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ATLAS CONF NoteATLAS-CONF-2017-004

Measurement of jet fragmentation in 5.02 TeVproton-lead and proton-proton collisions with the

ATLAS detector

The ATLAS Collaboration

5th February 2017

A measurement of the fragmentation functions of jets into charged particles in p+Pb colli-sions and pp collisions is presented. The analysis utilizes 28 nb−1 of p+Pb data and 26 pb−1

of pp data, both at √sNN = 5.02 TeV, collected in 2013 and 2015, respectively, with theATLAS detector at the LHC. The measurement is reported in the centre-of-mass frame ofthe nucleon–nucleon system for jets in the rapidity range |y∗ | <1.6 and with transverse mo-mentum 45 < pT < 260 GeV. Results are presented both as a function of the charged particletransverse momentum and as a function of the longitudinal momentum fraction of the parti-cle with respect to the jet. The pp fragmentation functions are compared with results fromMonte Carlo generators and two theoretical models. The ratios of the p+Pb to pp fragmen-tation functions are found to be consistent with unity.

c© 2017 CERN for the benefit of the ATLAS Collaboration.Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license.

1 Introduction

Heavy ion collisions at the Large Hadron Collider (LHC) are performed in order to produce and studythe quark-gluon plasma (QGP), a phase of strongly interacting matter which emerges at very high energydensities; a recent review can be found in Ref. [1]. Measurements of jets and the modifications to theirproperties in heavy ion collisions are sensitive to the properties of the QGP. In order to quantify jetmodifications in heavy ion collisions, proton-proton (pp) collisions are often used as a reference system.Using this reference, the rates of jet production are observed to be reduced in lead-lead (Pb+Pb) collisionscompared to expectations from the jet production cross section measured in pp interactions scaled bythe nuclear thickness function of Pb+Pb collisions [2, 3]. Charged particle longitudinal fragmentationfunctions are also observed to be modified in Pb+Pb collisions compared to pp collisions [4, 5].

In addition to final state differences, Pb+Pb collisions also differ from pp collisions in the initial statedue to the participation of the lead nucleus in the collision. Proton-nucleus collisions are used to pro-vide measurements of modifications from pp collisions that would be present in the initial conditions ofPb+Pb collisions as well. The inclusive jet production rate in proton-lead (p+Pb) collisions at 5.02 TeVwas measured [6–8] and found to have only small modifications after accounting for the partonic over-lap in p+Pb compared to pp collisions. Measurements made at the Relativistic Heavy Ion Collider withdeuteron-gold collisions yield similar results [9]. At high pT, charged hadrons originate from the frag-mentation of jets and provide a complementary observable to reconstructed jets. The CMS collaborationobserves a small excess in the charged particle spectrum measured in p+Pb for pT > 20 GeV comparedto pp collisions [10]. It is of great interest to measure the charged particle fragmentation functions inp+Pb and pp collisions for different intervals of jet pT at the LHC to connect the jet and charged particleresults. These measurements are necessary to both determine modifications to jet fragmentation in p+Pbcollisions and to establish a reference for jet fragmentation measurements in Pb+Pb.

In this note, the jet momentum structure in pp and p+Pb collisions is studied using the distributions ofcharged particles associated with jets which have a transverse momentum in the range 45–260 GeV. Jetsare reconstructed with the anti-kt algorithm [11] using a distance parameter R = 0.4. The associationis done via an angular matching ∆R < 0.41, where ∆R is the angular distance between the jet axis andthe charged particle position. Results on fragmentation functions are presented as a function of both,the charged particle transverse momentum with respect to the beam direction, pT, and the longitudinalmomentum fraction with respect to the jet direction, z ≡ pT cos∆R / pjet

T :

D(pT) ≡1

Njet

dNch

dpT, (1)

andD(z) ≡

1Njet

dNch

dz, (2)

where Nch is the number of charged particles and Njet is the number of jets under consideration. TheD(pT) distributions are the transverse momentum spectra of charged particles within a jet without the

1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of thedetector and the z-axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y axis pointsupward. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe.The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2). Angular distance is measured in units of

∆R ≡√

(∆η)2 + (∆φ)2.

2

projection onto the jet axis as the D(z) distributions have. The D(pT) distributions differ from typicalfragmentation functions but have been studied in Pb+Pb collisions at the LHC [4, 5].

The fragmentation functions in p+Pb are compared to√

s = 5.02 TeV pp data. In order to quantify anydifferences between p+Pb and pp collisions, the ratios of the fragmentation functions are measured:

RD(z) ≡D(z)pPb

D(z)pp(3)

and

RD(pT) ≡D(pT)pPb

D(pT)pp. (4)

The fragmentation functions as a function of z are more commonly used, but the distributions as a functionof pT are less sensitive to jet-related uncertainties and are also used in Pb+Pb measurements [4].

