Measurement of inclusive jet charged-particle fragmentation functions in Pb+Pb collisions at √sNN=2.76 TeV with the ATLAS detector

Article

Reference

Measurement of inclusive jet charged-particle fragmentation functions in Pb+Pb collisions at √sNN=2.76 TeV with the ATLAS detector

ATLAS Collaboration

ALEXANDRE, Gauthier (Collab.), et al.

Abstract

Measurements of charged-particle fragmentation functions of jets produced in ultra-relativistic nuclear collisions can provide insight into the modification of parton showers in the hot, dense medium created in the collisions. ATLAS has measured jets in sNN=2.76 TeV Pb+Pb collisions at the LHC using a data set recorded in 2011 with an integrated luminosity of 0.14 nb −1 . Jets were reconstructed using the anti- kt algorithm with distance parameter values R=0.2,0.3,and 0.4 . Distributions of charged-particle transverse momentum and longitudinal momentum fraction are reported for seven bins in collision centrality for R=0.4 jets with pTjet>100 GeV . Commensurate minimum pT values are used for the other radii. Ratios of fragment distributions in each centrality bin to those measured in the most peripheral bin are presented. These ratios show a reduction of fragment yield in central collisions relative to peripheral collisions at intermediate z values, 0.04≲z≲0.2 , and an enhancement in fragment yield for z≲0.04 . A smaller, less significant enhancement is observed at large z and large pT in central collisions.

ATLAS Collaboration, ALEXANDRE, Gauthier (Collab.), et al . Measurement of inclusive jet charged-particle fragmentation functions in Pb+Pb collisions at √sNN=2.76 TeV with the ATLAS detector. Physics Letters. B , 2014, vol. 739, p. 320-342

DOI : 10.1016/j.physletb.2014.10.065

Available at:

http://archive-ouverte.unige.ch/unige:55764

Disclaimer: layout of this document may differ from the published version.

1 / 1

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Measurement of inclusive jet charged-particle fragmentation functions in Pb + ^{Pb collisions at} √

s _NN = ² . 76 TeV with the ATLAS detector

.ATLAS Collaboration

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received11June2014

Receivedinrevisedform27October2014 Accepted30October2014

Availableonline4November2014 Editor:D.F.Geesaman

Measurements ofcharged-particlefragmentationfunctions ofjetsproducedinultra-relativisticnuclear collisionscanprovideinsightintothemodificationofpartonshowersinthehot,densemediumcreated in the collisions. ATLAShas measured jetsin √_s

NN=².76 TeV Pb+^{Pb collisions atthe LHC using a} datasetrecordedin2011withanintegratedluminosityof0.14 nb⁻¹.Jetswerereconstructedusingthe anti-ktalgorithmwithdistanceparametervaluesR=⁰.2,0.3,and 0.4.Distributionsofcharged-particle transverse momentum and longitudinal momentum fraction are reported for seven bins in collision centralityforR=⁰.4 jetswithp^jet_T >100 GeV.CommensurateminimumpTvaluesareusedfortheother radii.Ratiosoffragmentdistributionsineachcentralitybintothosemeasuredinthemostperipheralbin arepresented.Theseratiosshowareductionoffragmentyieldincentralcollisionsrelativetoperipheral collisionsatintermediatez values,0.04^z0.2,andanenhancementinfragmentyieldforz⁰.04.

A smaller,lesssignificantenhancementisobservedatlargez andlargepTincentralcollisions.

©2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/3.0/).FundedbySCOAP³.

1. Introduction

Collisionsbetweenlead nucleiattheLHC are thoughtto pro- duce a quark–gluonplasma (QGP), a formof stronglyinteracting matterinwhichquarksandgluonsbecomelocallydeconfined.One predictedconsequenceofQGPformationisthe“quenching”ofjets generatedinhard-scatteringprocessesduring theinitial stagesof thenuclearcollisions[1].Jetquenchingrefers,collectively,toaset of possiblemodifications ofparton showersby the QGPthrough interactions of the constituents of the shower with the colour charges in the plasma [2,3]. In particular, quarks and gluons in theshowermaybeelasticallyorinelasticallyscatteredresultingin bothdeflectionandenergylossoftheconstituentsoftheshower.

The deflection and the extra radiation associated with inelastic processes maybroaden the partonshower andeject partons out ofan experimental jet cone [4–9]. Asa result, jet quenchingcan potentiallybothsoftenthespectrumofthemomentumofhadrons insidethejetandreducethetotalenergyofthereconstructedjet.

Acompletecharacterization oftheeffectsofjet quenchingthere- forerequiresmeasurementsofboththesingle-jetsuppressionand thejetfragmentdistributions.

Observationsofmodifieddijetasymmetrydistributions[10–12], modified balance-jet transverse momentum (pT) distributions in

γ

+^{jet events [13], andsuppressed inclusivejet yield inPb}+^Pb collisionsattheLHC[14,15]are consistentwiththeoreticalcalcu-

E-mailaddress:atlas.publications@cern.ch.

lations of jet quenching. However, it has been argued that those measurements do not sufficiently discriminate between calcula- tions that make different assumptions regarding the relative im- portance ofthecontributions described above [16].Based on the above arguments,theoreticalanalyses areincompletewithoutex- perimental constraints on the theoretical description of jet frag- mentdistributions.

