlso at Tomsk State University, Tomsk, and Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia. lAlso at The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing, China. mAlso at Universita di Napoli Parthenope, Napoli, Italy. nAlso at Institute of Particle Physics (IPP), Victoria, BC, Canada. oAlso at Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy. pAlso at Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania. qAlso at CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France. rAlso at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg, Russia. sAlso at Borough of Manhattan Community College, City University of New York, NY, USA. tAlso at Department of Financial and Management Engineering, University of the Aegean, Chios, Greece. uAlso at Centre for High Performance Computing, CSIR Campus, Rosebank, Cape Town, South Africa. vAlso at Louisiana Tech University, Ruston, LA, USA. wAlso at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain. xAlso at Department of Physics, University of Michigan, Ann Arbor, MI, USA. yAlso at LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France. zAlso at Graduate School of Science, Osaka University, Osaka, Japan. aaAlso at Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany. abAlso at Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, Netherlands. acAlso at Near East University, Nicosia, North Cyprus, Mersin, Turkey. adAlso at Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia. aeAlso at CERN, Geneva, Switzerland. afAlso at Manhattan College, New York, NY, USA. agAlso at Hellenic Open University, Patras, Greece. ahAlso at The City College of New York, New York, NY, USA. aiAlso at Departamento de Física Teorica y del Cosmos, Universidad de Granada, Granada, Spain. ajAlso at Department of Physics, California State University, Sacramento, CA, USA. akAlso at Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia. alAlso at Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève, Switzerland. amAlso at Department of Physics and Astronomy, University of Sheffield, Sheffield, United Kingdom. anAlso at School of Physics, Sun Yat-sen University, Guangzhou, China. aoAlso at Department of Applied Physics and Astronomy, University of Sharjah, Sharjah, United Arab Emirates. apAlso at Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germany. aqAlso at National Research Nuclear University MEPhI, Moscow, Russia. arAlso at Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest, Hungary. asAlso at Giresun University, Faculty of Engineering, Giresun, Turkey. atAlso at Department of Physics, Nanjing University, Nanjing, China. auAlso at Institute of Physics, Academia Sinica, Taipei, Taiwan. 024908-34