2 Experimental Setup

The measurements presented here are performed using the ATLAS calorimeter, inner detector, trigger,and data acquisition systems [12]. The calorimeter system consists of a sampling liquid argon (LAr)electromagnetic (EM) calorimeter covering |η | < 3.2, a steel–scintillator sampling hadronic calorimetercovering |η | < 1.7, a LAr hadronic calorimeter covering 1.5 < |η | < 3.2, and two LAr forward calorime-ters (FCal) covering 3.2 < |η | < 4.9. The hadronic calorimeter has three sampling layers longitudinalin shower depth. The EM calorimeters are segmented longitudinally in shower depth into three layersplus an additional pre-sampler layer. The EM calorimeter has a granularity that varies with layer andpseudorapidity, but which is generally much finer than that of the hadronic calorimeter. The minimum-bias trigger scintillators (MBTS) [12] detect charged particles over 2.1 < |η | < 3.9 using two segmentedcounters placed at z = ±3.6 m. Each counter provides measurements of both, the pulse heights and thearrival times of ionization energy deposits.

A two-level trigger system was used to select the p+Pb and pp collisions analyzed here. The first, thehardware-based trigger stage Level-1, is implemented with custom electronics. The second level is thesoftware-based High Level Trigger (HLT). Jet events were selected by the HLT with Level-1 seeds fromjet, minimum bias, and total-energy triggers. The total-energy trigger required a total transverse energymeasured in the calorimeter of greater than 5 GeV. The HLT jet trigger operated a jet reconstructionalgorithm similar to that applied in the offline analysis and selected events containing jets with transverseenergy thresholds ranging from 20 GeV to 75 GeV in p+Pb collisions and up to 85 GeV in pp collisions.In both, pp and p+Pb collisions, the highest threshold jet trigger sampled the full delivered luminosity.Minimum-bias p+Pb events were required to have at least one hit in a counter in each side of the MBTSdetector at Level-1 trigger.

The inner detector measures charged particles within the pseudorapidity interval |η | < 2.5 using a combi-nation of silicon pixel detectors, silicon microstrip detectors (SCT), and a straw-tube transition radiationtracker (TRT), all immersed in a 2 T axial magnetic field [12]. Each of the three detectors are composedof a barrel and two symmetric end-cap sections. The pixel detector is composed of three layers of sensorswith a nominal pixel size of 50 µm × 400 µm. Following the p+Pb data taking and prior to the 5 TeVpp data-taking an additional silicon tracking layer, the "insertable B-layer" (IBL) [13, 14], was installedcloser to the interaction point than the other three layers. The SCT barrel section contains four layers of

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modules with 80 µm pitch sensors on both sides, and each end-cap consists of nine layers of double-sidedmodules with radial strips having a mean pitch of 80 µm. The two sides of each SCT layer in both thebarrel and the end-caps have a relative stereo angle of 40 mrad. The TRT contains up to 73 (160) layersof staggered straws interleaved with fibres in the barrel (end-cap).

3 Event Selection and Data Sets

The p+Pb data used in this analysis were recorded in 2013. The LHC was configured with a 4 TeV protonbeam and a 1.57 TeV per nucleon Pb beam producing collisions with √sNN = 5.02 TeV and a rapidityshift of the centre-of-mass frame, ∆y = 0.465, relative to the lab frame. The data collection was splitinto two periods with opposite beam configurations. The first period consists of approximately 55% ofthe integrated luminosity with the Pb beam traveling to positive rapidity and the proton beam to negativerapidity. The remaining data was taken with the beams of protons and Pb nuclei swapped. The total p+Pbintegrated luminosity is 28 nb−1. Approximately 26 pb−1 of

√s = 5.02 TeV pp data from 2015 was used.

The instantaneous luminosity conditions provided by the LHC resulted in an average number of p+Pbinteractions per bunch crossing of 0.03. During pp data taking, the average number of interactions perbunch crossing varied from 0.6 to 1.3.

The p+Pb events selected are required to have a reconstructed vertex, at least one hit in each MBTSdetector, and a time difference measured between the two MBTS sides of less than 10 ns. The pp eventsused in this analysis are required to have a reconstructed vertex; no requirement on the signal in the MBTSdetector is imposed. In p+Pb collisions the event centrality is determined by the FCal in the Pb-goingdirection as in Ref. [6]. The p+Pb events used here belong to the 0–90% centrality interval.

