PHYSICAL REVIEW D 100, 052011 (2019) Properties of jet fragmentation using charged particles pffiffi measured with the ATLAS detector in pp collisions at s = 13 TeV G. Aad et al.* (ATLAS Collaboration) (Received 24 June 2019; published 19 September 2019) This paper presents a measurement of quantities related to the formation of jets from high-energy quarks and gluons (fragmentation). Jets with transverse momentum 100 GeV < pT < 2.5 TeV and pseudorapidity pffiffiffi jηj < 2.1 from an integrated luminosity of 33 fb−1 of s ¼ 13 TeV proton-proton collisions are reconstructed with the ATLAS detector at the Large Hadron Collider. Charged-particle tracks with pT > 500 MeV and jηj < 2.5 are used to probe the detailed structure of the jet. The fragmentation properties of the more forward and the more central of the two leading jets from each event are studied. The data are unfolded to correct for detector resolution and acceptance effects. Comparisons with parton shower Monte Carlo generators indicate that existing models provide a reasonable description of the data across a wide range of phase space, but there are also significant differences. Furthermore, the data are interpreted in the context of quark- and gluon-initiated jets by exploiting the rapidity dependence of the jet flavor fraction. A first measurement of the charged-particle multiplicity using model-independent jet labels (topic modeling) provides a promising alternative to traditional quark and gluon extractions using input from simulation. The simulations provide a reasonable description of the quark-like data across the jet pT range presented in -this measurement, but the gluon-like data have systematically fewer charged particles than the simulation. DOI: 10.1103/PhysRevD.100.052011 I. INTRODUCTION for parameter optimizations (tunes) of the PYTHIA 8 Monte Carlo (MC) generator [6]. A measurement of pffiffiffithe Jets are collimated sprays of particles resulting from average number of charged particles inside jets at s ¼ high-energy quark and gluon production. The details of the 8 TeV [7] was also used as input to recent developments in process that underlies the fragmentation of quarks and the HERWIG 7 MC program [8]. Further measurements of jet gluons with net quantum chromodynamic (QCD) charge constituent multiplicity and energy sharing will provide into net neutral hadrons are not fully understood. Jet powerful constraints for future generator optimizations. formation is a complex multiscale problem, including Quark- and gluon-initiated jets (henceforth quark and important contributions from QCD effects that cannot be gluon jets) have different radiation patterns (see e.g., described by perturbation theory. Measuring basic quan- Ref. [9]). As many analyses at the LHC target either tities related to fragmentation is therefore essential to quark-enriched or gluon-enriched processes, these radi- furthering our understanding of the emergent properties ation-pattern differences can be useful for jet tagging of QCD. [10,11]. Measurements of jet structure can be used to Perturbative and nonperturbative physically inspired calibrate quark-versus-gluon jet taggers. By exploiting models have free parameters that are tuned to data in order the rapidity dependence of the relative quark and gluon to best describe the radiation pattern inside jets [1]. This is jet rates, ATLAS [7] extracted the average charged- in turn an important input to all analyses at the Large particle multiplicity for quark and gluon jets separately. Hadron Collider (LHC) due to the ubiquity of jets. This was then combined with detector-level systematic Measurements of jet substructure in proton-proton pffiffiffi (pp) uncertainties pffiffiffi to provide quark/gluon tagger uncertainties collisions at a center-of-mass energy of s ¼ 7 TeV [2–5] at s ¼ 13 TeV [12]. A more complex tagger based on have already been used by the ATLAS collaboration several jet shapes could be calibrated in a similar manner using extended results. The benefit of a particle-level * Full author list given at the end of the article. measurement is that a portion of the calibration can be independent of ATLAS and LHC operating conditions. Published by the American Physical Society under the terms of Uncertainties in detector effects can be updated with the the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to changing detector environment. Adding more observ- the author(s) and the published article’s title, journal citation, ables and measuring their differential distributions will and DOI. Funded by SCOAP3. improve this calibration. 2470-0010=2019=100(5)=052011(38) 052011-1 © 2019 CERN, for the ATLAS Collaboration G. AAD et al. PHYS. REV. D 100, 052011 (2019) Although the full radiation pattern inside jets is not results are presented in Sec. VIII. Section IX provides calculable from first principles, the energy dependence of conclusions and future outlook. many observables can be calculated in perturbation theory. There have been significant theoretical advances in soft- II. OBSERVABLES collinear effective theory (SCET) [13–16] to derive fac- This analysis builds upon the previous ATLAS jet torization theorems that describe the evolution of universal structure measurements presented in Refs. [7,21,59]. nonperturbative functions [17–20]. pffiffiffi This was applied to the The fundamental quantity is the fragmentation function measurement of jet charge at s ¼ 8 TeV [21]. There have also been predictions and comparisons with the jet trans- Dhp ðz; EÞ, which describes the probability of finding a verse momentum (pT ) dependence of the average number hadron h with energy fraction z of the parton p that has of charged particles inside jets (see Ref. [7] and references energy E. At a hadron collider, the jet transverse momen- therein). This quantity does not have a perturbative tum, pT ,1 is a better proxy for the starting scale (μ) of jet expansion in the usual sense (as a series in αS ); instead evolution. To avoid confusion with previous measurements pffiffiffiffiffi of similar observables, the transverse momentum fraction is there is a series expansion in αS [22,23]. This behavior is predicted for a wide class of Sudakov safe observables [24]. denoted in this paper by the symbol ζ ¼ pparticle T =pjet T . The At least for the case of charged-particle multiplicity, this fragmentation function itself, like parton distribution func- nonstandard expansion seems to be an excellent model of tions (PDFs), cannot be calculated from first principles in the data [7]. perturbation theory. However, it has a Dokshitzer-Gribov- The goal of this paper is to measure properties of jet Lipatov-Altarelli-Parisi (DGLAP) evolution [70–72] and so fragmentation using charged-particle tracks. Such proper- the pT dependence of many observables can be calculated. ties have been measured at many colliders at various center- In particular, of-mass energies, including the SPS [25–27], PETRA X Z   ∂ h 1 dζ 0 αS ðμÞPp0 ←p ðζ 0 ; μÞ ζ [28,29], PEP [30–33], TRISTAN [34], CESR [35], LEP μ Dp ðζ; μÞ ¼ Dhp0 ; μ ; [36–47], HERA [48,49], and the Tevatron [50–53]. ∂μ p0 ζ ζ0 π ζ0 Previous measurements by p theffiffiffi ATLAS and CMS collab- pffiffiffi orations were performed at s ¼ 2.76 TeV [54,55], s¼ ð1Þ pffiffiffi pffiffiffi 5.02 TeV [56–58], s ¼ 7 TeV [2,59,60] and s ¼ 8 TeV where Pp0 ←p ðζ; μÞ are the Altarelli-Parisi splitting func- [7,21,61] in pp collisions and are also compared with jet fragmentation measured in Pb þ Pb collisions [54,56–58, tions [70] and depend on the scale μ through αS . Charged 62,63] and p þ Pb collisions [56]. The measurement particles are studied because they provide a way to presented here represents a significant extension of pre- measure single hadrons inside the jet (as opposed to vious work. In particular, the calorimeter energy deposits, which can P result from pffiffiffi accessible jet energy range is multiple particles) which gives access to h Dhp . A basic increased due to the larger s ¼ 13 TeV. There are enough events in the 2016 dataset to probe the substructure of jets quantity related to the fragmentation function is the with pT up to 2.5 TeV. Next, the precision of the charged-particle multiplicity. The average charged- measurement has improved due to advances in track particle multiplicity is an integral over ζ and a sum over reconstruction inside jets during the long shutdown h and p of Dhp ðζÞ. An extension of the multiplicity is the between LHC runs 1 and 2, including the additional set of ζ moments of D. The zeroth moment is the average insertable B-layer (IBL) detector [64,65] and new algo- multiplicity. The full distribution of multiplicity depends rithms for tracking inside dense environments [66–68]. on (multihadron) fragmentation functions in a compli- Furthermore, detailed experimental studies to derive uncer- cated way; a more direct probe of D is to measure hadron tainties in all aspects of tracking inside jets extend the production as a function of ζ, which is a sum of D over p capabilities of previous measurements to a wider region of and h (but no integral over ζ). Additional observables phase space and also allow differential analyses [67,69]. are also studied in order to probe the angular spread of These new data therefore probe broader and deeper aspects jet fragmentation beyond the collinear limit. All of the of the radiation pattern inside jets across an extended observables are described below. phase space. The paper is organized as follows. Section II introduces 1 ATLAS uses a right-handed coordinate system with its the observables to be measured. Then, following a brief origin at the nominal interaction point (IP) in the center of the description of the ATLAS detector in Sec. III, the data and detector and the z-axis along the beam pipe. The x-axis points simulation samples are documented in Sec. IV. Charged- from the IP to the center of the LHC ring, and the y-axis points upwards. Cylindrical coordinates ðr; ϕÞ are used in the transverse particle track, jet, and event reconstruction are detailed in plane, ϕ being the azimuthal angle around the z-axis. The Sec. V. Corrections for detector effects (unfolding) are pseudorapidity is defined in terms of the polar angle θ as documented in Sec. VI. A description of the corresponding η ¼ − ln ptanðθ=2Þ. Angular ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi distance is measured in units of systematic uncertainties can be found in Sec. VII and the ΔR ≡ ðΔηÞ2 þ ðΔϕÞ2 . 052011-2 PROPERTIES OF JET FRAGMENTATION USING CHARGED … PHYS. REV. D 100, 052011 (2019) A. Charged-particle multiplicity (nch ) Each of these derived quantities is extracted from the The number of charged particles inside a jet with pT measured FðζÞ distribution. More details about the pro- above some threshold. In terms of the fragmentation cedure for unfolding these derived quantities are presented function, in Sec. VI. X X Z 1 C. Transverse momentum hnch iðpjet T Þ ¼ jet f p ðpT Þ dζDhp ðζ; pjet T Þ; p h charged threshold=pjet T ≡ prel T pcharged T particle sin Δϕ, where Δϕ is the angle between the momentum of the constituent charged particle where f p is the fraction of parton type p at a given jet pT . and the jet axis in the transverse plane. The quantity that is jet measured is fðprel T ; pT Þ ¼ ð1=N Rjet Þdnch =dpT R rel The multiplicity is not calculable in perturbation theory, but . The aver- pffiffiffiffiffi to lowest order in αS , the ratio of the multiplicity for age value is defined by hpT i ¼ pT fðpT Þ= fðprel rel rel rel T Þ. quark-initiated jets to that for gluon-initiated jets is the ratio of color factors CA =CF ¼ 9=4. The fraction of quark jets D. Radial profile increases with pT , which decreases the inclusive multi- The number of charged particles in various annuli around plicity. However, this is compensated by an inherent increase in the multiplicity with pT for both quark and the jet axis. The quantity that is measured is ρch ðr; pjet T Þ¼ gluon jets [73]. In addition to the mean, the full ð1=N jet Þdnch =2πrdr, where r ¼ ΔRðcharged R particle; R jetÞ. ð1=N jet ÞdN jet =dnch distribution is measured. The average value is defined by hri ¼ rρch ðrÞ= ρch ðrÞ. The last two quantities are not simple derivatives of the fragmentation function as they additionally depend on B. Summed fragmentation function finite opening angles encoded in the dθ=θ emission phase The distribution of the momentum fraction ζ is studied space. Since quantities are measured as a function of jet pT inside jets summed over charged-hadron types. The quan- which is defined using charged and neutral particles, the tity that is measured is Fðζ; pjet T Þ ¼ ð1=N jet Þdnch =dζ. In observables are sensitive to the charged-to-neutral fraction terms of the fragmentation function, inside jets. However, this fraction is robust to mismodeling as isospin is an approximate symmetry of the strong force. X X Fðζ; pjet T Þ¼ f p ðpjet T Þ Dhp ðζ; pjet T Þ: p h charged III. ATLAS DETECTOR R The ATLAS detector [75] at the LHC covers nearly the By definition, dζFðζÞ ¼ hnch i. In addition to measur- entire solid angle around the collision point. It consists of ing the distribution FðζÞ in bins of jet pT , summary an inner tracking detector surrounded by a thin super- statistics of the FðζÞ distribution are extracted to show conducting solenoid, electromagnetic and hadronic calo- how the distribution evolves with jet pT . The following rimeters, and a muon spectrometer incorporating three large properties of the ζ distribution areRextracted: R superconducting toroidal magnets. The inner-detector sys- (i) Partial fractions of FðζÞ: 0X FðζÞdζ= FðζÞdζ ¼ tem (ID) is immersed in a 2 T axial magnetic field and nch ðζ < XÞ=nch to show how much of the jet energy provides charged-particle tracking in the range jηj < 2.5. is carried by particles of a given pT fraction. For The high-granularity silicon pixel detector covers the illustration, the values considered are X ∈ f0.1; 0.01; vertex region and typically provides four measurements 0.001g. As X → 1, these partial fractions become a per track, the first hit being normally in the IBL. It constant value of 1.0, independent R of the R jet pT . is followed by the silicon microstrip tracker which (ii) Moments of FðζÞ: hζ κ i ¼ ζ κ FðζÞdζ= FðζÞdζ. The usually provides eight measurements per track. These distribution of FðζÞ is nearly normally distributed silicon detectors are complemented by the transition in logðζÞ, which means that it is defined by its first radiation tracker, which enables radially extended track two moments [73]. For this reason, κ ¼ 2 is measured reconstruction up to jηj ¼ 2.0. as a function of the jet pT . For illustration, the case The calorimeter system covers the pseudorapidity κ ¼ 1=2 is also considered. P R range jηj < 4.9. Within the region jηj < 3.2, electromag- (iii) Weighted sums over the jet: h i∈jet ζ κi i ¼ ζ κ FðζÞdζ. netic calorimetry is provided by barrel and end cap high- The values P considered are κ ∈ f1=2; 2g. The observ- granularity lead/liquid-argon (LAr) calorimeters, with an able i∈jet ζ 2i is often called pD T and can be used for additional thin LAr presampler covering jηj < 1.8, to quark/gluon jet tagging [74]. For a given jet type, these correct for energy loss in material upstream of the calo- observables increase monotonically with increasing rimeters. Hadronic calorimetry is provided by the steel/ jet pT for κ ≲ 1 and decrease monotonically for κ ≳ 1 scintillating-tile calorimeter, segmented into three barrel (see Sec. VIII B); the κ values chosen are represen- structures within jηj < 1.7, and two copper/LAr hadronic tative of these trends. end cap calorimeters. The solid angle coverage is 052011-3 G. AAD et al. PHYS. REV. D 100, 052011 (2019) completed with forward copper/LAr and tungsten/LAr used in the measurement. The former are chosen to be as calorimeter modules optimized for electromagnetic and close as possible to the latter in order to minimize the model hadronic measurements respectively. dependence caused by an extrapolation from the measured Interesting events are selected to be recorded by the first- phase space at detector level to the phase space at particle level trigger system implemented in custom hardware, level. Section VA describes the definition of charged- followed by selections made by algorithms implemented particle tracks and jets. Following the discussion of objects, in software in the high-level trigger [76]. The first-level Sec. V B describes the particle-level and detector-level event trigger reduces the 40 MHz bunch crossing rate to below selection criteria. 