ThisLetterpresentsmeasurements ofcharged-particlejet frag- mentation functions in √

sNN=².76 TeV Pb+^{Pb collisions using} 0.14 nb⁻¹ofdatarecordedin2011.Thejetsusedinthemeasure- ments were reconstructed with the anti-kt [17] algorithm using distance parameter values R=⁰.2,0.3,and 0.4. Results are pre- sented for the charged-particle transverse momentum (^pch_T ^{) and} longitudinal momentum fraction (z≡ ^pch_T · ^pjet_T /|^pjet_T |^{2) distribu-} tions,

D

(

p_T

) ≡

¹ N_jet

dN_ch

dp^ch_T

,

(1)

D

(

z

) ≡

¹ N_jet

dNch

dz

,

(2)

ofchargedparticleswithp^ch_T >2 GeV producedwithinanangular range R=⁰.4 of the reconstructed jet directions forjets with p^jet_T >85, 92, and 100 GeV for R=⁰.2, 0.3, and 0.4, respec- tively.Here,R=

(φ)²+(

η

)² whereφ (

η

) isthediffer- ence inazimuthal angles (pseudorapidities)betweenthe charged http://dx.doi.org/10.1016/j.physletb.2014.10.065

0370-2693/©^{2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/3.0/).Fundedby SCOAP³.

ATLAS Collaboration / Physics Letters B 739 (2014) 320–342 321

particle and jet directions.¹ The p^jet_T thresholds for the three R valueswere chosento matchthe R-dependenceofthe measured transverse momentum of a typical jet. For simplicity, the terms

“fragmentation functions” are used to describe the distributions definedin Eq.(2) with the understanding that D(z) is different fromatheoreticalfragmentationfunction, D(z,Q²),calculatedus- ingunquenchedjetenergiesandwithnorestrictionontheangles ofparticleswithrespect tothe jetaxis.Earlier measurements by CMS of jet fragmentation functions [18] in Pb+^{Pb collisions at} theLHCshownosignificantmodification,buttheuncertaintieson thatmeasurement werenot sufficienttoexclude modificationsat thelevelof∼^{10%.CMSrecentlyreleaseda newresult[19]using} higherstatisticsdatafrom2011thatshowfragmentationfunction modifications which are consistent with the resultspresented in thisLetter.

2. Experimentalsetup

ThemeasurementspresentedinthisLetterwereperformedus- ingtheATLAScalorimeter,innerdetector,muonspectrometer,trig- ger,anddataacquisitionsystems[20].TheATLAScalorimetersys- temconsistsofaliquidargon(LAr)electromagnetic(EM)calorime- tercovering|

η

_|<3.2,asteel-scintillatorsamplinghadroniccalorime- tercovering |

η

|<1.7,a LAr hadroniccalorimetercovering 1.5<

|

η

|<3.2,andtwoLArforwardcalorimeters(FCal)covering3.2<

|

η

_|<4.9.Thehadroniccalorimeterhasthreesamplinglayers lon- gitudinal in shower depth and has a

η

_×φ granularity of 0.1×⁰.1 for |

η

|<2.5 and 0.2×⁰.2 for 2.5<|

η

|<4.9.² The EM calorimeters are segmented longitudinally in shower depth into three compartments with an additional pre-sampler layer.

The EM calorimeter hasa granularity that varies with layer and pseudorapidity,butwhichisgenerallymuchfinerthanthatofthe hadroniccalorimeter. The middle sampling layer, which typically hasthelargestenergydepositinEMshowers, hasagranularityof 0.025×⁰.025 over|

η

_|<2.5.

Theinner detector[21] measures chargedparticleswithin the pseudorapidity interval |

η

_|<2.5 using a combination of silicon pixel detectors, silicon microstrip detectors (SCT), and a straw- tubetransitionradiationtracker(TRT), all immersedina 2 Tax- ial magnetic field. All three detectors are composed of a barrel andtwo symmetricallyplaced end-capsections. The pixeldetec- toris composed of3layers of sensors withnominalfeature size 50 μm×400 μm.TheSCTbarrelsectioncontains4layersofmod- uleswith80 μmpitchsensors onbothsides, whileeachend-cap consistsofnine layers ofdouble-sidedmodules withradialstrips havinga meanpitch of 80 μm.The two sidesof each SCT layer inboth the barrel andthe end-caps havea relative stereoangle of40 mrad. The TRTcontains up to 73(160)layers of staggered strawsinterleavedwithfibresinthebarrel(end-cap).Chargedpar- ticles with p^ch_T ⁰.5 GeV typically traverse three layers of pixel sensors,fourlayers ofdouble-sided SCT sensors,and, inthe case of|

η

|<2.0,36TRTstraws.