The performance of the detector for measuring fragmentation functions in p+Pb collisions is evaluatedusing a sample of Monte Carlo (MC) events obtained by overlaying simulated hard-scattering eventsgenerated with Pythia version 6.423 (Pythia6) [15] onto minimum-bias p+Pb events recorded duringthe same data-taking period. A sample consisting of 2.4×107 Pythia6 pp events using the AUET2Btune [16] and the CTEQ6L1 parton distribution function (PDF) set [17], at 5.02 TeV and a rapidity shiftequivalent to that in the p+Pb collisions is generated. Half of the events are simulated with one beamconfiguration and the second half with the other. The detector response is simulated using GEANT4 [18,19], and the simulated hits are combined with those from the data event. A separate sample of 2.6×107

simulated 5.02 TeV Pythia version 8.212 (Pythia8) pp hard scattering events with the A14 tune [20] andNNPDF23LO PDF set [21] is used to evaluate the performance for measuring fragmentation functionsin the 2015 pp data. Finally, the fragmentation functions at the generator level in 1.5×107 5.02 TeVHerwig++ events [22] using the UEEE5 tune [23] and the CTEQ6L1 PDFs [17] are compared to thefragmentation function measurement in 5.02 TeV pp data.

4 Jet and Track Selection

Jets are reconstructed via the same heavy ion jet reconstruction algorithm used in previous measurementsin p+Pb collisions [6]. The anti-kt algorithm [11] is first run in four-momentum recombination mode, on∆η × ∆φ = 0.1 × 0.1 calorimeter towers with the anti-kt distance parameter R set to 0.4 and 0.2 (R = 0.4jets are used for the main analyisis and the R = 0.2 jets are used to improve the jet position resolutionas discussed below). The energies in the towers are obtained by summing the energies of calorimeter

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cells at electromagnetic energy scale within the tower boundaries. Then, an iterative procedure is used toestimate the layer- and η-dependent underlying event (UE) transverse energy density, while excluding theregions populated by jets. The UE transverse energy is subtracted from each calorimeter cell within thetowers included in the reconstructed jet and the four-momentum of the jet is updated accordingly. Then,a jet η- and pT-dependent correction factor derived from the simulation samples is applied to correct forthe calorimeter response. An additional correction based on in situ studies of the momentum balance ofjets recoiling against photons, Z bosons, and jets in other regions of the calorimeter is applied [24, 25].

Jets are required to have |y∗jet | < 1.6 (y∗jet ≡ y − ∆y), which is the largest symmetric overlap betweenthe two collision systems for which there is full charged particle tracking coverage within a jet cone ofR = 0.4. To prevent neighbouring jets from distorting the measurement of the fragmentation functions,jets are rejected if there is another jet with higher pT within a distance ∆R < 1.0. To reduce the effectsof the broadening of the jet position measurement due to the UE, for R = 0.4 jets, the jet direction wastaken from that of the closest matching R = 0.2 jet within ∆R = 0.3 when such a matching jet was found.All jets included in the analysis are required to have a pjet

T such that the jet trigger efficiency was greaterthan 99%. Jets originating from high-pT electrons [26] are excluded from this analysis.

The MC samples are used to evaluate the jet reconstruction performance and to correct the measureddistributions. The p+Pb jet performance is described in Ref. [6]; the jet performance in pp collisions isfound to be similar to that in p+Pb collisions. In the MC samples, the kinematics of the truth jets arereconstructed from primary particles2 with the anti-kt algorithm with radius R = 0.4. In these studies,generator level “truth jets” are matched to reconstructed jets with a ∆R < 0.2.

Tracks used in the analysis of p+Pb collisions are required to have at least one hit in the pixel detectorand at least six hits in the SCT. Tracks used in the analysis of pp collisions are required to have at least9 or 11 total silicon hits for |η| < 1.65 and |η| > 1.65, respectively, including both the pixel layers andthe SCT. This includes a hit in the first (first or second) pixel layer if expected by the track model for thep+Pb (pp) data. All tracks used in this analysis are required to have pT > 1 GeV. In order to suppress acontribution of secondary particles, the distance of closest approach of the track to the primary vertex isrequired be less than a value which varies from approximately 0.6 mm at pT = 1 GeV to approximately0.2 mm at pT = 20 GeV in the transverse plane and less than 1.5 mm in the longitudinal plane.