100 kHz, which the high-level trigger further reduces in order to record events to disk at about 1 kHz. A. Object reconstruction While it is not possible to separate the underlying event IV. DATASETS AND SIMULATED SAMPLES from the hard scatter at particle level, it is possible to These measurements use the dataset of pp collisions remove the contribution from pileup. Therefore, the recorded by the ATLAS detector in 2016, corresponding unfolding target is particle-level distributions produced −1 in single proton-proton interactions. However, at detector pffiffiffi luminosity of 33 fb at a center-of-mass to an integrated level, there is ambiguity about which pp collision vertex energy of s ¼ 13 TeV. Events are only considered if they are collected during stable beam conditions and satisfy all corresponds to the hard-scatter event. Collision vertices are data quality requirements. Due to the high instantaneous reconstructed from tracks in the inner detector. Each vertex luminosity and the large total inelastic proton-proton cross is required to be associated with at least two tracks with section, on average there are about 25 simultaneous pT > 0.4 GeV. The primary hard-scattering vertex P of the (pileup) collisions in each bunch crossing. event is chosen to be the one with the highest pT 2 The measurements presented in this paper use a variety calculated using all tracks associated with the vertex. of MC samples for estimating correction factors as well as Particle-level jets are built from MC-simulated stable for comparison with the corrected data. Dijet events were particles (cτ > 10 mm) excluding muons and neutrinos. generated at leading order (LO) with PYTHIA 8.186 [77], By definition, particles from pileup and from interactions with the 2 → 2 matrix element convolved with the with the detectors are not included. These jets are clustered NNPDF2.3LO PDF set [78] and using the A14 tune of using the anti-kt [90] algorithm with radius parameter multiple-parton-interaction and shower parameters [6]. R ¼ 0.4 as implemented in FASTJET [91]. Detector-level PYTHIA uses a pT -ordered parton shower model. jets are built from topological calorimeter-cell energy Additional dijet events were simulated using different clusters [92] using the same algorithm as is used at particle generators, in order to study the impact of modeling level. A series of simulation- and data-based correction and uncertainties. SHERPA 2.1 [79] events were generated using calibration factors are applied to ensure that the resulting jet multileg 2 → 2 and 2 → 3 matrix elements, which were pT is the same as the particle-level value on average [93]. matched to parton showers following the Catani-Krauss- Jets are required to have pT > 60 GeV so that the rate of Kuhn-Webber prescription [80]. These SHERPA events were jets originating from pileup is negligible. The detector-level simulated using the CT10 PDF set [81] and the default phase space includes one bin at low jet pT (60–100 GeV) SHERPA event tune. HERWIG++ 2.7 [82,83] was used to which is not in the fiducial phase space of the measurement provide a sample of events with an angle-ordered parton due to the large impact of migrations into and out of the shower model. These events were generated with the 2 → 2 acceptance. matrix element, convolved with the CTEQ6L1 PDF set [84] Charged particles are used to compute the particle-level and configured with the UE-EE-5 tune [85]. definitions of all observables if they are clustered within a All simulated events were passed through a full simu- particle-level jet and have pT > 500 MeV and jηj < 2.5. lation of the ATLAS detector [86] implemented in GEANT 4 The detector-level analog to charged particles is tracks. Tracks are reconstructed from hits in the inner detector (see [87], which describes the interactions of particles with the e.g., Ref. [67]) and a series of quality criteria are applied detector and the subsequent digitization of analog signals. to the selected tracks to reject those originating from hits The effects of multiple simultaneous pp collisions were due to multiple charged particles (fake tracks) and from simulated with inelastic pp collisions using the PYTHIA pileup. The transverse momentum resolution is appro- 8.186 generator with the A2 [88] set of tuned parameters ximately σðpT Þ=pT ≈ 0.05% × pT =GeV ⊕ 1%, with a sig- and the MSTW2008LO [89] PDF set; these events were nificant degradation in the core of high-pT jets due to overlaid on the nominal dijet events. challenges associated with pattern recognition.2 Tracks are required to pass the tight primary selection as well as the V. OBJECT AND EVENT SELECTION Since the data are unfolded to particle level, it is necessary 2 For example, the pT resolution is approximately 30% at to define both the particle-level and detector-level objects 100 GeV when five or more particles are within ΔR < 0.015. 052011-4 PROPERTIES OF JET FRAGMENTATION USING CHARGED … PHYS. REV. D 100, 052011 (2019) 0.4 1013 ATLAS ATLAS -1 s = 13 TeV, 33 fb s = 13 TeV, 33 fb-1, p > 60 GeV T dN / dp [1/100 GeV] (1/N ) dN / d [1/0.42] Detector-level Detector-level 1010 Data 0.3 Data Pythia 8.186 A14 More Forward Pythia 8.186 A14 Herwig++ 2.7 Herwig++ 2.7 107 Sherpa 2.1 0.2 More Central Sherpa 2.1 T jet 104 0.1 10 500 1000 1500 2000 2500 2 1 0 1 2 MC / Data MC / Data Jet p [GeV] Jet 1.2 T 1.2 1 1 0.8 0.8 500 1000 1500 2000 2500 2 1 0 1 2 Jet p [GeV] Jet T FIG. 1. Left: The transverse momentum, pT , spectrum for the selected jets; the simulation is normalized to the data. The normalization is dominated by the first bin, which accounts for the overall offset in the other bins for some of the predictions. Right: The pseudorapidity, η, distribution for the selected jets, split into the more forward and the more central of the two jets. Error bars only include the statistical uncertainty. loose track-to-vertex association [94]. In particular, they jets must satisfy plead T =pT sublead < 1.5. Figure 1 shows the must have pT > 500 MeV and jηj < 2.5, and the number basic kinematic properties of the two leading jets passing of pixel and strip clusters associated with the track is this event selection compared with various MC predic- required to be at least 9 (11) for jηj < 1.65 (≥1.65). In tions at detector level. addition, the transverse impact parameter d0 relative to the The substructure of the two leading jets is used in the beam line must be less than 2 mm and the longitudinal analysis. Figure 2 shows detector-level distributions for a impact parameter, z0 , is required to satisfy jz0 sin θj < selection of the observables that were introduced in Sec. II. 3 mm. Tracks are matched to jets via ghost association For the jets with pT ∼ 1 TeV shown in Fig. 2, the most [95]. This matching procedure creates ghost versions of the probable number of tracks is about 15 and the most tracks with the same direction but infinitesimal pT . Jet probable momentum fraction is about 1%. The radiation clustering is repeated and tracks are assigned to the jet that pattern is peaked at the center of the jet, so both the prel T and contains their ghosted version. For the isolated, high pT jets r distributions are peaked at zero. The PYTHIA, HERWIG++, used in this measurement, ghost association is nearly and SHERPA distributions generally bracket the data and are identical to a geometric matching based on ΔR < 0.4. accurate to within about 20%. In order to expose differences between quark and gluon B. Event selection jets, the more forward and more central of the two jets are Particle-level events are required to have at least two jets distinguished and measured separately. Figure 3 shows with jηj < 2.1 (within the tracking detector acceptance) and the gluon-jet fraction as a function of jet pT and jet η the leading two such jets must satisfy pleadT =pT sublead < 1.5. (more details about quark/gluon definitions are given in This jet-pT balance requirement simplifies the interpreta- Sec. VIII B). For a fixed jet pT , higher-jηj jets are more tion of the final state in terms of a 2 → 2 scattering process. often quark initiated due to valence quarks scattering off Detector-level events are selected using single-jet gluons. For a fixed η, the quark fraction increases with jet triggers. Due to the large cross section for jet production, pT due to the relative increase in valence-quark scattering most of the jet triggers are prescaled: events that pass the off a quark or gluon compared with gluon-gluon scattering. trigger are randomly discarded with a fixed probability. Table I summarizes the object and event selections from The trigger used for a particular jet pT is chosen to ensure Secs. VA and V B. that the trigger is 100% efficient (for the measurement phase space and prior to prescaling) and has the lowest VI. UNFOLDING prescale factor. Events in data are weighted by the prescale. The lowest-threshold unprescaled jet trigger The data are corrected for resolution and acceptance is used for jets with pT > 600 GeV. Detector-level events effects, and the fiducial phase space of the measurement are required to pass the same selection requirements as is described by the particle-level object and event selection particle-level events: there must be at least two off-line in Sec. V. Equation (2) symbolically summarizes the calibrated jets with jηj < 2.1 and the leading two of these unfolding procedure for a binned distribution x: 052011-5 G. AAD et al. PHYS. REV. D 100, 052011 (2019) 0.4 ATLAS ATLAS s = 13 TeV, 33 fb-1 3 s = 13 TeV, 33 fb-1 Detector-level Data Detector-level Data track 0.3 /d 1000 < Jet p / GeV < 1200 Pythia 8.186 A14 1000 < Jet p / GeV < 1200 Pythia 8.186 A14 (1/N ) dN / dn T T Herwig++ 2.7 Herwig++ 2.7 track Sherpa 2.1 2 Sherpa 2.1 (1/N ) dN 0.2 jet jet 1 0.1 0 0 1.5 1.5 MC/Data MC/Data 1 1 0.5 0.5 0 20 40 10 3 10 2 10 1 1 ntrack 102 ATLAS ATLAS 103 / d(prel/GeV) s = 13 TeV, 33 fb-1 s = 13 TeV, 33 fb-1 / 2 rdr Detector-level Data Detector-level Data 10 Pythia 8.186 A14 102 Pythia 8.186 A14 T 1000 < Jet p / GeV < 1200 1000 < Jet p / GeV < 1200 T T Herwig++ 2.7 Herwig++ 2.7 track Sherpa 2.1 10 Sherpa 2.1 1 track (1/N ) dN (1/N ) dN jet 1 1 10 jet 1 10 2 10 10 2 MC/Data 1.2 1.2 MC/Data 1 1 0.8 0.8 0 1 2 3 0 0.1 0.2 0.3 0.4 prel [GeV] r T FIG. 2. The detector-level distributions of (top left) the number of charged-particle tracks ntrack , (top right) the transverse momentum fraction ζ, (bottom left) the transverse momentum prel T , and (bottom right) the radial profile in bins of the distance r from the jet axis for jets with transverse momentum 1 TeV < pjet T < 1.2 TeV. Error bars include the statistical uncertainty only. 1 1 2 ATLAS Simulation ATLAS Simulation s = 13 TeV s = 13 TeV NNPDF2.3LO + Pythia 8.186 A14 0.8 0.8 NNPDF2.3LO + Pythia 8.186 A14 1 More Central Gluon fraction Gluon fraction 0.6 0.6 More Forward 0 Jet 0.4 0.4 1 0.2 0.2 2 0 0 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Jet p [GeV] Jet p [GeV] T T FIG. 3. Left: The gluon-jet fraction as a function of jet transverse momentum pT and jet pseudorapidity η. Right: the fraction of the more forward and the more central jets that are gluon initiated. The error bars in the right plot represent the uncertainty computed from the 100 NNPDF2.3LO replicas [78]. See Sec. VIII B for more details about quark/gluon definitions and uncertainties. 052011-6 PROPERTIES OF JET FRAGMENTATION USING CHARGED … PHYS. REV. D 100, 052011 (2019) TABLE I. A summary of the object and event selection criteria at particle level and detector level. Particle level Detector level Pileup Not applicable Identify primary vertex Jet algorithm Anti-kt , R ¼ 0.4 Jet requirements jηj < 2.1 Jet constituents Particles with cτ > 10 mm prior to detector Calorimeter energy clusters interactions excluding μ and ν Measurement inputs Charged jet constituents, Ghost-associated tracks, pT > 500 MeV and jηj < 2.5 pT > 500 MeV and jηj < 2.5 Event selection At least two jets, with the leading two satisfying plead sublead < 1.5 T =pT Jet selection Leading two, separated by η (more forward/central)   1 X N total 1 − ϵreco not true;j hxκ iunfolded ðpT bin jÞ xunfolded;i ¼ θij xdetected;j ; Pnbins njets;unfolded 1 − ϵtrue not reco;i x × ðbin center iÞκ j¼1 Pnbins ¼ cbinning;j ðκÞ i¼1 unfolded;i ; ð3Þ ð2Þ i¼1 xunfolded;i where the sum is over all i that correspond to pT bin j. Since where njets;unfolded is the unfolded number of forward or the bin center is used to calculate the average, a correction central jets (depending on the bin), determined by the cbinning is applied to account for the difference between the number of entries in the nch unfolding (as there is one entry bin center and the mean of the distribution within the bin. per jet). The symbols θ and ϵ represent the unfolding matrix This correction is calculated using PYTHIA, and is computed and correction factors, described in more detail below. by reweighting PYTHIA so that it agrees with the unfolded The jet substructure observables are simultaneously distribution. For ζ, prelT , and r, Eq. (3) represents the κ moment unfolded with the jet pT and for the more forward and for individual particles. P For ζ, the jet-based moments are the more central jets at the same time. For an observable also computed: h i∈jet ζ κi i. For these jet-based moments, with nbins bins in a given pT bin, this results in a total of Eq. N total ¼ 2 × ðnbins Þ × ðpT binsÞ bins. All of these bins are Pnbins(3) is modified by removing the denominator i¼1 xunfolded;i . By construction, the κ ¼ 0 jet-based moment concatenated to form a one-dimensional input. To begin the of ζ is the κ ¼ 1 moment of nch . The binning correction factor unfolding, the data are corrected for the fraction of events is mostly near unity, deviating by less than 1% for nch and up that pass the detector-level selection but not the particle- to about 10% for the other observables. level selection, ϵreco not true . This also corrects for nondijet Figure 4 shows the response matrix normalized per events, but their rate is negligible. Then, an iterative particle-level bin. As stated above, the observable bins Bayesian (IB) unfolding technique [96] is used as a are concatenated with the jet pT and for both the more regularized matrix inversion to correct for the detector forward and more central jets to form a one-dimensional resolution in events that pass both the detector-level and distribution that is unfolded. A diagonal stripe represents particle-level selections. The IB method is implemented events where the detector-level jet pT is the same as the in the ROOUNFOLD framework [97] with the unfolding particle-level value; off-diagonal components represent matrix θ and one iteration, is chosen to minimize the total jet pT migrations. Within a jet pT bin, there is a small uncertainty. After the application of the response matrix, a dependence on ζ, with a worse resolution at high ζ due to final correction is applied to account for the fraction of the deteriorating momentum resolution at high track pT . events that pass the particle-level but not detector-level The diagonal strips in the upper left and lower right selection, ϵtrue not reco . The resulting unfolded measurement quadrants correspond to events where the more forward is reorganized into individual distributions with nbins per pT particle-level jet is the more central detector-level jet and bin for each of the more forward and more central jets. vice versa. This migration happens in about 1% of events. The jet pT is also unfolded in parallel and each pT bin of Within a given jet pT bin, the migrations to neighboring ζ the jet substructure observable is normalized by the number bins are small. Except at high ζ and high jet pT where the of measured jets in that bin. For nch, this renders the migrations can reach 50%, the off-diagonal components of distributions normalized to unity per jet pT bin; for the the response matrix are about 10%. other observables, the normalization in each pT bin is (up to acceptance effects) hnch i, as discussed in Sec. II. VII. UNCERTAINTIES To illustrate the jet-pT dependence of the measured observables, the evolution with the jet pT of various Systematic and statistical uncertainties are assessed for moments (κ) is computed using Eq. (3): each step of the analysis, including the acceptance 052011-7 G. AAD et al. PHYS. REV. D 100, 052011 (2019) 600 ATLAS Simulation with the tracking uncertainties matching in size in the highest jet-pT bins. The tracking and jet energy uncertain- More Forward Jet s = 13 TeV 500 measurement 10 1 ties are about the same size for hprel T i. Fragmentation Pr(Detector-level | Particle-level) modeling uncertainties are large for hnch i at low jet pT Detector-level Bin Number and for hζi at high jet pT . While the size of the binning 400 correction uncertainty is less than 2% for hprel T i and hri, it is still the dominant uncertainty for these observables. Further 300 0.1 < p T,jet /TeV < 2.5 0.1 < p T,jet /TeV < 2.5 details about each uncertainty source are given below and 10 2 the full covariance matrices, including all correlation information, are made available in Ref. [99]. T,jet T,jet More Central Jet 200 increasing p increasing p 100 A. Track and jet reconstruction Except for ζ, the jet energy is only used to determine increasing p increasing p T,jet T,jet 10 3 the pT bin. Since the fragmentation properties vary slowly 200 400 600 with jet pT , the resulting impact of jet energy scale and More Central Jet More Forward Jet resolution uncertainties on the analysis is often less Particle-level Bin Number important than other sources of uncertainty. Nonetheless, the impact of a 19-parameter decomposition of the jet FIG. 4. The probability distribution for the detector-level combined transverse momentum fraction ζ and jet transverse energy scale uncertainty was evaluated [93]. Six of these 19 momentum pT distribution normalized in bins of the particle- components are due to in situ constraints on the jet energy level variable using the PYTHIA simulation. The ζ distribution is scale from various multiobject balance studies, such as concatenated with the jet pT so that every 21 bins is a different Z þ jets. Additional sources of uncertainty are related to jet-pT bin. The first 315 bins represent the more central of the two pileup, jet flavor, and extrapolations to high pT . The total jets and the second 315 bins correspond to the more forward jet. uncertainty in the jet energy scale is about 1% for jets with The z-axis is truncated at 10−3 for visualization only, to aid pT between 100 and 1000 GeV and the impact on this readability. measurement is much less than 1% except at high ζ, where it can reach as high as 2%. The impact of the jet energy correction factors, response matrix, and unfolding method. resolution is determined from an ensemble of event For each uncertainty, some component of the analysis samples with jet energies smeared within the uncertainty. chain is varied and then the entire unfolding procedure is The most important experimental uncertainties are repeated. Data and simulation statistical uncertainties are related to track reconstruction and cover the track determined from pseudo-experiments using the bootstrap reconstruction efficiency, the rate of fake and secondary method [98]. The details of the experimental systematic tracks, the momentum scale, and density effects from pixel uncertainties related to track and jet reconstruction are and strip cluster merging. In the PYTHIA simulation, given in Sec. VII A and the uncertainties in the unfolding approximately 60% of the charged particles/tracks inside method and fragmentation modeling are described in jets are charged pions that are well matched,3 10% are well- Sec. VII B. An additional source of uncertainty arising matched kaons, 5% are well-matched protons, 15% are from binning effects is evaluated when computing the charged particles that are not matched to reconstructed average value of an observable as a function of jet pT . The tracks (inefficiency), 5% are secondaries (split equally average values are determined using the bin centers, so between photon conversions and nuclear interactions), the correction described in Sec. VI relies on the simulation 1% are not well-matched tracks (fake tracks), and about for the distribution within a given bin. An uncertainty in Oð0.1%Þ are pileup tracks wrongly matched to the primary the binning correction is estimated by comparing the hard-scattering vertex. The pileup contribution decreases correction factors derived from PYTHIA with those from with jet pT and momentum fraction, but increases with jet SHERPA, where both simulations are reweighted to match cone size (reaching 1% at Δ ¼ 0.4). In contrast, the fake- the unfolded data distribution. track rate increases slightly with jet pT and has a con- Figure 5 provides an overview of the systematic uncer- tribution at high-momentum fraction of a few percent from tainties for a selection of observables, using the average 3 value vs pT for illustration. The uncertainty in the rate of Reconstructed tracks are matched to charged particles by fake and secondary tracks is the leading experimental examining the pattern of sensors where energy was deposited. If reconstruction uncertainty for hnch i and hri except at over 50% of the weighted number of measurements on a track are due to one charged particle, it is declared matched to the track. low jet pT where the uncertainties from the inclusive The weights are chosen to reflect the amount of information tracking efficiency and the unfolding procedure are larger. present in each detector and are ten for the pixel detector, five for The jet energy uncertainties are the most important for ζ, the strip detector, and one for the straw tube tracker. 052011-8 PROPERTIES OF JET FRAGMENTATION USING CHARGED … PHYS. REV. D 100, 052011 (2019) 5 ATLAS ATLAS -1 -1 s = 13 TeV, 33 fb s = 13 TeV, 33 fb All selected jets 2 More forward jet nch uncertainty [%] uncertainty [%] 0 0 Total Frag. Unfolding Jet p 2 Total Frag. Unfolding Jet p T T 5 Tracking Binning Data Stats. Tracking Binning Data Stats. 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Jet p [GeV] Jet p [GeV] T T 5 ATLAS ATLAS -1 -1 s = 13 TeV, 33 fb s = 13 TeV, 33 fb All selected jets 2 All selected jets p / GeV uncertainty [%] r uncertainty [%] 0 0 rel T Total Frag. Unfolding Jet p 2 Total Frag. Unfolding Jet p T T 5 Tracking Binning Data Stats. Tracking Binning Data Stats. 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Jet p [GeV] Jet p [GeV] T T FIG. 5. An overview of the statistical and systematic uncertainties for the average value of (top left) charged-particle multiplicity nch, (top right) transverse momentum fraction ζ, (bottom left) transverse momentum prel T , and (bottom right) radial profile as a function of jet transverse momentum pT . The MC statistical uncertainties are negligible and are not shown. When the uncertainties go through zero (as for the unfolding uncertainty in the top left), the signed uncertainty has changed from positive to negative or vice versa. Most of the lines are the sum in quadrature of individual sources of uncertainty in each category, such as the various sources of tracking uncertainties as described in Sec. VII A. kinked tracks reconstructed with a very high pT . The applied in the simulation by randomly removing tracks reconstruction inefficiency grows with jet pT , and is peaked with a pT - and jηj-dependent probability. This uncertainty at both low and high radial distance from the center of the dominates the nch measurement for jet pT ≲ 1 TeV. jet and is reduced at high momentum fraction. This is Since the ATLAS pixel detector measures the charge because tracks with a larger radial distance from the jet axis collected from ionization, it is possible to constrain the tend to have lower pT (larger material effects and thus inefficiency from density effects by looking for single lower efficiency), while tracks in the core of the jet suffer tracks with pixel charge consistent with two minimum- from an inefficiency in the pattern recognition in the dense ionizing particles [67]. The resulting uncertainty is about environment. 0.4% for tracks with ΔR < 0.1 and is validated with The uncertainty in the inclusive track reconstruction additional studies related to the charged-to-neutral ratio efficiency is dominated by the uncertainty in the amount of in the jet as well as the geometric orientation of pixel material in the inner detector. Variations in the amount clusters [68]. This uncertainty is most important for the of material that are consistent with detector construction radial energy measurement at small radii from the jet axis knowledge and measurements from secondary vertices and for the nch measurement in the highest jet-pT bins. [100] result in an uncertainty of 0.5% for jηj < 0.1, which The rate of fake tracks is studied inside jets by inverting grows to 2.7% for 2.3 < jηj < 2.5. This uncertainty is some of the track quality criteria such as the fit χ 2 =NDF and 052011-9 G. AAD et al. PHYS. REV. D 100, 052011 (2019) 30 0.1 ATLAS ATLAS s = 13 TeV, 33 fb-1 s = 13 TeV, 33 fb-1 25 0.08 More central Data More forward Data 20 0.06 More central Pythia 8.186 A14 More forward Pythia 8.186 A14 nch 15 0.04 More central Data More forward Data 10 0.02 More central Pythia 8.186 A14 More forward Pythia 8.186 A14 5 0 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Jet p [GeV] Jet p [GeV] T T 0.8 0.1 ATLAS ATLAS s = 13 TeV, 33 fb-1 s = 13 TeV, 33 fb-1 0.08 0.6 More central Data More forward Data [GeV] 0.06 More central Pythia 8.186 A14 r More forward Pythia 8.186 A14 0.4 rel pT 0.04 More central Data 0.2 More forward Data 0.02 More central Pythia 8.186 A14 More forward Pythia 8.186 A14 0 0 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Jet p [GeV] Jet p [GeV] T T FIG. 6. The unfolded measured averages for the (top left) charged-particle multiplicity nch, (top right) transverse momentum fraction ζ, (bottom left) transverse momentum prel T , and (bottom right) radial profile as a function of the jet transverse momentum pT for the more forward and more central of the two jets, separately. The uncertainty bands show the combined statistical and systematic uncertainty. is found to agree between data and simulation at the 30% The impact on the measurement is smaller than the other level [68]. A related source of uncertainty is due to the tracking uncertainties. rate of secondary tracks. These tracks originate from real charged particles, but are the result of interactions in B. Unfolding method and fragmentation modeling detector material and not direct fragmentation processes. An uncertainty resulting from the unfolding method The rate of secondaries is estimated by fitting the track d0 described in Sec. VI is determined by unfolding the distribution and is found to agree with simulation within prediction from a reweighted simulation with the nominal about 30%. These rates are then varied to determine an procedure. The reweighted simulation is constructed by uncertainty in the measurement. The fake-track rate is the leading source of uncertainty for nch when pT ≳ 1 TeV and modifying the nominal PYTHIA 8 particle-level spectrum when ζ ∼ 1 or r ≲ 0.05 for all jet-pT bins. Uncertainties so that the simulated detector-level spectrum, from pro- related to the modeling of pileup have a negligible impact. pagating the reweighted particle-level spectrum through The leading source of uncertainty in the track param- the response matrix, has significantly improved agreement eters is in the q=pT (q is the electric charge) from a with the data. The modified detector-level distribution potential sagitta distortion due to detector misalignment is unfolded with the nominal response matrix and the weak modes [94]. This bias is corrected and the uncer- difference between this and the reweighted particle- tainty in the correction is about 0.1=TeV except at ϕ ≈ 0 level spectrum is an indication of the bias due to the and jηj ∼ 2.5 where the correction can reach 1=TeV. unfolding method (in particular, the choice of prior) [101]. 052011-10 PROPERTIES OF JET FRAGMENTATION USING CHARGED … PHYS. REV. D 100, 052011 (2019) 0.1 40 ATLAS ATLAS -1 Data (stat. uncert.) -1 Data (stat. uncert.) s = 13 TeV, 33 fb s = 13 TeV, 33 fb Stat. syst. uncert. Stat. syst. uncert. All selected jets Pythia 8.186 A14 0.08 All selected jets Pythia 8.186 A14 Herwig++ 2.7 Herwig++ 2.7 30 Sherpa 2.1 Sherpa 2.1 0.06 nch 20 0.04 10 0.02 1.2 1.2 MC / Data MC / Data 1 1 0.8 0.8 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Jet p [GeV] Jet p [GeV] T T 1 0.1 ATLAS ATLAS -1 Data (stat. uncert.) -1 Data (stat. uncert.) s = 13 TeV, 33 fb s = 13 TeV, 33 fb Stat. syst. uncert. Stat. syst. uncert. 