The efficiency for reconstructing charged particles within jets in p+Pb and pp collisions is evaluatedusing Pythia6 and Pythia8 MC samples, respectively, based on matching the tracks to MC primary“truth" particles. The efficiencies are determined separately for the two p+Pb running configurationsbecause the η regions of the detector used for the track measurement are different between the beamconfigurations. The charged particle reconstruction efficiencies as a function of the primary particletransverse momentum, ptruth

T , are shown in Figure 1 in pp and p+Pb collisions. The tracking efficienciesare determined in coarse ηtruth intervals. The ptruth

T dependence of the efficiencies is parameterized usinga fifth order polynomial in log(ptruth

T ) which describes trends in the range of particle ptruthT from 1.0 to 150

GeV. A constant efficiency value is used for particles with ptruthT > 150 GeV due to the limited size of the

MC samples. To account for the finer scale variations of the tracking efficiency with pseudorapidity, theparameterizations are multiplied by an η-dependent scale factor evaluated in ηtruth intervals of 0.1 units incoarse ptruth

T intervals. The dependence of the charged particle efficiency on pjetT is found to be negligible

for the pjetT selections used here. The contribution of reconstructed tracks which cannot be associated to a

generated primary particle in the MC samples produced without data overlay and the residual contribution

2 Primary particles are defined as particles with a mean lifetime τ > 0.3 × 10−10 s either directly produced in pp interactionsor from subsequent decays of particles with a shorter lifetime. All other particles are considered to be secondary.

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< -2.0truthη-2.5 <

< -1.0truthη-2.0 <

< 1.0truthη-1.0 <

< 2.0truthη1.0 <

Figure 1: Tracking efficiency as a function of ptruthT in pp collisions (left) and in p+Pb collisions (first beam config-

uration). The different sets of points show the ηtruth regions selected to determine the track reconstruction efficiencyas a function of ptruth

T . The different ηtruth selections between the pp and p+Pb efficiencies reflect the differentregions of the tracking system used in the two systems due to the boosted p+Pb system. The solid curves showparameterizations of efficiencies.

of tracks associated to secondary particles are together called the contribution from “fake” tracks. Thefraction of fake tracks is found to be below 2% of the tracks that pass the selection in any track and jetkinematic region. The contribution from these tracks to the fragmentation functions is subtracted fromthe measured fragmentation functions in both pp and p+Pb collisions.

5 Analysis Procedure

Reconstructed charged tracks are associated with a reconstructed jet if they fall within ∆R < 0.4 of thejet axis. For each of these particles the longitudinal momentum fraction, z, is calculated. The measuredfragmentation functions are constructed as:

D(z)meas ≡1

Njet

1ε(η,pT)

∆Nch(z)∆z

(5)

andD(pT)meas ≡

1Njet

1ε(η,pT)

∆Nch(pT)∆pT

, (6)

where ε(η,pT) is the track reconstruction efficiency, and Njet is the total number of jets in a given pjetT

bin. The quantities ∆Nch(z) and ∆Nch(pT) are the numbers of associated tracks within the given z or pTrange, respectively. The efficiency correction is applied on a track-by-track basis, assuming pT = ptruth

T .While that assumption is not strictly valid, the efficiency varies sufficiently slowly with ptruth

T that the errorintroduced by this assumption is negligible.

In p+Pb collisions contribution to the fragmentation functions from the UE charged particles needs tobe subtracted. This background is determined event-by-event for each measured jet by using a grid ofR = 0.4 cones that span the full coverage of the inner detector. The cones have a fixed distance betweentheir centers chosen such that the coverage of the inner detector is maximized while the cones do notoverlap each other. Any such cone having a charged particle with pT > 3.5 GeV is assumed to be

6

associated with a real jet and is excluded from the UE contribution. The estimated contribution from UEparticles is corrected to account difference in the average UE particle yield at given pT between the ηposition of the cone and η positions of the jet. The UE contribution is further corrected for the correlationbetween the actual UE yield underneath the jet and the jet energy resolution. This effect is corrected forby a multiplicative correction factors, dependent on pT (track z) and jet pT. The correction is estimated inMC samples as the ratio of the UE contribution calculated from tracks within the area of a jet that does nothave an associated truth particle and the UE contribution estimated by the cone method. Corrected UEcontributions are then subtracted from measured distributions. The maximum size of the UE contributionis 20% for the lowest pT (track z). No UE subtraction is performed for the pp measurement due tonegligible UE contribution.

The measured D(z) and D(pT) distributions are corrected for detector effects by means of a two-dimensionalBayesian unfolding procedure [27] using the RooUnfold package [28]. The unfolding procedure removesthe effect of bin migration due to the finite jet energy resolution and the track momentum resolution.Using the MC samples, four-dimensional response matrices are created using the truth and reconstructedpjet

T , and the truth and reconstructed z (or pT). Separate unfolding matrices are constructed for the p+Pband pp data. An independent bin-by-bin unfolding is used to correct the measured pjet

T spectra, which isneeded to normalize the unfolded fragmentation functions by the number of jets. To achieve better corre-spondence with the data, the simulated jet spectra and fragmentation functions are re-weighted to matchthe shapes of the reconstructed data. The number of iterations in the Bayesian unfolding is selected to bethe minimum number for which the relative change in the fragmentation function at z = 0.1 is smallerthan 0.2% per additional iteration in all pjet

T bins. This condition ensures the stability of the unfoldingand minimizes fluctuations due to the unfolding in the high z and pT regions. The resulting number ofiteration is driven by the low pjet

T intervals, which require the most iterations to converge. The systematicuncertainty due to the unfolding is typically much larger than the impact of the stability requirement,especially for the lowest pjet

T values used in this analysis (discussed in Section 6). Following this crite-rion, fourteen iterations are used for both the p+Pb and pp datasets. The analysis procedure is tested bydividing the MC events in half and using one half to generate response matrices with which the otherhalf is unfolded. Good recovery of the truth MC distributions is observed for the unfolded events and thedeviations from perfect closure are incorporated into the systematic uncertainties.

6 Systematic Uncertainties

The systematic uncertainties in the measurement of the fragmentation functions and their ratios are de-scribed in this section. The following sources of systematic uncertainty are considered: the jet energyscale (JES), the jet energy resolution (JER), the sensitivity of the unfolding to the prior, the residual non-closure of the unfolding and the tracking-related uncertainties. For each systematic variation the frag-mentation functions are re-evaluated and the difference between the varied and nominal fragmentationfunctions is used as an estimate of the uncertainty. The systematic uncertainties on the D(z) and D(pT)measurements in both collision systems are summarized in Figures 2 and 3, respectively, for two differentjet pT bins. The systematic uncertainties from each source are taken as uncorrelated and combined inquadrature to obtain the total systematic uncertainty.

The JES uncertainty is determined from in situ studies of the calorimeter response [24, 25, 29], and studiesof the relative energy scale difference between the jet reconstruction procedure in heavy-ion collisions andthe procedure used in pp collisions [30]. Each component that contributes to the JES uncertainty is varied

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Figure 2: Summary of the systematic uncertainties on the D(z) distributions in p+Pb collisions (top) and pp col-lisions (bottom) for jets in the 45–60 GeV pjet

T interval (left) and in the 160–210 GeV pjetT interval (right). The

systematic uncertainties due to JES, JER, unfolding, MC non-closure and tracking are shown along with the totalsystematic uncertainty from all sources.

separately by ± 1 standard deviation for each pjetT and the response matrix is computed accordingly. The

data are unfolded with these matrices. The JES uncertainty increases with increasing z and particle pT atfixed pjet

T and decreases with increasing pjetT .

The uncertainty on the fragmentation functions due to the JER is evaluated by repeating the unfoldingprocedure with modified response matrices, where an additional increase to the resolution of the recon-structed jet pjet

T is added with a Gaussian smearing. The smearing factor is evaluated using an in situtechnique involving studies of dijet energy balance [31, 32]. The systematic uncertainty due to the JERincreases with increasing z and particle pT at fixed pjet

T and decreases with increasing pjetT .

The unfolding uncertainty is estimated by generating the response matrices from the MC distributionswithout re-weighting in pjet

T and D(z). A separate uncertainty for residual limitations in the unfoldingprocedure was assigned by evaluating the non-closure of the unfolded distributions in simulations, asdescribed in Sec. 5. The magnitude of both of these uncertainties is typically below 5% except for thehighest z and track pT bins.

The uncertainties related to track reconstruction and selection originate from several sources. Uncertain-ties related to the fake rate, the material description in the simulation, and the track momentum wereobtained from studies in data and simulation described in Ref. [33]. The systematic uncertainty on thefake track rate is 30% in pp collisions and 50% in p+Pb. Since the contamination of fake tracks is at most

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Figure 3: Summary of the systematic uncertainties on the D(pT) distributions in p+Pb collisions (top) and ppcollisions (bottom) for jets in the 45–60 GeV pjet

T interval (left) and in the 160–210 GeV pjetT interval (right). The

systematic uncertainties due to JES, JER, unfolding, MC non-closure and tracking are shown along with the totalsystematic uncertainty from all sources.