0.8 All selected jets Pythia 8.186 A14 0.08 All selected jets Pythia 8.186 A14 Herwig++ 2.7 Herwig++ 2.7 Sherpa 2.1 Sherpa 2.1 / GeV 0.6 0.06 r rel T p 0.4 0.04 0.2 0.02 1.2 1.2 MC / Data MC / Data 1 1 0.8 0.8 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Jet p [GeV] Jet p [GeV] T T FIG. 7. The unfolded measured averages (top left) charged-particle multiplicity nch, (top right) transverse momentum fraction ζ, (bottom left) transverse momentum prel T , and (bottom right) radial profile as a function of the jet transverse momentum pT . The lower panel shows the ratio of various MC predictions to the data, with the total uncertainty band centered on the data at unity. The weights are chosen by comparing the PYTHIA 8 ϵtrue not reco in Eq. (2). All three components are added in particle-level spectrum with the unfolded data. After quadrature to determine the total uncertainty due to applying the reweighting, the χ 2 =NDF calculated using fragmentation modeling. Even though these sources of only the statistical uncertainties improves significantly in uncertainty are correlated, they were treated as indepen- each jet pT bin. The resulting systematic uncertainties are dent because the level of correlation is unknown given generally much smaller than the detector-level differences that there are only two alternative models. The resulting between the data and simulation, as desired. uncertainty is much smaller than the difference between The unfolded result depends on the modeling of jet PYTHIA 8 and HERWIG++ at particle level. For nch, the fragmentation through the prior, the response matrix, response matrix is the dominant contribution to this and the correction factors. Variations in the prior are uncertainty, except in the first jet-pT bin where the already accounted for in the data-driven nonclosure correction factors and their uncertainty are also impor- uncertainty described above. The other contributions tant. For the per-particle observables (ζ, r, prel T ), the are evaluated by comparing the result using PYTHIA 8 correction factors dominate the uncertainty because with the result using the alternative HERWIG++ sample acceptance effects are much more important. described in Sec. IV. A similar uncertainty is obtained when using HERWIG++ or SHERPA as the alternative VIII. RESULTS model. This comparison is decomposed into components corresponding to varying only the response matrix or The unfolded data are presented in two ways. only the initial/final correction factors, ϵreco not true and Section VIII A focuses on the inclusive spectra for both 052011-11 G. AAD et al. PHYS. REV. D 100, 052011 (2019) ATLAS ATLAS -1 Data (stat. uncert.) -1 Data (stat. uncert.) 1.1 s = 13 TeV, 33 fb s = 13 TeV, 33 fb ch Stat. syst. uncert. Stat. syst. uncert. ch All selected jets 1 All selected jets 0.01) / n Pythia 8.186 A14 Pythia 8.186 A14 0.1) / n Herwig++ 2.7 Herwig++ 2.7 Sherpa 2.1 Sherpa 2.1 1 nch( < 1.5-5 nch( < 1.5-11 0.5 0.9 1.02 1.2 MC / Data MC / Data Jet p [GeV] Jet p [GeV] T T 1 1 0.98 0.8 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Jet p [GeV] Jet p [GeV] T T ATLAS ch -1 Data (stat. uncert.) s = 13 TeV, 33 fb 0.001) / n Stat. syst. uncert. All selected jets Pythia 8.186 A14 Herwig++ 2.7 0.2 Sherpa 2.1 nch( < 1.5-17 0.1 1.2 MC / Data Jet p [GeV] T 1 0.8 500 1000 1500 2000 2500 Jet p [GeV] T FIG. 8. The unfolded fraction of charged particles carrying a fraction ζ ≲ 10% (top left), 1% (top right), and 0.1% (bottom) of the jet transverse momentum pT . The exact fractions are given in the figures and correspond to powers of 1.5 so that the values align precisely with bin edges and thus no binning correction is required. The lower panels show the ratio of various MC predictions to the data, with the total uncertainty band centered on the data at unity. jets together, while Sec. VIII B uses the differences forward/backward jets and is described in detail for the all- between forward and central jets to determine the unique jet spectra only. features of quark-initiated and gluon-initiated jets, some of As the jet pT increases, the average charged-particle which can be compared with perturbative QCD calcula- multiplicity increases, the average momentum fraction tions. These sections show a selection of jet pT bins; a decreases, the average prelT increases, and the average complete set of results can be found in Ref. [99]. multiplicity-weighted radius decreases. Charged-particle multiplicity increases from about 10 at jet pT of A. Inclusive distributions 100 GeV to just over 20 at 2.5 TeV. In most cases, PYTHIA 8 and SHERPA bracket the data, and are accurate The unfolded averages of the measured observables to better than 10%; HERWIG++ is often between these two are presented as a function of the jet pT in Fig. 6 for and closer to the data. As the distribution of nch is almost the more forward and more central jets separately and then Poissonian, nearly all of the information about the distri- combined in Fig. 7. All other figures in this section bution is encoded in the mean value. In contrast, the combine measurements of both jets. The more central jets distribution of ζ is more complicated.4 The average show properties that are more gluon-like than the more forward jets: they have a larger charged-particle multiplic- ity and a softer momentum-fraction spectrum. The model- The distribution is nearly Gaussian in log ζ, so it is well 4 ing of the all-jet spectra is very similar to that of the more specified by two parameters instead of one [73]. 052011-12 PROPERTIES OF JET FRAGMENTATION USING CHARGED … PHYS. REV. D 100, 052011 (2019) ATLAS ATLAS -1 Data (stat. uncert.) 0.01 -1 Data (stat. uncert.) 0.25 s = 13 TeV, 33 fb s = 13 TeV, 33 fb Stat. syst. uncert. Stat. syst. uncert. All selected jets Pythia 8.186 A14 All selected jets Pythia 8.186 A14 Herwig++ 2.7 Herwig++ 2.7 Sherpa 2.1 0.008 Sherpa 2.1 0.2 1/2 2 0.006 0.15 0.004 0.1 1.2 1.2 MC / Data MC / Data 1 1 0.8 0.8 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Jet p [GeV] Jet p [GeV] T T 0.3 ATLAS ATLAS 8 -1 Data (stat. uncert.) -1 Data (stat. uncert.) s = 13 TeV, 33 fb s = 13 TeV, 33 fb Stat. syst. uncert. Stat. syst. uncert. All selected jets Pythia 8.186 A14 All selected jets Pythia 8.186 A14 Herwig++ 2.7 0.25 Herwig++ 2.7 Sherpa 2.1 Sherpa 2.1 1/2 2 i i 6 i in jet i in jet 0.2 4 0.15 1.2 1.2 MC / Data MC / Data 1 1 0.8 0.8 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Jet p [GeV] Jet p [GeV] T T FIG. 9. Top: The unfolded (left) 1=2 and (right) second moments of the transverse P momentum fraction, P ζ, distribution as a function of the jet transverse momentum pT . Bottom: The unfolded moment of (left) i∈jet ζ 1=2 and (right) i∈jet ζ 2 as a function of the jet pT . Section II presents the definitions of both classes of observables. The lower panels show the ratio of various MC predictions to the data, with the total uncertainty band centered on the data at unity. The values are computed from the moments of the unfolded distributions in each jet-pT bin, with a small correction added to account for binning effects. momentum fraction is about 5% at jet pT of 100 GeV and particular, the jets become more collimated. This is also decreases to about 2.5% at 2.5 TeV (the most probable consistent with direct measurement of the radial profile, value, shown below, is lower). The distributions of prel T and where the average value drops from about 0.06 at pjet T ¼ the radial profiles fall steeply (nearly exponentially) away jet 100 GeV to about 0.03 at pT ¼ 2.5 TeV. While PYTHIA 8, from zero and the average values in Fig. 7 give a sense of SHERPA, and HERWIG++ agree well with the data for prel T , how fast they fall (exponential distributions are uniquely SHERPA provides a poorer model of the average radial jet specified by their mean). The average prel T at pT ¼ profile as a function of the jet pT . 100 GeV is about 0.35 GeV and increases to about As noted above, the distribution of ζ cannot be described 0.55 GeV at pjet T ¼ 2.5 TeV. If the angular distribution simply by its average value, in contrast to nch , prel T and r, about the jet axis is independent of pT , the average value which are nearly Poisson or exponentially distributed. jet T should be proportional to hζiðpT Þ × pT . This of prel jet Therefore, it is useful to summarize the pjet T dependence would suggest an increase by a factor of ð2.5%=5%Þ × of other aspects of the ζ distribution. Figure 8 shows partial ð2500=100Þ ∼ 12.5 across the measured range; instead it integrals of the ζ distribution and Fig. 9 shows the average P P only increases by a factor of about 1.5. This means that values of ζ 1=2 , ζ 2 , i∈jet ζ 1=2 and 2 i∈jet ζ . Figure 8 the angular distribution is not independent of pT and in illustrates how the average fraction of charged particles 052011-13 G. AAD et al. PHYS. REV. D 100, 052011 (2019) ATLAS 0.8 ATLAS -1 -1 s = 13 TeV, 33 fb s = 13 TeV, 33 fb ch All selected jets, 100 < Jet p / GeV < 200 All selected jets, 400 < Jet p / GeV < 500 ch ) dN/dn T T 0.6 ) dN/dn 1 Data (stat. uncert.) Data (stat. uncert.) Stat. syst. uncert. Stat. syst. uncert. Pythia 8.186 A14 Pythia 8.186 A14 events events Herwig++ 2.7 0.4 Herwig++ 2.7 Sherpa 2.1 Sherpa 2.1 0.5 (1/N (1/N 0.2 0 0 1.5 1.5 / True True / Data MC/ /Data / Data 11 11 Reco Reco MC MC 0.5 0.5 0 10 20 30 40 50 60 0 10 20 30 40 50 60 nch nch nch nch ATLAS 0.6 ATLAS 0.6 -1 -1 s = 13 TeV, 33 fb s = 13 TeV, 33 fb ch All selected jets, 900 < Jet p / GeV < 1000 All selected jets, 2000 < Jet p / GeV < 2500 ch ) dN/dn T T ) dN/dn Data (stat. uncert.) 0.4 Data (stat. uncert.) 0.4 Stat. syst. uncert. Stat. syst. uncert. Pythia 8.186 A14 Pythia 8.186 A14 events events Herwig++ 2.7 Herwig++ 2.7 Sherpa 2.1 Sherpa 2.1 (1/N (1/N 0.2 0.2 0 0 1.5 1.5 True True MC/ /Data MC/ /Data / Data / Data 1 1 Reco Reco MC MC 0.5 0.5 00 10 10 20 20 30 30 40 40 50 50 60 60 00 10 10 20 20 30 30 40 40 50 50 60 60 nch nch nch nch FIG. 10. The distribution of charged-particle multiplicity nch in four bins of jet transverse momentum: (top left) 100 GeV < pjet jet jet T < 200 GeV, (top right) 400 GeV < pT < 500 GeV, (bottom left) 900 GeV < pT < 1000 GeV, and (bottom right) jet 2000 GeV < pT < 2500 GeV. The lower panels show the ratio of various MC predictions to the data, with the total uncertainty band centered on the data at unity. Additional pjet T bins can be found in Ref. [99]. with a given momentum fraction evolves with pjetT . There is example, PYTHIA 8 disagrees with the exact value at low no correction for binning effects, as the measured ζ pjet jet T for ζ < 1% and all pT for ζ < 0.1%. For the ζ < 0.1% distribution has bin edges which nearly align with 0.1%, case, SHERPA and PYTHIA 8 bracket the data, with SHERPA 1%, and 10%. In particular, the ζ bins are 1=1.5n , for predicting more particles with a lower ζ fraction, while n ¼ 0; …; 21, and the fractions in Fig. 8 are estimated HERWIG++ is much closer to the data. The average values of pffiffiffi as 0.1% ≈ 1=1.517 , 1% ≈ 1=1.511 , and 10% ≈ 1=1.55 . ζ and ζ 2 for individual particles as a function of jet pjet T in The fraction of particles carrying 10% or less of the the top panel of Fig. 9 show a decreasing trend that is momentum changes very little across the entire pjet T range qualitatively pffiffiffi similar to the trend for the average ζ in Fig. 7. and is also near unity (>90% for all pjetT ). A strong pjet T For ζ, PYTHIA 8/HERWIG++ and SHERPA bracket the data, dependence is introduced when the ζ threshold is lowered although PYTHIA 8 agrees with the data within the uncer- to 1% and to 0.1%. Since charged particles are required to tainty. SHERPA predicts a significantly higher average ζ 2 have pT > 500 MeV, only jets with pjet thanPis present in the data. As with hnch i, the average value T > 500 GeV can 1=2 have particles with ζ < 0.1%. The fraction of particles of i∈jet ζ increases with the jet pT , while the pT P with ζ < 1% has a logarithmic increase while the fraction dependence of h i∈jet ζ 2 i is more complicated as it first of particles with ζ < 0.1% appears to increase faster than decreases and then slowly increases with jet pT . This trend linearly with pjet T . Both of these general trends are repro- is well reproduced by PYTHIA and HERWIG++, but not by duced by PYTHIA 8, SHERPA, and HERWIG++, although for SHERPA. 052011-14 PROPERTIES OF JET FRAGMENTATION USING CHARGED … PHYS. REV. D 100, 052011 (2019) ATLAS 8 ATLAS -1 -1 6 s = 13 TeV, 33 fb s = 13 TeV, 33 fb All selected jets, 100 < Jet p / GeV < 200 All selected jets, 400 < Jet p / GeV < 500 T T (1/N ) dN / d (1/N ) dN / d 6 Data (stat. uncert.) Data (stat. uncert.) ch ch 4 Stat. syst. uncert. Stat. syst. uncert. Pythia 8.186 A14 Pythia 8.186 A14 Herwig++ 2.7 4 Herwig++ 2.7 jet jet Sherpa 2.1 Sherpa 2.1 2 2 0 0 1.5 1.5 / True True // Data / Data / Data 1 1 Reco Reco MC MC MC 0.5 33 0.5 33 10 10 22 10 11 1 10 10 22 10 11 1 10 10 ATLAS ATLAS -1 -1 s = 13 TeV, 33 fb s = 13 TeV, 33 fb All selected jets, 900 < Jet p / GeV < 1000 All selected jets, 2000 < Jet p / GeV < 2500 T T (1/N ) dN / d (1/N ) dN / d Data (stat. uncert.) Data (stat. uncert.) ch ch Stat. syst. uncert. Stat. syst. uncert. 5 Pythia 8.186 A14 5 Pythia 8.186 A14 Herwig++ 2.7 Herwig++ 2.7 jet jet Sherpa 2.1 Sherpa 2.1 0 0 1.5 1.5 True True // Data // Data / Data / Data 1 1 Reco Reco MC MC MC MC 0.5 33 0.5 33 10 10 22 10 11 1 10 10 22 10 11 1 FIG. 11. The transverse momentum fraction ζ distribution in four bins of jet transverse momentum: (top left) 100 GeV < pjet jet jet T < 200 GeV, (top right) 400 GeV < pT < 500 GeV, (bottom left) 900 GeV < pT < 1000 GeV, and (bottom right) jet 2000 GeV < pT < 2500 GeV. The lower panels show the ratio of various MC predictions to the data, with the total uncertainty band centered on the data at unity. Additional pjet T bins can be found in Ref. [99]. To present more differential information, the full hfi ¼ f fq hqi þ ð1 − f fq Þhgi ; ð4Þ unfolded distributions for nch, ζ, prel T , and r are shown hci ¼ f cq hqi þ ð1 − f cq Þhgi ; ð5Þ in Figs. 10–13, respectively, for representative pjet T bins. Many of the relevant trends are captured in the above where f xq is the fraction of quark jets in sample x (see Fig. 3 discussion about the pjet T dependence of the moments. for the gluon fraction) and the nominal fractions are taken However, finer information that may be useful for generator from the default PYTHIA simulation described in Sec. IV. tuning is provided by the differential distributions. The flavor of a jet is defined as the type of the highest- energy parton from the event record (all partons prior to B. Quark and gluon distributions hadronization) matched to the jet via ghost association. As discussed in Sec. V B, the more forward and the more This definition is not unique because quark and gluon central of the two selected jets can be separated to study labels are not universal due to color connections with other differences between the radiation patterns within quark and partons in the event.5 In addition to the uncertainty in hfi gluon jets. Using the fraction of quark jets f q in the two jet samples (forward f and central c), one can extract the quark 5 However, for isolated jets, the topology dependence is (hqi ) and gluon (hgi ) jet fragmentation properties separately predicted to be much smaller than the difference between quark by solving a system of equations per bin i of an observable: and gluon jets [102]. 052011-15 G. AAD et al. PHYS. REV. D 100, 052011 (2019) 103 ATLAS ATLAS -1 103 -1 s = 13 TeV, 33 fb s = 13 TeV, 33 fb 2 10 rel rel All selected jets, 100 < Jet p / GeV < 200 All selected jets, 400 < Jet p / GeV < 500 T T 102 (1/N ) dN / dp T T (1/N ) dN / dp 10 Data (stat. uncert.) Data (stat. uncert.) ch ch Stat. syst. uncert. 10 Stat. syst. uncert. Pythia 8.186 A14 Pythia 8.186 A14 1 Herwig++ 2.7 Herwig++ 2.7 1 jet jet Sherpa 2.1 Sherpa 2.1 1 10 1 2 10 10 2 10 3 10 1.5 1.5 / True True // Data / Data MC/ Data 1 1 Reco Reco MC MC 0.5 0.5 0 0.5 1 1.5 2 2.5 3 0 0.5 0.5 1 1.5 1.5 2 2.5 2.5 3 prel [GeV] prel [GeV] prel [GeV] prel [GeV] T T T T ATLAS ATLAS 103 -1 103 -1 s = 13 TeV, 33 fb s = 13 TeV, 33 fb rel rel All selected jets, 900 < Jet p / GeV < 1000 All selected jets, 2000 < Jet p / GeV < 2500 T T 102 T T (1/N ) dN / dp (1/N ) dN / dp 102 Data (stat. uncert.) Data (stat. uncert.) ch ch Stat. syst. uncert. Stat. syst. uncert. 