2%, the resulting uncertainty on the fragmentation functions is at most 1%. The sensitivity of the trackingefficiency to the description of the inactive material in the MC samples is evaluated by varying the mate-rial description. This uncertainty is between 0.5 and 2% (depending on track η) in the track pT range usedin the analysis. The uncertainty on the track momentum from a possible detector mis-alignment results inan at most 1% uncertainty on the fragmentation functions. Measurements of muons in the inner detectorand in the muon spectrometer show that the track pT scale differs by up to 2% between the data and theMC simulations in pp collisions. This effect introduces additional uncertainty on fragmentation functionsin pp collisions up to 10%. Uncertainty on the tracking efficiency due to the high local track density in thecore of jets is 0.4% [34] for all pjet

T selections in this analysis. The uncertainty due to the track selection isevaluated by repeating the analysis with an additional requirement on the significance of the distance ofclosest approach of the track to the primary vertex. This uncertainty affects both the track reconstructionefficiency and the rate of fake tracks. The resulting uncertainty typically varies from 1% at low track pTto 5% at high track pT. Additionally, there is a systematic uncertainty due to the parameterization of theefficiency corrections. The size of the uncertainty is less than 1% on the fragmentation functions. Finally,the track-to-particle association requirements are varied. This variation affects the track reconstructionefficiency, the track momentum resolution, and the rate of fake tracks. After deriving new response ma-trices and efficiency corrections, the resulting systematic uncertainty on the fragmentation functions isfound to be less than 0.5%. Figures 2 and 3 present the total tracking uncertainty where all track-related

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Figure 4: Summary of the systematic uncertainties for RD(z) ratios, for jets in the 45–60 GeV pT interval (left) andin the 160–210 GeV pT interval (right). The systematic uncertainties due to JES, JER, unfolding, MC non-closureand tracking are shown along with the total systematic uncertainty from all sources.

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Figure 5: Summary of the systematic uncertainties for RD(pT) ratios, for jets in the 45–60 GeV pT interval (left) andin the 160–210 GeV pT interval (right). The systematic uncertainties due to JES, JER, unfolding, MC non-closureand tracking are shown along with the total systematic uncertainty from all sources.

systematic uncertainties are added in quadrature.

The correlations between the various systematic components in the two collision systems are consideredwhen taking the ratios of p+Pb to pp fragmentation functions. For the JES uncertainty each source ofuncertainty is classified as either correlated or uncorrelated between the two systems depending on itsorigin. The JER, unfolding and MC non-closure uncertainties are taken to be uncorrelated. For thetracking-related uncertainties the variation in the selection requirements, tracking in dense environments,fake rates, and parameterization of the efficiency corrections are taken as uncorrelated. The first threeof these are conservatively considered as uncorrelated because the tracking system was augmented withthe IBL and the tracking algorithm changed between the p+Pb and pp data-taking periods. For thecorrelated uncertainties the ratios are reevaluated applying the variation to both collision systems; theresulting variation in the ratio from the central values is used as the correlated systematic uncertainty.The uncertainties due to the track-to-particle matching and the inactive material in the MC samples aretaken as correlated between p+Pb and pp collisions. The total systematic uncertainties on the RD(z) andRD(pT) distributions are shown in Figures 4 and 5, respectively for two pjet

T intervals.

10

z

2−10 1−10 1

)

zD

(

4−10

2−10

1

210

410

610

810 -1 = 5.02 TeV, 26 pbs, pp

|<1.6jet *y|

ATLAS Preliminary

z

2−10 1−10 1

0 < 60 GeV x 10 jet

Tp45 <

1 < 80 GeV x 10 jet

Tp60 <

2 < 110 GeV x 10 jet

Tp80 <

3 < 160 GeV x 10 jet

Tp110 <

4 < 210 GeV x 10 jet

Tp160 <

5 < 260 GeV x 10 jet

Tp210 <

-1 = 5.02 TeV, 28 nbNNs+Pb, p0-90%

|<1.6jet *y|

ATLAS Preliminary

Figure 6: Fragmentation functions as a function of the track z in pp (left) and p+Pb collisions (right) for the pjetT

selections used in this analysis. The fragmentation functions in both collision systems are offset by multiplicativefactors for clarity as noted in the legend. The statistical uncertainties are shown as error bars and the systematicuncertainties are shown as shaded boxes. In many cases the statistical uncertainties are smaller than the markersize.

7 Results

The D(z) and D(pT) distributions in both collision systems are shown in Figures 6 and 7, respec-tively. Figure 8 compares the D(z) distribution in pp collisions at 5.02 TeV to the three event gener-ators (Pythia6, Pythia8, and Herwig++) using the tune and PDF sets described in Sec. 3 for the sixpjet

T intervals. The Pythia8 generator provides the best description of the data, generally agreeing withinabout 5% except for some deviations of 10% over the kinematic range used here. Pythia6 agrees withinapproximately 25% when compared with the central values of the data and Herwig++ agrees within ap-proximately 20% except for the highest z region where there are some larger deviations. Qualitativelysimilar agreement with these generators was reported by ATLAS in the measurement of fragmentationfunctions in 7 TeV pp collisions [35]. Figure 9 shows the pp fragmentation functions compared to twotheoretical calculations. These predictions use a slightly different definition of z that can introduce a dis-crepancy between the fragmentation functions of approximately 1%. The calculation in Ref. [36, 37]provides fragmentation functions with next-to-leading order (NLO) accuracy as well as a resummationof logarithms in the jet radius. The calculation in Ref. [38] is at NLO and uses the approximation thatthe jet cone is narrow. For the parton to charged hadron fragmentation functions, both calculations useDSS07 [39]. The uncertainties on the theoretical calculation are not evaluated, including the uncertaintyon DSS07 which is common to both calculations. The calculations are systematically higher than the data

11

[GeV] T

p1 10 210

) T

pD

(

4−10

2−10

1

210

410

610

810

| <1.6jet *y|

ATLAS

= 5.02 TeVs, pp -125 pb

Preliminary 5 < 260 GeV x 10 jet

Tp210 <

4 < 210 GeV x 10 jet

Tp160 <

3 < 160 GeV x 10 jet

Tp110 <

2 < 110 GeV x 10 jet

Tp80 <

1 < 80 GeV x 10 jet

Tp60 <

0 < 60 GeV x 10 jet

Tp45 <

[GeV] T

p1 10 210

) T

pD

( | <1.6jet *y|

ATLAS

= 5.02 TeV, 0-90%NNs+Pb, p -128 nb

Preliminary

Figure 7: Fragmentation functions as a function of the track pT in pp (left) and p+Pb collisions (right) for the pjetT

selections used in this analysis. The fragmentation functions in both collision systems are offset by multiplicativefactors for clarity as noted in the legend. The statistical uncertainties are shown as error bars and the systematicuncertainties are shown as shaded boxes. In many cases the statistical uncertainties are smaller than the markersize.

and agree generally within 20–30%. Larger deviations are observed at low and high z regions. The DSS07fragmentation functions have a minimum z of 0.05 and the calculations use extrapolated fragmentationfunctions in the region below z = 0.05.

Figures 10 and 11 show the ratios of fragmentation functions in p+Pb collisions to those in pp collisions,as a function of z and pT respectively for pjet

T from 45 to 260 GeV. Over the kinematic range selectedhere, the D(z) and D(pT) distributions show deviations from unity of up to approximately 5% (up to10% for 60–80 GeV jet selections) for z < 0.1 and pT < 10 GeV. The deviations are outside the reportedsystematic uncertainties by at most a couple of percent and always less than 1.5 σ of the systematicuncertainties. At higher z and pT values the ratios are consistent with unity. At the highest z points for the160–210 GeV and 210–260 GeV jet selections deviations from unity of approximately 1.4 σ and 2.4 σof combined statistic and systematic uncertainties, respectively are observed. This is not observed in theD(pT) distributions. In some pjet

T bins there is a slight decrease of the values of RD(z) and RD(pT) withincreasing z and pT; however, the effect is not significant within the systematic uncertainties.

12

z

1−10 1

sim

ulat

ion

/ dat

a

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1

1.5 PYTHIA6 AUET2B CTEQ6L1

< 60 GeV jet

Tp45 <

ATLAS Preliminary

-1 = 5.02 TeV, 25 pbs pp

z

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sim

ulat

ion

/ dat

a

PYTHIA8 A14 NNPDF23LO

< 80 GeV jet

Tp60 <

| < 1.6jet *y|

ATLASPreliminary

z

1−10 1

sim

ulat

ion

/ dat

a

HERWIG++ UEEE5 CTEQ6L1

< 110 GeV jet

Tp80 <

ATLASPreliminary

z

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sim

ulat

ion

/ dat

a

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1

1.5 PYTHIA6 AUET2B CTEQ6L1

< 160 GeV jet

Tp110 <

ATLAS Preliminary

-1 = 5.02 TeV, 25 pbs pp

z

2−10 1−10 1

sim

ulat

ion

/ dat

a

PYTHIA8 A14 NNPDF23LO

< 210 GeV jet

Tp160 <

| < 1.6jet *y|

ATLAS Preliminary

z

2−10 1−10 1

sim

ulat

ion

/ dat

a

HERWIG++ UEEE5 CTEQ6L1

< 260 GeV jet

Tp210 <

ATLAS Preliminary

Figure 8: Ratios of the truth level D(z) distributions from Pythia6, Pythia8, and Herwig++ to the unfolded ppdata for the six pjet

T selections used in this analysis. The statistical uncertainties are shown as error bars and thesystematic uncertainties on the data are shown as the shaded region around unity.

z

1−10 1

theo

ry /

data

0.5

1

1.5 < 60 GeV jet

Tp45 <

ATLAS Preliminary

-1 = 5.02 TeV, 25 pbs pp

z

1−10 1

theo

ry /

data

< 80 GeV jet

Tp60 <

| < 1.6jet *y|

ATLASPreliminary

z

1−10 1

theo

ry /

data

Kang et al. Kaufmann et al.