10 10 Pythia 8.186 A14 Pythia 8.186 A14 Herwig++ 2.7 Herwig++ 2.7 jet jet Sherpa 2.1 Sherpa 2.1 1 1 1 10 1 10 2 10 1.5 1.5 True True // Data // Data MC/ Data MC/ Data 1 1 Reco Reco MC MC 0.5 0.5 0 0.5 0.5 1 1.5 1.5 2 2.5 2.5 3 0 0.5 0.5 1 1.5 1.5 2 2.5 2.5 3 prel [GeV] prel [GeV] prel [GeV] prel [GeV] T T T T jet FIG. 12. The transverse momentum prel T distribution in four bins of jet transverse momentum: (top left) 100 GeV < pT < 200 GeV, (top right) 400 GeV < pjet jet T < 500 GeV, (bottom left) 900 GeV < pT < 1000 GeV, and (bottom right) 2000 GeV < jet pT < 2500 GeV. The lower panels show the ratio of various MC predictions to the data, with the total uncertainty band centered on the data at unity. Additional pjet T bins can be found in Ref. [99]. and hci from the unfolding method, uncertainties in the at a fixed jet pT [102]. When presenting the average extracted hgi and hqi distributions arise from the PDF choice, properties in bins of jet pT , the binning correction described from the matrix elements, from the fragmentation model in Sec. VI is also applied and the corresponding uncertainty (due to flavor changing), and from the method nonclosure. contributes to the total uncertainty (though it is smaller than The determination of the uncertainty from the choice of other sources of uncertainty). PDF uses the NNPDF uncertainty set [NNPDF 2.3 at The matrix-element uncertainty dominates the total LO in QCD and QED with αS ðmZ Þ ¼ 0.119] and the uncertainty in the extraction procedure, resulting in an matrix-element uncertainty is estimated by comparing uncertainty that is about 1% at high jet pT and about 5% the nominal fractions from PYTHIA with those from at low to moderate jet pT for quark jets, with the inverse 6 HERWIG. The nonclosure uncertainty is due to the small trend for gluon jets (low uncertainty at low jet pT and large (subpercent level) differences between forward and central uncertainty at high jet pT ). The extractions presented here quark jets, as well as forward and central gluon jets, use leading-order matrix elements and leading-logarithm resulting from an η dependence in the jet fragmentation parton shower programs; higher-order effects that modify the fractions f are not included in this leading-order 6 extraction. Figure 14 shows the extracted quark and gluon These two generators also use different PDF sets, so this uncertainty is double counted in the overall uncertainty. distributions for jets with 1000 GeV < pjet T < 1200 GeV. 052011-16 PROPERTIES OF JET FRAGMENTATION USING CHARGED … PHYS. REV. D 100, 052011 (2019) 104 ATLAS 104 ATLAS -1 -1 103 s = 13 TeV, 33 fb s = 13 TeV, 33 fb (1/N ) dN / d2 rdr (1/N ) dN / d2 rdr All selected jets, 100 < Jet p / GeV < 200 T 103 All selected jets, 400 < Jet p / GeV < 500 T 102 Data (stat. uncert.) Data (stat. uncert.) 2 Stat. syst. uncert. 10 Stat. syst. uncert. ch ch Pythia 8.186 A14 Pythia 8.186 A14 10 Herwig++ 2.7 10 Herwig++ 2.7 Sherpa 2.1 Sherpa 2.1 jet jet 1 1 1 10 1 10 1.5 1.5 / True True // Data / Data MC/ Data 1 1 Reco Reco MC MC 0.5 0.5 0 0.05 0.1 0.1 0.15 0.2 0.2 0.25 0.3 0.3 0.35 0.4 0.4 0 0.05 0.05 0.1 0.1 0.15 0.15 0.2 0.2 0.25 0.25 0.3 0.3 0.35 0.35 0.4 0.4 r r r r ATLAS ATLAS 104 -1 104 -1 s = 13 TeV, 33 fb s = 13 TeV, 33 fb (1/N ) dN / d2 rdr (1/N ) dN / d2 rdr 3 All selected jets, 900 < Jet p / GeV < 1000 All selected jets, 2000 < Jet p / GeV < 2500 10 T 103 T Data (stat. uncert.) Data (stat. uncert.) 102 Stat. syst. uncert. 102 Stat. syst. uncert. ch ch Pythia 8.186 A14 Pythia 8.186 A14 Herwig++ 2.7 Herwig++ 2.7 10 Sherpa 2.1 10 Sherpa 2.1 jet jet 1 1 1 1 10 10 1.5 1.5 1.5 True True // Data // Data MC/ Data MC/ Data 1 1 Reco Reco MC MC 0.5 0.5 0.5 0 0.05 0.05 0.1 0.1 0.15 0.15 0.2 0.2 0.25 0.25 0.3 0.3 0.35 0.35 0.4 0.4 0 0.05 0.05 0.1 0.1 0.15 0.15 0.2 0.2 0.25 0.25 0.3 0.3 0.35 0.35 0.4 0.4 r r r r FIG. 13. Distribution of track radial profile in bins of the radial distance r from the jet axis in four bins of jet transverse momentum: (top left) 100 GeV < pjet jet T < 200 GeV, (top right) 400 GeV < pT < 500 GeV, (bottom left) 900 GeV < pT < 1000 GeV, and jet jet (bottom right) 2000 GeV < pT < 2500 GeV. The lower panels show the ratio of various MC predictions to the data, with the total uncertainty band centered on the data at unity. Additional pjetT bins can be found in Ref. [99]. To reinforce the simulation dependence of these extrac- in the limit that minj fhgj =hqj g ¼ minj fhqj =hgj g ¼ 0, hT 1 ¼ tions, the data distributions are referred to as “extracted hq and hT 2 ¼ hg . When this is not exactly the case, the quark-like” and “extracted gluon-like.” topics are universal but not pure combinations of quarks A key challenge with the extraction based on Eqs. (4) and gluons. The extracted topics using nch in two jet pT and (5) is that it strongly depends on simulation for the bins are shown in Fig. 15. The very low nch region is fractions f q and f g . A new approach that does not require dominated by quarks and the very high nch region is the input of any fractions is topic modeling [103,104], dominated by gluons and therefore nch nearly has the which holds great promise for learning about quark- and property that minj fhgj =hqj g ≈ minj fhqj =hgj g ≈ 0. Therefore, gluon-like jets with less input from theory. In this approach, the first topic is well aligned with quarks and the second one can extract distributions of “topics” T 1 and T 2 : topic is more gluon-like. This alignment is better for quarks than for gluons, but the second topic does converge to hfi − ðminj fhfj =hcj gÞ × hci the gluon distribution at high jet pT . Other observables hTi 1 ¼ ; 1 − minj hfj =hcj aside from nch are not considered for topic modeling because there are no bins where hgj =hqj ¼ 0 or hqj =hgj ¼ 0 hci − ðminj fhcj =hfj gÞ × hfi hTi 2 ¼ ; is approximately true and therefore the topics do not align 1 − minj hcj =hfj with quark- and gluon-like quantities. 052011-17 G. AAD et al. PHYS. REV. D 100, 052011 (2019) 0.5 8 ATLAS ATLAS s = 13 TeV, 33 fb-1 s = 13 TeV, 33 fb-1 1000 < Jet p / GeV < 1200 1000 < Jet p / GeV < 1200 0.4 T T 6 Extracted Quark-like Data Extracted Quark-like Data ch (1/N ) dN / d Extracted Gluon-like Data Extracted Gluon-like Data (1/N ) dN / dn 0.3 ch Quarks Pythia 8.186 A14 Quarks Pythia 8.186 A14 Gluons Pythia 8.186 A14 4 Gluons Pythia 8.186 A14 jet jet 0.2 2 0.1 0 0 0 20 40 60 10 3 10 2 10 1 1 nch 103 103 ATLAS ATLAS s = 13 TeV, 33 fb-1 s = 13 TeV, 33 fb-1 2 1000 < Jet p / GeV < 1200 2 1000 < Jet p / GeV < 1200 10 T 10 T (1/N ) dN / d(p /GeV) Extracted Quark-like Data Extracted Quark-like Data (1/N ) dN / d2 rdr Extracted Gluon-like Data Extracted Gluon-like Data rel T 10 10 Quarks Pythia 8.186 A14 Quarks Pythia 8.186 A14 ch Gluons Pythia 8.186 A14 Gluons Pythia 8.186 A14 ch 1 1 jet jet 1 1 10 10 2 2 10 10 0 1 2 3 0 0.1 0.2 0.3 0.4 prel [GeV] r T FIG. 14. The extracted quark- and gluon-like distributions of (top left) charged-particle multiplicity nch, (top right) transverse momentum fraction ζ, (bottom right) transverse momentum prel T , and (bottom right) the radial profile in bins of the radial distance r from the jet axis for jets with transverse momentum 1000 GeV < pjet T < 1200 GeV. The quark- and gluon-jet distributions from PYTHIA are also shown for comparison. The uncertainty bands on the data include both statistical and systematic uncertainties while the error bars are due to statistical uncertainties only. While the full quark and gluon distributions presented in for κ ≠ 0.8 where P̃g←g switches sign. Therefore, away Fig. 14 cannot be predicted from perturbative QCD, it is from κ ≈ 0.8 and in the modified leading-logarithm possible to model the pjetT dependence of the moments of the ζ approximation8 [73,108,109], distribution. Positive moments of the fragmentation function X  have a perturbative evolution with a proper αS power series ∝ via DGLAP-like equations. In general, there are two terms ζκ i∈jet i ðpT Þ ∼ logðp2T =Λ2 Þ2Pg←g ðκÞ=β0 ; ð6Þ gluons that contribute to the right-hand side of Eq. (1) that prevent an analytic solution: one term proportional to Dhg and one term where β0 is the first term in the QCD β-function and Λ is a proportional to Dhq , where the coefficients for the κ sums are nonperturbative parameter (of order ΛQCD ). The predictions R the Mellin transforms P̃p0 ←p ðκÞ ¼ 01 dζζ κ Pp0 ←p ðζÞ for p0 ¼ g and p0 ¼ q, respectively. For gluon jets (p ¼ g), 8 This means resummation that includes the leading-order the g → qq0 splitting function is finite,7 so jP̃g←g j ≫ jP̃q←g j splitting functions and the first-order running of the strong coupling. A more refined calculation [18,19] using SCET 7 [13–16] and fragmenting jet functions [105–107] is possible. The splitting function P̃q←q is also finite, but is not However, the deviations from this simple approach are higher- numerically small compared with P̃g←q except when κ is very order corrections and do not qualitatively change the comparisons small so this case is not considered further. in this section. 052011-18 PROPERTIES OF JET FRAGMENTATION USING CHARGED … PHYS. REV. D 100, 052011 (2019) 0.5 0.5 ATLAS ATLAS -1 s = 13 TeV, 33 fb s = 13 TeV, 33 fb-1 900 < Jet p / GeV < 1000 1400 < Jet p / GeV < 1600 0.4 T 0.4 T Topic 1 Data Topic 1 Data ch ch Topic 2 Data Topic 2 Data (1/N ) dN / dn (1/N ) dN / dn 0.3 Topic 1 Pythia 8.186 A14 0.3 Topic 1 Pythia 8.186 A14 Topic 2 Pythia 8.186 A14 Topic 2 Pythia 8.186 A14 Quarks Pythia 8.186 A14 Quarks Pythia 8.186 A14 jet jet Gluons Pythia 8.186 A14 Gluons Pythia 8.186 A14 0.2 0.2 0.1 0.1 0 0 0 20 40 60 0 20 40 60 nch nch FIG. 15. The jet topics extracted using charged-particle multiplicity nch for jets in two transverse momentum, pT , bins together with the topics and quark and gluon distributions from PYTHIA. The uncertainty bands on the data include both statistical and systematic uncertainties while the error bars are due to statistical uncertainties only. 1.5 ATLAS ATLAS s = 13 TeV, 33 fb-1 s = 13 TeV, 33 fb-1 6 Extracted Gluon-like Data Extracted Gluon-like Data Gluons Pythia 8.186 A14 Gluons Pythia 8.186 A14 1 Gluon Jets (LL pQCD) Gluon Jets (LL pQCD) 1/2 i in jet i 4 i in jet i 0.5 2 anchor bin anchor bin 0 0 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Jet p [GeV] Jet p [GeV] T T 0.15 ATLAS s = 13 TeV, 33 fb-1 Extracted Gluon-like Data Gluons Pythia 8.186 A14 0.1 Gluon Jets (LL pQCD) 2 i in jet i 0.05 anchor bin 0 500 1000 1500 2000 2500 Jet p [GeV] T FIG. P 16. The dependence on transverse momentum pT of the average extracted gluon-like transverse-momentum-fraction weighted sum i∈jet ζ κi for (top left) κ ¼ 0.5, (top right) κ ¼ 1.0, and κ ¼ 2.0 (bottom). For comparison, the results from PYTHIA and a simple leading-logarithm (LL) calculation are also presented. The prediction is normalized to the data in the sixth jet pT bin, called the anchor bin and indicated by an arrow. The uncertainty band on the calculation is from varying Λ in Eq. (6) up and down by a factor of 2 from its nominal value of 400 MeV (in most regions, this band is not much wider than the linewidth and thus not visible). The uncertainty bands on the data include both statistical and systematic uncertainties while the error bars are due to statistical uncertainties only. 052011-19 G. AAD et al. PHYS. REV. D 100, 052011 (2019) 40 40 ATLAS ATLAS s = 13 TeV, 33 fb-1 s = 13 TeV, 33 fb-1 30 30 nch ch 20 20 n Extracted Quark-like Data Topic 1 Data anchor bin Extracted Gluon-like Data Topic 2 Data 10 Quarks Pythia 8.186 A14 10 Topic 1 Pythia 8.186 A14 Gluons Pythia 8.186 A14 Topic 2 Pythia 8.186 A14 3 Quark Jets (N LO pQCD) Quarks Pythia 8.186 A14 3 Gluon Jets (N LO pQCD) Gluons Pythia 8.186 A14 0 0 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Jet p [GeV] Jet p [GeV] T T FIG. 17. Left (right): The dependence on jet transverse momentum pT of the mean charged-particle multiplicity hnch i for quark and gluon jets (topic 1 and topic 2) in data and in PYTHIA as well as from a calculation using perturbative QCD. The calculation cannot predict the overall normalization and therefore the prediction is normalized to the data in the sixth pT bin, called the anchor bin and indicated by an arrow. The binning correction is not applied to the average topics, as this correction is very sensitive to fluctuations due to the limited number of simulated events. The uncertainty bands on the data include both statistical and systematic uncertainties while the error bars are due to statistical uncertainties only. pffiffiffiffiffi are scaled to match the data in the sixth jet pT bin (referred to “N3 LO” where the series is in αS instead of αS to as the “anchor bin”). There is no a priori reason to [22,23]. Figure 17 shows hnch i as a function of pjet T for select any particular bin as the anchor bin so one of the both extracted quark-like and gluon-like jets as well as first bins after the lowest-threshold unprescaled jet trigger the topic extraction along with the prediction for the is selected. P Figure 16 shows the distributions of the pure quark/gluon case. Gluon jets from data deviate average i∈jet ζκi for κ ¼ 0.5, 1.0, and 2.0 for gluon jets. significantly from simulation and from the calculation at As mentioned above, P̃g←g is predicted to change sign at high jet pT ; this is also true to a lesser extent for quark κ ¼ 0.8, a trend which is supported by the data: for low κ, jets, which seem to have a different slope that is most the average value increases with pT and when κ is large, the prominent at low jet pT . A similar trend was first average decreases with pT . For κ ¼ 1, momentum con- observed in Ref. [7], albeit with lower precision in servation P and isospin symmetry predict that the average the highest pT bins. There are several possibilities for value of i∈jet ζ i should be constant and approximately this discrepancy, such as an unaccounted for potential 2=3, the ratio of charged pions to all pions.9 The leading- source of bias in the quark/gluon jet fractions. The data logarithm (LL) calculation predicts P̃g←g ð1Þ ≈ 0 so the in the right panel of Fig. 17 do not yet conclusively pT dependence is already negligible compared with the support or reject this hypothesis; with more data, it may κ ¼ 0.5 and κ ¼ 2 cases. be possible to determine if the data match topic 2 in When κ → 0, both the quark and gluon fragmentation- PYTHIA or deviate as is the case for gluons in the left function Mellin transforms diverge and so the analysis panel of Fig. 17. with Eq. (6) is not accurate. The κ → 0 limit is hnch i and The pT dependence of the average ζ, prel T , and r are there is no known series in αS to describe its pjet shown in Fig. 18. Gluon jets have more constituents than T quark jets on average so their average ζ is lower. For dependence. Despite this, the anomalous dimension both quark and gluon jets, hζi decreases with the jet pT for the pjetT dependence of hnch i has been calculated in part because constituent multiplicity increases with pT . Gluon jets are wider than quark jets on average, but both quark and gluon jets become denser with increasing 9 The measured value is not exactly 2=3 because a jet’s energy jet pT . The data show nearly the same trends as PYTHIA is only about 60% due to pions. in all cases. 052011-20 PROPERTIES OF JET FRAGMENTATION USING CHARGED … PHYS. REV. D 100, 052011 (2019) 0.1 1 ATLAS ATLAS s = 13 TeV, 33 fb-1 s = 13 TeV, 33 fb-1 0.08 Extracted Quark-like Data 0.8 Extracted Gluon-like Data Quarks Pythia 8.186 A14 0.06 0.6 [GeV] Gluons Pythia 8.186 A14 prel T 0.04 0.4 Extracted Quark-like Data Extracted Gluon-like Data Quarks Pythia 8.186 A14 0.02 0.2 Gluons Pythia 8.186 A14 0 0 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Jet p [GeV] Jet p [GeV] T T 0.1 ATLAS s = 13 TeV, 33 fb-1 0.08 Extracted Quark-like Data Extracted Gluon-like Data Quarks Pythia 8.186 A14 0.06 Gluons Pythia 8.186 A14 r 0.04 0.02 0 500 1000 1500 2000 2500 Jet p [GeV] T FIG. 18. The dependence on jet transverse momentum pT of the average extracted quark and gluon (top left) transverse momentum fraction ζ, (top right) transverse momentum prel T , and (bottom) radial profile (per particle and not per jet). The uncertainty bands on the data include both statistical and systematic uncertainties while the error bars are due to statistical uncertainties only. IX. CONCLUSION precision of this measurement. Near 1 TeV in jet pT , these measurements have achieved percent-level uncertainties for This paper documents a measurement of track-based jet pffiffiffi a variety of observables. In addition to measuring the fragmentation functions in pp collisions at s ¼ 13 TeV. forward, central, and combined jet distributions, the for- The analysis uses a dataset corresponding to an integrated ward and central jet spectra are considered separately to luminosity of 33 fb−1 recorded by the ATLAS detector at study quark- and gluon-like distributions. A first measure- the LHC. Multiple jet properties, including the charged- ment of topic modeling for the charged-particle multiplicity particle multiplicity, the momentum fraction carried by provides a promising alternative to traditional methods of charged particles, and angular properties of the radiation extracting quark- and gluon-jet distributions that use input pattern inside jets are studied. There are key areas where from simulation. The simulations provide a reasonable there are significant disagreements between the ATLAS description of the quark-like data across the jet pT range default MC simulation (PYTHIA 8.2 with the A14 tune, presented in this measurement, but the gluon-like data have HERWIG++, and SHERPA) and the data, especially for the systematically fewer charged particles than the simulations radial profiles and momentum distributions in SHERPA. The by about 10%. radial profile is systematically broader in data than in The unfolded data are made public through HEPDATA to simulation, but the momentum transverse to the jet axis provide input to help improve both perturbative and non- and the momentum fraction are well modeled within the perturbative aspects of fragmentation modeling in the future. 052011-21 G. AAD et al. PHYS. REV. D 100, 052011 (2019) ACKNOWLEDGMENTS and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom; DOE and NSF, United States of We thank CERN for the very successful operation of the America. In addition, individual groups and members have LHC, as well as the support staff from our institutions received support from BCKDF, CANARIE, CRC and without whom ATLAS could not be operated efficiently. We Compute Canada, Canada; COST, ERC, ERDF, Horizon acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; 2020, and Marie Skłodowska-Curie Actions, European ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Union; Investissements d’ Avenir Labex and Idex, ANR, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, France; DFG and AvH Foundation, Germany; Herakleitos, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Thales and Aristeia programs cofinanced by EU-ESF and the Colombia; MSMT CR, MPO CR and VSC CR, Czech Greek NSRF, Greece; BSF-NSF and GIF, Israel; CERCA Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS, Programme Generalitat de Catalunya, Spain; The Royal CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF, Society and Leverhulme Trust, United Kingdom. The crucial and MPG, Germany; GSRT, Greece; RGC, Hong Kong computing support from all WLCG partners is acknowl- SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; edged gratefully, in particular from CERN, the ATLAS Tier- MEXT and JSPS, Japan; CNRST, Morocco; NWO, 1 facilities at TRIUMF (Canada), NDGF (Denmark, Netherlands; RCN, Norway; MNiSW and NCN, Poland; Norway, Sweden), CC-IN2P3 (France), KIT/GridKA FCT, Portugal; MNE/IFA, Romania; MES of Russia and (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), NRC KI, Russian Federation; JINR; MESTD, Serbia; PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, (USA), the Tier-2 facilities worldwide and large non- South Africa; MINECO, Spain; SRC and Wallenberg WLCG resource providers. Major contributors of computing Foundation, Sweden; SERI, SNSF and Cantons of Bern resources are listed in Ref. [110]. [1] A. Buckley et al., General-purpose event generators for [11] A. J. Larkoski, I. 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Costanzo,149 G. Cowan,93 J. W. Cowley,32 J. Crane,100 K. Cranmer,124 S. J. Crawley,57 R. A. Creager,137 S. Crépé-Renaudin,58 F. Crescioli,136 M. Cristinziani,24 V. Croft,120 G. Crosetti,41b,41a A. Cueto,5 T. Cuhadar Donszelmann,149 A. R. Cukierman,153 S. Czekierda,84 P. Czodrowski,36 M. J. Da Cunha Sargedas De Sousa,60b J. V. Da Fonseca Pinto,80b C. Da Via,100 W. Dabrowski,83a T. Dado,28a S. Dahbi,35e T. Dai,105 C. Dallapiccola,102 M. Dam,40 G. D’amen,23b,23a V. D’Amico,74a,74b J. Damp,99 J. R. Dandoy,137 M. F. Daneri,30 N. P. Dang,181 N. D Dann,100 M. Danninger,175 V. Dao,36 G. Darbo,55b O. Dartsi,5 A. Dattagupta,131 T. Daubney,46 S. D’Auria,68a,68b W. Davey,24 C. David,46 T. Davidek,143 D. R. Davis,49 I. Dawson,149 K. De,8 R. De Asmundis,69a M. De Beurs,120 S. De Castro,23b,23a S. De Cecco,72a,72b N. De Groot,119 P. de Jong,120 H. De la Torre,106 A. De Maria,15c D. De Pedis,72a A. De Salvo,72a 052011-26 PROPERTIES OF JET FRAGMENTATION USING CHARGED … PHYS. REV. D 100, 052011 (2019) U. De Sanctis,73a,73b M. De Santis,73a,73b A. De Santo,156 K. De Vasconcelos Corga,101 J. B. De Vivie De Regie,132 C. Debenedetti,146 D. V. Dedovich,79 A. M. Deiana,42 M. Del Gaudio,41b,41a J. Del Peso,98 Y. Delabat Diaz,46 D. Delgove,132 F. Deliot,145,q C. M. Delitzsch,7 M. Della Pietra,69a,69b D. Della Volpe,54 A. Dell’Acqua,36 L. Dell’Asta,73a,73b M. Delmastro,5 C. Delporte,132 P. A. Delsart,58 D. A. DeMarco,167 S. Demers,183 M. Demichev,79 G. Demontigny,109 S. P. Denisov,123 D. Denysiuk,120 L. D’Eramo,136 D. Derendarz,84 J. E. Derkaoui,35d F. Derue,136 P. Dervan,90 K. Desch,24 C. Deterre,46 K. Dette,167 C. Deutsch,24 M. R. Devesa,30 P. O. Deviveiros,36 A. Dewhurst,144 S. Dhaliwal,26 F. A. Di Bello,54 A. Di Ciaccio,73a,73b L. Di Ciaccio,5 W. K. Di Clemente,137 C. Di Donato,69a,69b A. Di Girolamo,36 G. Di Gregorio,71a,71b B. Di Micco,74a,74b R. Di Nardo,102 K. F. Di Petrillo,59 R. Di Sipio,167 D. Di Valentino,34 C. Diaconu,101 F. A. Dias,40 T. 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Eggleston,49 T. Eifert,36 G. Eigen,17 K. Einsweiler,18 T. Ekelof,172 H. El Jarrari,35e M. El Kacimi,35c R. El Kosseifi,101 V. Ellajosyula,172 M. Ellert,172 F. Ellinghaus,182 A. A. Elliot,92 N. Ellis,36 J. Elmsheuser,29 M. Elsing,36 D. Emeliyanov,144 A. Emerman,39 Y. Enari,163 M. B. Epland,49 J. Erdmann,47 A. Ereditato,20 M. Errenst,36 M. Escalier,132 C. Escobar,174 O. Estrada Pastor,174 E. Etzion,161 H. Evans,65 A. Ezhilov,138 F. Fabbri,57 L. Fabbri,23b,23a V. Fabiani,119 G. Facini,94 R. M. Faisca Rodrigues Pereira,140a R. M. Fakhrutdinov,123 S. Falciano,72a P. J. Falke,5 S. Falke,5 J. Faltova,143 Y. Fang,15a Y. Fang,15a G. Fanourakis,44 M. Fanti,68a,68b M. Faraj,66a,66c A. Farbin,8 A. Farilla,74a E. M. Farina,70a,70b T. Farooque,106 S. Farrell,18 S. M. Farrington,50 P. Farthouat,36 F. Fassi,35e P. Fassnacht,36 D. Fassouliotis,9 M. Faucci Giannelli,50 W. J. Fawcett,32 L. Fayard,132 O. L. Fedin,138,r W. Fedorko,175 M. Feickert,42 S. Feigl,134 L. Feligioni,101 A. Fell,149 C. Feng,60b E. 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Gabrielli,18 G. P. Gach,83a S. Gadatsch,54 P. Gadow,115 G. Gagliardi,55b,55a L. G. Gagnon,109 C. Galea,27b B. Galhardo,140a G. E. Gallardo,135 E. J. Gallas,135 B. J. Gallop,144 G. Galster,40 R. Gamboa Goni,92 K. K. Gan,126 S. Ganguly,180 J. Gao,60a Y. Gao,50 Y. S. Gao,31,h C. García,174 J. E. García Navarro,174 J. A. García Pascual,15a C. Garcia-Argos,52 M. Garcia-Sciveres,18 R. W. Gardner,37 N. Garelli,153 S. Gargiulo,52 V. Garonne,134 A. Gaudiello,55b,55a G. Gaudio,70a I. L. Gavrilenko,110 A. Gavrilyuk,111 C. Gay,175 G. Gaycken,46 E. N. Gazis,10 A. A. Geanta,27b C. N. P. Gee,144 J. Geisen,53 M. Geisen,99 M. P. Geisler,61a C. Gemme,55b M. H. Genest,58 C. Geng,105 S. Gentile,72a,72b S. George,93 T. Geralis,44 L. O. Gerlach,53 P. Gessinger-Befurt,99 G. Gessner,47 S. Ghasemi,151 M. Ghasemi Bostanabad,176 M. Ghneimat,24 A. Ghosh,132 A. Ghosh,77 B. Giacobbe,23b S. Giagu,72a,72b N. Giangiacomi,23b,23a P. Giannetti,71a A. Giannini,69a,69b S. M. Gibson,93 M. Gignac,146 D. Gillberg,34 G. 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Handl,114 B. Haney,137 R. Hankache,136 E. Hansen,96 J. B. Hansen,40 J. D. Hansen,40 M. C. Hansen,24 P. H. Hansen,40 E. C. Hanson,100 K. Hara,169 A. S. Hard,181 T. Harenberg,182 S. Harkusha,107 P. F. Harrison,178 N. M. Hartmann,114 Y. Hasegawa,150 A. Hasib,50 S. Hassani,145 S. Haug,20 R. Hauser,106 L. B. Havener,39 M. Havranek,142 C. M. Hawkes,21 R. J. Hawkings,36 D. Hayden,106 C. Hayes,155 R. L. Hayes,175 C. P. Hays,135 J. M. Hays,92 H. S. Hayward,90 S. J. Haywood,144 F. He,60a M. P. Heath,50 V. Hedberg,96 L. Heelan,8 S. Heer,24 K. K. Heidegger,52 W. D. Heidorn,78 J. Heilman,34 S. Heim,46 T. Heim,18 B. Heinemann,46,y J. J. Heinrich,131 L. Heinrich,36 C. Heinz,56 J. Hejbal,141 L. Helary,61b A. Held,175 S. Hellesund,134 C. M. Helling,146 S. Hellman,45a,45b C. Helsens,36 R. C. W. Henderson,89 Y. Heng,181 S. Henkelmann,175 A. M. Henriques Correia,36 G. H. Herbert,19 H. Herde,26 V. Herget,177 Y. Hernández Jiménez,33c H. Herr,99 M. G. Herrmann,114 T. Herrmann,48 G. Herten,52 R. Hertenberger,114 L. Hervas,36 T. C. Herwig,137 G. G. Hesketh,94 N. P. Hessey,168a A. Higashida,163 S. Higashino,81 E. Higón-Rodriguez,174 K. Hildebrand,37 E. Hill,176 J. C. Hill,32 K. K. Hill,29 K. H. Hiller,46 S. J. Hillier,21 M. Hils,48 I. Hinchliffe,18 F. Hinterkeuser,24 M. Hirose,133 S. Hirose,52 D. Hirschbuehl,182 B. Hiti,91 O. Hladik,141 D. R. Hlaluku,33c X. Hoad,50 J. Hobbs,155 N. Hod,180 M. C. Hodgkinson,149 A. Hoecker,36 F. Hoenig,114 D. Hohn,52 D. Hohov,132 T. R. Holmes,37 M. Holzbock,114 L. B. A. H Hommels,32 S. Honda,169 T. Honda,81 T. M. Hong,139 A. Hönle,115 B. H. Hooberman,173 W. H. Hopkins,6 Y. Horii,117 P. Horn,48 L. A. Horyn,37 A. Hostiuc,148 S. Hou,158 A. Hoummada,35a J. Howarth,100 J. Hoya,88 M. Hrabovsky,130 J. Hrdinka,76 I. Hristova,19 J. Hrivnac,132 A. Hrynevich,108 T. Hryn’ova,5 P. J. Hsu,64 S.-C. Hsu,148 Q. Hu,29 S. Hu,60c Y. Huang,15a Z. Hubacek,142 F. Hubaut,101 M. Huebner,24 F. Huegging,24 T. B. Huffman,135 M. Huhtinen,36 R. F. H. Hunter,34 P. Huo,155 A. M. 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Kelsey,156 J. J. Kempster,21 J. Kendrick,21 O. Kepka,141 S. Kersten,182 B. P. Kerševan,91 S. Ketabchi Haghighat,167 M. Khader,173 F. Khalil-Zada,13 M. Khandoga,145 A. Khanov,129 A. G. Kharlamov,122b,122a T. Kharlamova,122b,122a E. E. Khoda,175 A. Khodinov,166 T. J. Khoo,54 E. Khramov,79 J. Khubua,159b S. Kido,82 M. Kiehn,54 C. R. Kilby,93 Y. K. Kim,37 N. Kimura,66a,66c O. M. Kind,19 B. T. King,90,a D. Kirchmeier,48 J. Kirk,144 A. E. Kiryunin,115 T. Kishimoto,163 D. P. Kisliuk,167 V. Kitali,46 O. Kivernyk,5 E. Kladiva,28b,a T. Klapdor-Kleingrothaus,52 M. Klassen,61a M. H. Klein,105 M. Klein,90 U. Klein,90 K. Kleinknecht,99 P. Klimek,121 A. Klimentov,29 T. Klingl,24 T. Klioutchnikova,36 F. F. Klitzner,114 P. Kluit,120 S. Kluth,115 E. Kneringer,76 E. B. F. G. Knoops,101 A. Knue,52 D. Kobayashi,87 T. Kobayashi,163 M. Kobel,48 M. Kocian,153 P. Kodys,143 P. T. Koenig,24 052011-28 PROPERTIES OF JET FRAGMENTATION USING CHARGED … PHYS. REV. D 100, 052011 (2019) T. Koffas,34 N. M. Köhler,36 T. Koi,153 M. Kolb,61b I. Koletsou,5 T. Komarek,130 T. Kondo,81 N. Kondrashova,60c K. Köneke,52 A. C. König,119 T. Kono,125 R. Konoplich,124,ee V. Konstantinides,94 N. Konstantinidis,94 B. Konya,96 R. Kopeliansky,65 S. Koperny,83a K. Korcyl,84 K. Kordas,162 G. Koren,161 A. Korn,94 I. Korolkov,14 E. V. Korolkova,149 N. Korotkova,113 O. Kortner,115 S. Kortner,115 T. Kosek,143 V. V. Kostyukhin,24 A. Kotwal,49 A. Koulouris,10 A. Kourkoumeli-Charalampidi,70a,70b C. Kourkoumelis,9 E. Kourlitis,149 V. Kouskoura,29 A. B. Kowalewska,84 R. Kowalewski,176 C. Kozakai,163 W. Kozanecki,145 A. S. Kozhin,123 V. A. Kramarenko,113 G. Kramberger,91 D. Krasnopevtsev,60a M. W. Krasny,136 A. Krasznahorkay,36 D. Krauss,115 J. A. Kremer,83a J. Kretzschmar,90 P. Krieger,167 F. Krieter,114 A. Krishnan,61b K. Krizka,18 K. Kroeninger,47 H. Kroha,115 J. Kroll,141 J. Kroll,137 J. Krstic,16 U. Kruchonak,79 H. Krüger,24 N. Krumnack,78 M. C. Kruse,49 J. A. Krzysiak,84 T. Kubota,104 O. Kuchinskaia,166 S. Kuday,4b J. T. Kuechler,46 S. Kuehn,36 A. Kugel,61a T. Kuhl,46 V. Kukhtin,79 R. Kukla,101 Y. Kulchitsky,107,ff S. Kuleshov,147b Y. P. Kulinich,173 M. Kuna,58 T. Kunigo,85 A. Kupco,141 T. Kupfer,47 O. Kuprash,52 H. Kurashige,82 L. L. Kurchaninov,168a Y. A. Kurochkin,107 A. Kurova,112 M. G. Kurth,15a,15d E. S. Kuwertz,36 M. Kuze,165 A. K. Kvam,148 J. Kvita,130 T. Kwan,103 A. La Rosa,115 L. La Rotonda,41b,41a F. La Ruffa,41b,41a C. Lacasta,174 F. Lacava,72a,72b D. P. J. Lack,100 H. Lacker,19 D. Lacour,136 E. Ladygin,79 R. Lafaye,5 B. Laforge,136 T. Lagouri,33c S. Lai,53 S. Lammers,65 W. Lampl,7 C. Lampoudis,162 E. Lançon,29 U. Landgraf,52 M. P. J. Landon,92 M. C. Lanfermann,54 V. S. Lang,46 J. C. Lange,53 R. J. Langenberg,36 A. J. Lankford,171 F. Lanni,29 K. Lantzsch,24 A. Lanza,70a A. Lapertosa,55b,55a S. Laplace,136 J. F. Laporte,145 T. Lari,68a F. Lasagni Manghi,23b,23a M. Lassnig,36 T. S. Lau,63a A. Laudrain,132 A. Laurier,34 M. Lavorgna,69a,69b M. Lazzaroni,68a,68b B. Le,104 E. Le Guirriec,101 M. LeBlanc,7 T. LeCompte,6 F. Ledroit-Guillon,58 C. A. Lee,29 G. R. Lee,17 L. Lee,59 S. C. Lee,158 S. J. Lee,34 B. Lefebvre,168a M. Lefebvre,176 F. Legger,114 C. Leggett,18 K. Lehmann,152 N. Lehmann,182 G. Lehmann Miotto,36 W. A. Leight,46 A. Leisos,162,gg M. A. L. Leite,80d C. E. Leitgeb,114 R. Leitner,143 D. Lellouch,180,a K. J. C. Leney,42 T. Lenz,24 B. Lenzi,36 R. Leone,7 S. Leone,71a C. Leonidopoulos,50 A. Leopold,136 G. Lerner,156 C. Leroy,109 R. Les,167 C. G. Lester,32 M. Levchenko,138 J. Levêque,5 D. Levin,105 L. J. Levinson,180 D. J. Lewis,21 B. Li,15b B. Li,105 C-Q. Li,60a F. Li,60c H. Li,60a H. Li,60b J. Li,60c K. Li,153 L. Li,60c M. Li,15a Q. Li,15a,15d Q. Y. Li,60a S. Li,60d,60c X. Li,46 Y. Li,46 Z. Li,60b Z. Liang,15a B. Liberti,73a A. Liblong,167 K. Lie,63c S. Liem,120 C. Y. Lin,32 K. Lin,106 T. H. Lin,99 R. A. Linck,65 J. H. Lindon,21 A. L. Lionti,54 E. Lipeles,137 A. Lipniacka,17 M. Lisovyi,61b T. M. Liss,173,hh A. Lister,175 A. M. Litke,146 J. D. Little,8 B. Liu,78,ii B. L Liu,6 H. B. Liu,29 H. Liu,105 J. B. Liu,60a J. K. K. Liu,135 