< 110 GeV jet

Tp80 <

ATLASPreliminary

z

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theo

ry /

data

0.5

1

1.5 < 160 GeV jet

Tp110 <

ATLAS Preliminary

-1 = 5.02 TeV, 25 pbs pp

z

2−10 1−10 1

theo

ry /

data

< 210 GeV jet

Tp160 <

| < 1.6jet *y|

ATLAS Preliminary

z

2−10 1−10 1

theo

ry /

data

Kang et al. Kaufmann et al.

< 260 GeV jet

Tp210 <

ATLAS Preliminary

Figure 9: Ratios of theoretical calculations from Ref. [36, 37] (solid points) and Ref. [38] (open points) to theunfolded pp D(z) distributions for the six pjet

T selections used in this analysis. The statistical uncertainties areshown as error bars and the systematic uncertainties on the data are shown as the shaded region around unity. Theuncertainties on the theoretical calculations are not shown.

13

z1−10 1

)z

D(

R

0.6

0.8

1

1.2

1.4 < 60 GeV jet

Tp45 <

|<1.6jet *y|ATLAS Preliminary

z1−10 1

)z

D(

R

< 80 GeV jet

Tp60 <

ATLAS Preliminary

, 0-90%-1 = 5.02 TeV, 28 nbNNs+Pb, p-1 = 5.02 TeV, 25 pbs , pp

z1−10 1

)z

D(

R

< 110 GeV jet

Tp80 <

ATLAS Preliminary

z2−10 1−10 1

)z

D(

R

0.6

0.8

1

1.2

1.4 < 160 GeV jet

Tp110 <

|<1.6jet *y|ATLAS Preliminary

z2−10 1−10 1

)z

D(

R < 210 GeV jet

Tp160 <

ATLAS Preliminary

, 0-90%-1 = 5.02 TeV, 28 nbNNs+Pb, p-1 = 5.02 TeV, 25 pbs , pp

z2−10 1−10 1

)z

D(

R

< 260 GeV jet

Tp210 <

ATLAS Preliminary

Figure 10: Ratios of fragmentation functions as a function of z in p+Pb to those in pp collisions for the six pjetT

intervals. The statistical uncertainties are shown as error bars and the total systematic uncertainties are shown asshaded boxes.

[GeV] T

p1 10

)T

pD

(R

0.6

0.8

1

1.2

1.4 < 60 GeV jet

Tp45 <

|<1.6jet *y|ATLAS Preliminary

[GeV] T

p1 10

)T

pD

(R

< 80 GeV jet

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ATLAS Preliminary

, 0-90%-1 = 5.02 TeV, 28 nbNNs+Pb, p-1 = 5.02 TeV, 25 pbs , pp

[GeV] T

p1 10

)T

pD

(R

< 110 GeV jet

Tp80 <

ATLAS Preliminary

[GeV] T

p1 10 210

)T

pD

(R

0.6

0.8

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1.2

1.4 < 160 GeV jet

Tp110 <

|<1.6jet *y|ATLAS Preliminary

[GeV] T

p1 10 210

)T

pD

(R

< 210 GeV jet

Tp160 <

ATLAS Preliminary

, 0-90%-1 = 5.02 TeV, 28 nbNNs+Pb, p-1 = 5.02 TeV, 25 pbs , pp

[GeV] T

p1 10 210

)T

pD

(R

< 260 GeV jet

Tp210 <

ATLAS Preliminary

Figure 11: Ratios of fragmentation functions as a function of pT in p+Pb to those in pp collisions for the six pjetT

intervals. The statistical uncertainties are shown as error bars and the total systematic uncertainties are shown asshaded boxes.

14

8 Summary

This paper presents the jet charged particle fragmentation functions for |y∗jet | < 1.6 and for pjetT from 45 to

260 GeV in √sNN = 5.02 TeV p+Pb and pp collisions. The pp fragmentation functions are compared topredictions from the Pythia6, Pythia8 and Herwig++ generators. The generators show deviations fromthe pp data of up to approximately 25%, depending on z and the choice of generator. Pythia8 matches thedata most closely. The pp D(z) distributions are also compared with two theoretical calculations basedon next-to-leading order QCD and DSS07 fragmentation functions. The calculations are systematicallyhigher than the data and agree generally within 20–30%, with larger deviations at low and high z regions.These measurements help constrain jet fragmentation in pp collisions. No evidence for modification of jetfragmentation in p+Pb collisions compared to pp collisions is observed. Finally, these measurements ofjet fragmentation functions for different intervals of jet transverse momentum provide necessary baselinemeasurements for Pb+Pb collisions.

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