K. Liu,136 M. Liu,60a P. Liu,18 Y. Liu,15a,15d Y. L. Liu,105 Y. W. Liu,60a M. Livan,70a,70b A. Lleres,58 J. Llorente Merino,15a S. L. Lloyd,92 C. Y. Lo,63b F. Lo Sterzo,42 E. M. Lobodzinska,46 P. Loch,7 S. Loffredo,73a,73b T. Lohse,19 K. Lohwasser,149 M. Lokajicek,141 J. D. Long,173 R. E. Long,89 L. Longo,36 K. A. Looper,126 J. A. Lopez,147b I. Lopez Paz,100 A. Lopez Solis,149 J. Lorenz,114 N. Lorenzo Martinez,5 M. Losada,22 P. J. Lösel,114 A. Lösle,52 X. Lou,46 X. Lou,15a A. Lounis,132 J. Love,6 P. A. Love,89 J. J. Lozano Bahilo,174 M. Lu,60a Y. J. Lu,64 H. J. Lubatti,148 C. Luci,72a,72b A. Lucotte,58 C. Luedtke,52 F. Luehring,65 I. Luise,136 L. Luminari,72a B. Lund-Jensen,154 M. S. Lutz,102 D. Lynn,29 R. Lysak,141 E. Lytken,96 F. Lyu,15a V. Lyubushkin,79 T. Lyubushkina,79 H. Ma,29 L. L. Ma,60b Y. Ma,60b G. Maccarrone,51 A. Macchiolo,115 C. M. Macdonald,149 J. Machado Miguens,137 D. Madaffari,174 R. Madar,38 W. F. Mader,48 N. Madysa,48 J. Maeda,82 K. Maekawa,163 S. Maeland,17 T. Maeno,29 M. Maerker,48 A. S. Maevskiy,113 V. Magerl,52 N. Magini,78 D. J. Mahon,39 C. Maidantchik,80b T. Maier,114 A. Maio,140a,140b,140d O. Majersky,28a S. Majewski,131 Y. Makida,81 N. Makovec,132 B. Malaescu,136 Pa. Malecki,84 V. P. Maleev,138 F. Malek,58 U. Mallik,77 D. Malon,6 C. Malone,32 S. Maltezos,10 S. Malyukov,36 J. Mamuzic,174 G. Mancini,51 I. Mandić,91 L. Manhaes de Andrade Filho,80a I. M. Maniatis,162 J. Manjarres Ramos,48 K. H. Mankinen,96 A. Mann,114 A. Manousos,76 B. Mansoulie,145 I. Manthos,162 S. Manzoni,120 A. Marantis,162 G. Marceca,30 L. Marchese,135 G. Marchiori,136 M. Marcisovsky,141 C. Marcon,96 C. A. Marin Tobon,36 M. Marjanovic,38 Z. Marshall,18 M. U. F Martensson,172 S. Marti-Garcia,174 C. B. Martin,126 T. A. Martin,178 V. J. Martin,50 B. Martin dit Latour,17 L. Martinelli,74a,74b M. Martinez,14,u V. I. Martinez Outschoorn,102 S. Martin-Haugh,144 V. S. Martoiu,27b A. C. Martyniuk,94 A. Marzin,36 S. R. Maschek,115 L. Masetti,99 T. Mashimo,163 R. Mashinistov,110 J. Masik,100 A. L. Maslennikov,122b,122a L. H. Mason,104 L. Massa,73a,73b P. Massarotti,69a,69b P. Mastrandrea,71a,71b A. Mastroberardino,41b,41a T. Masubuchi,163 D. Matakias,10 A. Matic,114 P. Mättig,24 J. Maurer,27b B. Maček,91 D. A. Maximov,122b,122a R. Mazini,158 I. Maznas,162 S. M. Mazza,146 S. P. Mc Kee,105 T. G. McCarthy,115 L. I. McClymont,94 W. P. McCormack,18 E. F. McDonald,104 J. A. Mcfayden,36 M. A. McKay,42 K. D. McLean,176 S. J. McMahon,144 P. C. McNamara,104 C. J. McNicol,178 R. A. McPherson,176,p J. E. Mdhluli,33c Z. A. Meadows,102 S. Meehan,148 T. Megy,52 S. Mehlhase,114 A. Mehta,90 T. Meideck,58 B. Meirose,43 D. Melini,174 B. R. Mellado Garcia,33c J. D. Mellenthin,53 052011-29 G. AAD et al. PHYS. REV. D 100, 052011 (2019) M. Melo,28a F. Meloni,46 A. Melzer,24 S. B. Menary,100 E. D. Mendes Gouveia,140a,140e L. Meng,36 X. T. Meng,105 S. Menke,115 E. Meoni,41b,41a S. Mergelmeyer,19 S. A. M. Merkt,139 C. Merlassino,20 P. Mermod,54 L. Merola,69a,69b C. Meroni,68a O. Meshkov,113,110 J. K. R. Meshreki,151 A. Messina,72a,72b J. Metcalfe,6 A. S. Mete,171 C. Meyer,65 J. Meyer,160 J-P. Meyer,145 H. Meyer Zu Theenhausen,61a F. Miano,156 M. Michetti,19 R. P. Middleton,144 L. Mijović,50 G. Mikenberg,180 M. Mikestikova,141 M. Mikuž,91 H. Mildner,149 M. Milesi,104 A. Milic,167 D. A. Millar,92 D. W. Miller,37 A. Milov,180 D. A. Milstead,45a,45b R. A. Mina,153,dd A. A. Minaenko,123 M. Miñano Moya,174 I. A. Minashvili,159b A. I. Mincer,124 B. Mindur,83a M. Mineev,79 Y. Minegishi,163 Y. Ming,181 L. M. Mir,14 A. Mirto,67a,67b K. P. Mistry,137 T. Mitani,179 J. Mitrevski,114 V. A. Mitsou,174 M. Mittal,60c A. Miucci,20 P. S. Miyagawa,149 A. Mizukami,81 J. U. Mjörnmark,96 T. Mkrtchyan,184 M. Mlynarikova,143 T. Moa,45a,45b K. Mochizuki,109 P. Mogg,52 S. Mohapatra,39 R. Moles-Valls,24 M. C. Mondragon,106 K. Mönig,46 J. Monk,40 E. Monnier,101 A. Montalbano,152 J. Montejo Berlingen,36 M. Montella,94 F. Monticelli,88 S. Monzani,68a N. Morange,132 D. Moreno,22 M. Moreno Llácer,36 C. Moreno Martinez,14 P. Morettini,55b M. Morgenstern,120 S. Morgenstern,48 D. Mori,152 M. Morii,59 M. Morinaga,179 V. Morisbak,134 A. K. Morley,36 G. Mornacchi,36 A. P. Morris,94 L. Morvaj,155 P. Moschovakos,36 B. Moser,120 M. Mosidze,159b T. Moskalets,145 H. J. Moss,149 J. Moss,31,jj K. Motohashi,165 E. Mountricha,36 E. J. W. Moyse,102 S. Muanza,101 J. Mueller,139 R. S. P. Mueller,114 D. Muenstermann,89 G. A. Mullier,96 J. L. Munoz Martinez,14 F. J. Munoz Sanchez,100 P. Murin,28b W. J. Murray,178,144 A. Murrone,68a,68b M. Muškinja,18 C. Mwewa,33a A. G. Myagkov,123,kk J. Myers,131 M. Myska,142 B. P. Nachman,18 O. Nackenhorst,47 A. Nag Nag,48 K. Nagai,135 K. Nagano,81 Y. Nagasaka,62 M. Nagel,52 E. Nagy,101 A. M. Nairz,36 Y. Nakahama,117 K. Nakamura,81 T. Nakamura,163 I. Nakano,127 H. Nanjo,133 F. Napolitano,61a R. F. Naranjo Garcia,46 R. Narayan,42 I. Naryshkin,138 T. Naumann,46 G. Navarro,22 H. A. Neal,105,a P. Y. Nechaeva,110 F. Nechansky,46 T. J. Neep,21 A. Negri,70a,70b M. Negrini,23b C. Nellist,53 M. E. Nelson,135 S. Nemecek,141 P. Nemethy,124 M. Nessi,36,ll M. S. Neubauer,173 M. Neumann,182 P. R. Newman,21 Y. S. Ng,19 Y. W. Y. Ng,171 H. D. N. Nguyen,101 T. Nguyen Manh,109 E. Nibigira,38 R. B. Nickerson,135 R. Nicolaidou,145 D. S. Nielsen,40 J. Nielsen,146 N. Nikiforou,11 V. Nikolaenko,123,kk I. Nikolic-Audit,136 K. Nikolopoulos,21 P. Nilsson,29 H. R. Nindhito,54 Y. Ninomiya,81 A. Nisati,72a N. Nishu,60c R. Nisius,115 I. Nitsche,47 T. Nitta,179 T. Nobe,163 Y. Noguchi,85 I. Nomidis,136 M. A. Nomura,29 M. Nordberg,36 N. Norjoharuddeen,135 T. Novak,91 O. Novgorodova,48 R. Novotny,142 L. Nozka,130 K. Ntekas,171 E. Nurse,94 F. G. Oakham,34,e H. Oberlack,115 J. Ocariz,136 A. Ochi,82 I. Ochoa,39 J. P. Ochoa-Ricoux,147a K. O’Connor,26 S. Oda,87 S. Odaka,81 S. Oerdek,53 A. Ogrodnik,83a A. Oh,100 S. H. Oh,49 C. C. Ohm,154 H. Oide,55b,55a M. L. Ojeda,167 H. Okawa,169 Y. Okazaki,85 Y. Okumura,163 T. Okuyama,81 A. Olariu,27b L. F. Oleiro Seabra,140a S. A. Olivares Pino,147a D. Oliveira Damazio,29 J. L. Oliver,1 M. J. R. Olsson,171 A. Olszewski,84 J. Olszowska,84 D. C. O’Neil,152 A. Onofre,140a,140e K. Onogi,117 P. U. E. Onyisi,11 H. Oppen,134 M. J. Oreglia,37 G. E. Orellana,88 D. Orestano,74a,74b N. Orlando,14 R. S. Orr,167 V. O’Shea,57 R. Ospanov,60a G. Otero y Garzon,30 H. Otono,87 P. S. Ott,61a M. Ouchrif,35d J. Ouellette,29 F. Ould-Saada,134 A. Ouraou,145 Q. Ouyang,15a M. Owen,57 R. E. Owen,21 V. E. Ozcan,12c N. Ozturk,8 J. Pacalt,130 H. A. Pacey,32 K. Pachal,49 A. Pacheco Pages,14 C. Padilla Aranda,14 S. Pagan Griso,18 M. Paganini,183 G. Palacino,65 S. Palazzo,50 S. Palestini,36 M. Palka,83b D. Pallin,38 I. Panagoulias,10 C. E. Pandini,36 J. G. Panduro Vazquez,93 P. Pani,46 G. Panizzo,66a,66c L. Paolozzi,54 C. Papadatos,109 K. Papageorgiou,9,s A. Paramonov,6 D. Paredes Hernandez,63b S. R. Paredes Saenz,135 B. 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Piegaia,30 D. Pietreanu,27b J. E. Pilcher,37 A. D. Pilkington,100 M. Pinamonti,73a,73b J. L. Pinfold,3 M. Pitt,180 L. Pizzimento,73a,73b M.-A. Pleier,29 V. Pleskot,143 E. Plotnikova,79 P. Podberezko,122b,122a R. Poettgen,96 R. Poggi,54 L. Poggioli,132 I. Pogrebnyak,106 D. Pohl,24 I. Pokharel,53 G. Polesello,70a A. Poley,18 A. Policicchio,72a,72b R. Polifka,143 A. Polini,23b C. S. Pollard,46 V. Polychronakos,29 D. Ponomarenko,112 L. Pontecorvo,36 S. Popa,27a G. A. Popeneciu,27d D. M. Portillo Quintero,58 S. Pospisil,142 K. Potamianos,46 I. N. Potrap,79 C. J. Potter,32 H. Potti,11 T. Poulsen,96 J. Poveda,36 T. D. Powell,149 G. Pownall,46 M. E. Pozo Astigarraga,36 P. Pralavorio,101 S. Prell,78 D. Price,100 052011-30 PROPERTIES OF JET FRAGMENTATION USING CHARGED … PHYS. REV. D 100, 052011 (2019) M. Primavera,67a S. Prince,103 M. L. Proffitt,148 N. Proklova,112 K. Prokofiev,63c F. Prokoshin,79 S. Protopopescu,29 J. Proudfoot,6 M. Przybycien,83a D. Pudzha,138 A. Puri,173 P. Puzo,132 J. Qian,105 Y. Qin,100 A. Quadt,53 M. Queitsch-Maitland,46 A. Qureshi,1 P. Rados,104 F. Ragusa,68a,68b G. Rahal,97 J. A. Raine,54 S. Rajagopalan,29 A. Ramirez Morales,92 K. Ran,15a,15d T. Rashid,132 S. Raspopov,5 D. M. Rauch,46 F. Rauscher,114 S. Rave,99 B. Ravina,149 I. Ravinovich,180 J. H. Rawling,100 M. Raymond,36 A. L. Read,134 N. P. Readioff,58 M. Reale,67a,67b D. M. Rebuzzi,70a,70b A. Redelbach,177 G. Redlinger,29 K. Reeves,43 L. Rehnisch,19 J. Reichert,137 D. Reikher,161 A. Reiss,99 A. Rej,151 C. Rembser,36 M. Renda,27b M. Rescigno,72a S. Resconi,68a E. D. Resseguie,137 S. Rettie,175 E. Reynolds,21 O. L. Rezanova,122b,122a P. Reznicek,143 E. Ricci,75a,75b R. Richter,115 S. Richter,46 E. Richter-Was,83b O. Ricken,24 M. Ridel,136 P. Rieck,115 C. J. Riegel,182 O. Rifki,46 M. Rijssenbeek,155 A. Rimoldi,70a,70b M. Rimoldi,46 L. Rinaldi,23b G. Ripellino,154 B. Ristić,89 I. Riu,14 J. C. Rivera Vergara,176 F. Rizatdinova,129 E. Rizvi,92 C. Rizzi,36 R. T. Roberts,100 S. H. Robertson,103,p M. Robin,46 D. Robinson,32 J. E. M. Robinson,46 C. M. Robles Gajardo,147b A. Robson,57 E. Rocco,99 C. Roda,71a,71b S. Rodriguez Bosca,174 A. Rodriguez Perez,14 D. Rodriguez Rodriguez,174 A. M. Rodríguez Vera,168b S. Roe,36 O. Røhne,134 R. Röhrig,115 C. P. A. Roland,65 J. Roloff,59 A. Romaniouk,112 M. Romano,23b,23a N. Rompotis,90 M. Ronzani,124 L. Roos,136 S. Rosati,72a K. Rosbach,52 G. Rosin,102 B. J. Rosser,137 E. Rossi,46 E. Rossi,74a,74b E. Rossi,69a,69b L. P. Rossi,55b L. Rossini,68a,68b R. Rosten,14 M. Rotaru,27b J. Rothberg,148 D. Rousseau,132 G. Rovelli,70a,70b A. Roy,11 D. Roy,33c A. Rozanov,101 Y. Rozen,160 X. Ruan,33c F. Rubbo,153 F. Rühr,52 A. Ruiz-Martinez,174 A. Rummler,36 Z. Rurikova,52 N. A. Rusakovich,79 H. L. Russell,103 L. Rustige,38,47 J. P. Rutherfoord,7 E. M. Rüttinger,46,mm Y. F. Ryabov,138 M. Rybar,39 G. Rybkin,132 E. B. Rye,134 A. Ryzhov,123 G. F. Rzehorz,53 P. Sabatini,53 G. Sabato,120 S. Sacerdoti,132 H. F-W. Sadrozinski,146 R. Sadykov,79 F. 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Zwalinski36 (ATLAS Collaboration) 1 Department of Physics, University of Adelaide, Adelaide, Australia 2 Physics Department, SUNY Albany, Albany, New York, USA 3 Department of Physics, University of Alberta, Edmonton, Alberta, Canada 4a Department of Physics, Ankara University, Ankara, Turkey 4b Istanbul Aydin University, Istanbul, Turkey 4c Division of Physics, TOBB University of Economics and Technology, Ankara, Turkey 5 LAPP, Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS/IN2P3, Annecy, France 6 High Energy Physics Division, Argonne National Laboratory, Argonne, Illinois, USA 7 Department of Physics, University of Arizona, Tucson, Arizona, USA 8 Department of Physics, University of Texas at Arlington, Arlington, Texas, USA 9 Physics Department, National and Kapodistrian University of Athens, Athens, Greece 10 Physics Department, National Technical University of Athens, Zografou, Greece 11 Department of Physics, University of Texas at Austin, Austin, Texas, USA 12a Bahcesehir University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey 12b Istanbul Bilgi University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey 12c Department of Physics, Bogazici University, Istanbul, Turkey 12d Department of Physics Engineering, Gaziantep University, Gaziantep, Turkey 13 Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan 14 Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona, Spain 15a Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China 15b Physics Department, Tsinghua University, Beijing, China 15c Department of Physics, Nanjing University, Nanjing, China 15d University of Chinese Academy of Science (UCAS), Beijing, China 16 Institute of Physics, University of Belgrade, Belgrade, Serbia 17 Department for Physics and Technology, University of Bergen, Bergen, Norway 18 Physics Division, Lawrence Berkeley National Laboratory and University of California, Berkeley, California, USA 19 Institut für Physik, Humboldt Universität zu Berlin, Berlin, Germany 20 Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern, Switzerland 21 School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 22 Facultad de Ciencias y Centro de Investigaciónes, Universidad Antonio Nariño, Bogota, Colombia 052011-33 G. 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D 100, 052011 (2019) 23a INFN Bologna and Universita’ di Bologna, Dipartimento di Fisica, Italy 23b INFN Sezione di Bologna, Italy 24 Physikalisches Institut, Universität Bonn, Bonn, Germany 25 Department of Physics, Boston University, Boston, Massachusetts, USA 26 Department of Physics, Brandeis University, Waltham, Massachusetts, USA 27a Transilvania University of Brasov, Brasov, Romania 27b Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania 27c Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi, Romania 27d National Institute for Research and Development of Isotopic and Molecular Technologies, Physics Department, Cluj-Napoca, Romania 27e University Politehnica Bucharest, Bucharest, Romania 27f West University in Timisoara, Timisoara, Romania 28a Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovak Republic 28b Department of Subnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice, Slovak Republic 29 Physics Department, Brookhaven National Laboratory, Upton, New York, USA 30 Departamento de Física, Universidad de Buenos Aires, Buenos Aires, Argentina 31 California State University, California, USA 32 Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom 33a Department of Physics, University of Cape Town, Cape Town, South Africa 33b Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg, South Africa 33c School of Physics, University of the Witwatersrand, Johannesburg, South Africa 34 Department of Physics, Carleton University, Ottawa, Ontario, Canada 35a Faculté des Sciences Ain Chock, Réseau Universitaire de Physique des Hautes Energies— Université Hassan II, Casablanca, Morocco 35b Faculté des Sciences, Université Ibn-Tofail, Kénitra, Morocco 35c Faculté des Sciences Semlalia, Université Cadi Ayyad, LPHEA-Marrakech, Morocco 35d Faculté des Sciences, Université Mohamed Premier and LPTPM, Oujda, Morocco 35e Faculté des sciences, Université Mohammed V, Rabat, Morocco 36 CERN, Geneva, Switzerland 37 Enrico Fermi Institute, University of Chicago, Chicago, Illinois, USA 38 LPC, Université Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand, France 39 Nevis Laboratory, Columbia University, Irvington, New York, USA 40 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 41a Dipartimento di Fisica, Università della Calabria, Rende, Italy 41b INFN Gruppo Collegato di Cosenza, Laboratori Nazionali di Frascati, Italy 42 Physics Department, Southern Methodist University, Dallas, Texas, USA 43 Physics Department, University of Texas at Dallas, Richardson, Texas, USA 44 National Centre for Scientific Research “Demokritos”, Agia Paraskevi, Greece 45a Department of Physics, Stockholm University, Sweden 45b Oskar Klein Centre, Stockholm, Sweden 46 Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen, Germany 47 Lehrstuhl für Experimentelle Physik IV, Technische Universität Dortmund, Dortmund, Germany 48 Institut für Kern- und Teilchenphysik, Technische Universität Dresden, Dresden, Germany 49 Department of Physics, Duke University, Durham, North Carolina, USA 50 SUPA—School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom 51 INFN e Laboratori Nazionali di Frascati, Frascati, Italy 52 Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany 53 II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany 54 Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève, Switzerland 55a Dipartimento di Fisica, Università di Genova, Genova, Italy 55b INFN Sezione di Genova, Italy 56 II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany 57 SUPA—School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom 58 LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble, France 59 Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, Massachusetts, USA 60a Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei, China 052011-34 PROPERTIES OF JET FRAGMENTATION USING CHARGED … PHYS. REV. D 100, 052011 (2019) 60b Institute of Frontier and Interdisciplinary Science and Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University, Qingdao, China 60c School of Physics and Astronomy, Shanghai Jiao Tong University, KLPPAC-MoE, SKLPPC, Shanghai, China 60d Tsung-Dao Lee Institute, Shanghai, China 61a Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 61b Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 62 Faculty of Applied Information Science, Hiroshima Institute of Technology, Hiroshima, Japan 63a Department of Physics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China 63b Department of Physics, University of Hong Kong, Hong Kong, China 63c Department of Physics and Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China 64 Department of Physics, National Tsing Hua University, Hsinchu, Taiwan 65 Department of Physics, Indiana University, Bloomington, Indiana, USA 66a INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy 66b ICTP, Trieste, Italy 66c Dipartimento Politecnico di Ingegneria e Architettura, Università di Udine, Udine, Italy 67a INFN Sezione di Lecce, Italy 67b Dipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy 68a INFN Sezione di Milano, Italy 68b Dipartimento di Fisica, Università di Milano, Milano, Italy 69a INFN Sezione di Napoli, Italy 69b Dipartimento di Fisica, Università di Napoli, Napoli, Italy 70a INFN Sezione di Pavia, Italy 70b Dipartimento di Fisica, Università di Pavia, Pavia, Italy 71a INFN Sezione di Pisa, Italy 71b Dipartimento di Fisica E.Fermi, Università di Pisa, Pisa, Italy 72a INFN Sezione di Roma, Italy 72b Dipartimento di Fisica, Sapienza Università di Roma, Roma, Italy 73a INFN Sezione di Roma Tor Vergata, Italy 73b Dipartimento di Fisica, Università di Roma Tor Vergata, Roma, Italy 74a INFN Sezione di Roma Tre, Italy 74b Dipartimento di Matematica e Fisica, Università Roma Tre, Roma, Italy 75a INFN-TIFPA, Italy 75b Università degli Studi di Trento, Trento, Italy 76 Institut für Astro- und Teilchenphysik, Leopold-Franzens-Universität, Innsbruck, Austria 77 University of Iowa, Iowa City, Iowa, USA 78 Department of Physics and Astronomy, Iowa State University, Ames, Iowa, USA 79 Joint Institute for Nuclear Research, Dubna, Russia 80a Departamento de Engenharia Elétrica, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil 80b Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil 80c Universidade Federal de São João del Rei (UFSJ), São João del Rei, Brazil 80d Instituto de Física, Universidade de São Paulo, São Paulo, Brazil 81 KEK, High Energy Accelerator Research Organization, Tsukuba, Japan 82 Graduate School of Science, Kobe University, Kobe, Japan 83a AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Krakow, Poland 83b Marian Smoluchowski Institute of Physics, Jagiellonian University, Krakow, Poland 84 Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland 85 Faculty of Science, Kyoto University, Kyoto, Japan 86 Kyoto University of Education, Kyoto, Japan 87 Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka, Japan 88 Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina 89 Physics Department, Lancaster University, Lancaster, United Kingdom 90 Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom 91 Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics, University of Ljubljana, Ljubljana, Slovenia 92 School of Physics and Astronomy, Queen Mary University of London, London, United Kingdom 052011-35 G. AAD et al. PHYS. REV. D 100, 052011 (2019) 93 Department of Physics, Royal Holloway University of London, Egham, United Kingdom 94 Department of Physics and Astronomy, University College London, London, United Kingdom 95 Louisiana Tech University, Ruston, Louisiana, USA 96 Fysiska institutionen, Lunds universitet, Lund, Sweden 97 Centre de Calcul de l’Institut National de Physique Nucléaire et de Physique des Particules (IN2P3), Villeurbanne, France 98 Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid, Spain 99 Institut für Physik, Universität Mainz, Mainz, Germany 100 School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom 101 CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France 102 Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA 103 Department of Physics, McGill University, Montreal, Quebec, Canada 104 School of Physics, University of Melbourne, Victoria, Australia 105 Department of Physics, University of Michigan, Ann Arbor, Michigan, USA 106 Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan, USA 107 B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, Belarus 108 Research Institute for Nuclear Problems of Byelorussian State University, Minsk, Belarus 109 Group of Particle Physics, University of Montreal, Montreal, Quebec, Canada 110 P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia 111 Institute for Theoretical and Experimental Physics of the National Research Centre Kurchatov Institute, Moscow, Russia 112 National Research Nuclear University MEPhI, Moscow, Russia 113 D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow, Russia 114 Fakultät für Physik, Ludwig-Maximilians-Universität München, München, Germany 115 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München, Germany 116 Nagasaki Institute of Applied Science, Nagasaki, Japan 117 Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan 118 Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico, USA 119 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, Netherlands 120 Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, Netherlands 121 Department of Physics, Northern Illinois University, DeKalb, Illinois, USA 122a Budker Institute of Nuclear Physics and NSU, SB RAS, Novosibirsk, Russia 122b Novosibirsk State University Novosibirsk, Russia 123 Institute for High Energy Physics of the National Research Centre Kurchatov Institute, Protvino, Russia 124 Department of Physics, New York University, New York, New York, USA 125 Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo, Japan 126 The Ohio State University, Columbus, Ohio, USA 127 Faculty of Science, Okayama University, Okayama, Japan 128 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma, USA 129 Department of Physics, Oklahoma State University, Stillwater, Oklahoma, USA 130 Palacký University, RCPTM, Joint Laboratory of Optics, Olomouc, Czech Republic 131 Center for High Energy Physics, University of Oregon, Eugene, Oregon, USA 132 LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France 133 Graduate School of Science, Osaka University, Osaka, Japan 134 Department of Physics, University of Oslo, Oslo, Norway 135 Department of Physics, Oxford University, Oxford, United Kingdom 136 LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3, Paris, France 137 Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania, USA 138 Konstantinov Nuclear Physics Institute of National Research Centre “Kurchatov Institute”, PNPI, St. Petersburg, Russia 139 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania, USA 140a Laboratório de Instrumentação e Física Experimental de Partículas—LIP, Portugal 140b Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal 140c Departamento de Física, Universidade de Coimbra, Coimbra, Portugal 140d Centro de Física Nuclear da Universidade de Lisboa, Lisboa, Portugal 140e Departamento de Física, Universidade do Minho, Braga, Portugal 140f Universidad de Granada, Granada (Spain), Spain 052011-36 PROPERTIES OF JET FRAGMENTATION USING CHARGED … PHYS. REV. D 100, 052011 (2019) 140g Dep Física and CEFITEC of Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal 141 Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic 142 Czech Technical University in Prague, Prague, Czech Republic 143 Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic 144 Particle Physics Department, Rutherford Appleton Laboratory, Didcot, United Kingdom 145 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France 146 Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, California, USA 147a Departamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile 147b Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile 148 Department of Physics, University of Washington, Seattle, Washington, USA 149 Department of Physics and Astronomy, University of Sheffield, Sheffield, United Kingdom 150 Department of Physics, Shinshu University, Nagano, Japan 151 Department Physik, Universität Siegen, Siegen, Germany 152 Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada 153 SLAC National Accelerator Laboratory, Stanford, California, USA 154 Physics Department, Royal Institute of Technology, Stockholm, Sweden 155 Departments of Physics and Astronomy, Stony Brook University, Stony Brook, New York, USA 156 Department of Physics and Astronomy, University of Sussex, Brighton, United Kingdom 157 School of Physics, University of Sydney, Sydney, Australia 158 Institute of Physics, Academia Sinica, Taipei, Taiwan 159a E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia 159b High Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia 160 Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel 161 Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel 162 Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece 163 International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo, Japan 164 Graduate School of Science and Technology, Tokyo Metropolitan University, Tokyo, Japan 165 Department of Physics, Tokyo Institute of Technology, Tokyo, Japan 166 Tomsk State University, Tomsk, Russia 167 Department of Physics, University of Toronto, Toronto, Ontario, Canada 168a TRIUMF, Vancouver, British Columbia, Canada 168b Department of Physics and Astronomy, York University, Toronto, Canada, Canada 169 Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan 170 Department of Physics and Astronomy, Tufts University, Medford, Massachusetts, USA 171 Department of Physics and Astronomy, University of California Irvine, Irvine, California, USA 172 Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden 173 Department of Physics, University of Illinois, Urbana, Illinois, USA 174 Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia—CSIC, Valencia, Spain 175 Department of Physics, University of British Columbia, Vancouver, British Columbia, Canada 176 Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia, Canada 177 Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg, Germany 178 Department of Physics, University of Warwick, Coventry, United Kingdom 179 Waseda University, Tokyo, Japan 180 Department of Particle Physics, Weizmann Institute of Science, Rehovot, Israel 181 Department of Physics, University of Wisconsin, Madison, Wisconsin, USA 182 Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal, Germany 183 Department of Physics, Yale University, New Haven, Connecticut, USA 184 Yerevan Physics Institute, Yerevan, Armenia a Deceased. b Also at Department of Physics, King’s College London, London, United Kingdom. c Also at Istanbul University, Dept. of Physics, Istanbul, Turkey. d Also at Instituto de Fisica Teorica, IFT-UAM/CSIC, Madrid, Spain. e Also at TRIUMF, Vancouver, British Columbia, Canada. f Also at Department of Physics and Astronomy, University of Louisville, Louisville, Kentucky, USA. 052011-37 G. AAD et al. PHYS. REV. D 100, 052011 (2019) g Also at Physics Department, An-Najah National University, Nablus, Palestine. h Also at Department of Physics, California State University, Fresno, California, USA. i Also at Department of Physics, University of Fribourg, Fribourg, Switzerland. j Also at Physics Dept, University of South Africa, Pretoria, South Africa. k Also at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spain. l Also at Tomsk State University, Tomsk, and Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia. m Also at The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing, China. n Also at Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal. o Also at Universita di Napoli Parthenope, Napoli, Italy. p Also at Institute of Particle Physics (IPP), Canada. q Also at Department of Physics, University of Adelaide, Adelaide, Australia. r Also at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg, Russia. s Also at Department of Financial and Management Engineering, University of the Aegean, Chios, Greece. t Also at Department of Physics, California State University, East Bay, California, USA. u Also at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain. v Also at Department of Physics, University of Michigan, Ann Arbor, Michigan, USA. w Also at LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France. x Also at Graduate School of Science, Osaka University, Osaka, Japan. y Also at Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany. z Also at Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan. aa Also at Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, Netherlands. bb Also at Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia. cc Also at CERN, Geneva, Switzerland. dd Also at Department of Physics, Stanford University, Stanford, California, USA. ee Also at Manhattan College, New York, New York, USA. ff Also at Joint Institute for Nuclear Research, Dubna, Russia. gg Also at Hellenic Open University, Patras, Greece. hh Also at The City College of New York, New York, New York, USA. ii Also at Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China. jj Also at Department of Physics, California State University, Sacramento, USA. kk Also at Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia. ll Also at Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève, Switzerland. mm Also at Department of Physics and Astronomy, University of Sheffield, Sheffield, United Kingdom. nn Also at Louisiana Tech University, Ruston, Louisiana, USA. oo Also at School of Physics, Sun Yat-sen University, Guangzhou, China. pp Also at Institute for Nuclear Research and Nuclear Energy (INRNE) of the Bulgarian Academy of Sciences, Sofia, Bulgaria. qq Also at Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russia. rr Also at Department of Applied Physics and Astronomy, University of Sharjah, Sharjah, United Arab Emirates. ss Also at Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germany. tt Also at CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France. uu Also at National Research Nuclear University MEPhI, Moscow, Russia. vv Also at Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest, Hungary. ww Also at Giresun University, Faculty of Engineering, Giresun, Turkey. xx Also at Institute of Physics, Academia Sinica, Taipei, Taiwan. yy Also at LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3, Paris, France. zz Also at Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan, USA. 052011-38