Minimum bias Pb+^{Pb collisions were identified using mea-} surements from the zero degree calorimeters (ZDCs) and the minimum-biastriggerscintillator (MBTS)counters[20].TheZDCs are located symmetrically at z= ±^{140 m and cover} |

η

|>8.3.

1 ATLASusesaright-handedcoordinatesystemwithitsoriginatthenominalin- teractionpoint(IP)inthecentreofthedetectorandthez-axisalongthebeampipe.

Thex-axispointsfromtheIPtothecentreoftheLHCring,andthe y axispoints upward.Cylindricalcoordinates(r,φ)areusedinthetransverseplane,φbeingthe azimuthalanglearoundthebeampipe.Thepseudorapidityisdefinedintermsof thepolarangleθasη= −ln tan(θ/2).

2 Anexceptionisthethirdsamplinglayerthathasasegmentationof0.2×⁰.1 upto|η|=¹.4.

In Pb+^{Pbcollisions the ZDCsmeasure primarily} “spectator” neu- trons,whichoriginatefromtheincidentnucleianddonotinteract hadronically.TheMBTS detects chargedparticles over2.1<|

η

_|<

3.9 usingtwocountersplaced atz= ±³.6 m. MBTScountersare dividedinto16moduleswith8differentpositionsinazimuthand covering2different|

η

|^{intervals. Eachcounterprovides measure-} ment of both the pulse heights and arrival times of ionization energydeposits.

Events used in this analysis were selected for recording by a combination of Level-1 minimum-bias and High Level Trigger (HLT) jet triggers. The Level-1 trigger required a total transverse energy measured inthe calorimeterof greater than 10 GeV.The HLTjettriggerrantheofflinePb+^Pbjet reconstructionalgorithm, described below, for R=⁰.2 jets except for the application of the final hadronic energy scale correction. The HLT trigger se- lected events containing an R=⁰.2 jet with transverse energy ET>20 GeV.

3. Eventselectionanddatasets

Thisanalysisusesatotalintegratedluminosityof0.14 nb⁻¹ of Pb+^{Pb collisions recorded by ATLAS in 2011. Events selected by} theHLTjettriggerwererequiredtohaveareconstructedprimary vertexandatime differencebetweenhitsinthetwosidesofthe MBTS detector of less than 3 ns. The primary vertices were re- constructedfromcharged-particle trackswith p^ch_T >0.5 GeV.The trackswerereconstructedfromhitsintheinnerdetectorusingthe ATLAS track reconstruction algorithm described inRef. [22] with settingsoptimizedforthehighhitdensityinheavy-ioncollisions [23].Atotalof14.2millioneventspassedthedescribedselections.

ThecentralityofPb+^{Pbcollisionswas}characterizedby E^FCal_T , thetotal transverseenergymeasured inthe forwardcalorimeters [23].Jet fragmentationfunctionsweremeasuredinsevencentral- itybinsdefinedaccordingtosuccessivepercentilesofthe

E^FCal_T distributionorderedfromthemostcentraltothemostperipheral collisions:0–10%, 10–20%,20–30%,30–40%,40–50%, 50–60%,and 60–80%.Thepercentilesweredefinedaftercorrectingthe

E^FCal_T distributionfora2%minimum-biastriggerinefficiencythataffects themostperipheraleventswhicharenotincludedinthisanalysis.

The performance of the ATLAS detector and offline analysis in measuring jets and charged particles in the environment of Pb+^{Pb collisions was evaluated using a large Monte Carlo(MC)} eventsample obtainedby overlaying simulated[24] PYTHIA[25]

pp hard-scattering events at √

s= ².76 TeV onto 1.2 million minimum-bias Pb+^{Pb events recorded in 2011. The same num-} ber of PYTHIA events was produced for each of five intervals of

ˆ

p_T, the transverse momentum of outgoingpartons in the 2→² hard-scattering,withboundaries17,35,70,140,280,and560 GeV.

The detectorresponseto thePYTHIAevents was simulatedusing Geant4[26],andthesimulatedhitswerecombinedwiththedata fromtheminimum-biasPb+^{Pbeventstoproduce1.2millionover-} laideventsforeach ^pˆT interval.

4. Jetandcharged-particleanalysis

Chargedparticlesincludedinthefragmentationmeasurements were required to have at least two hits in the pixel detector, including a hit in the first pixel layer if the track trajectory makes such a hit expected, and seven hits in the silicon mi- crostripdetector.Inaddition,thetransverse (d0) andlongitudinal (z0sinθ) impact parameters of thetracks measured with respect to the primary vertex were required to satisfy |^d0/

σ

d₀|<3 and

|^z0sinθ/

σ

z|<3, where

σ

d0 and

σ

z are uncertainties on d0 and z₀sinθ,respectively,obtainedfromthetrack-fitcovariancematrix.

Table 1

Numberofjetsfortwocentralitybinsindataasafunctionoftheselectioncriteria applied.Eachlinespecifiesthenumberofjetspassingallcutsforthegivenlineand above.

Cutdescription Njet

0–10% 60–80%

All jets 41 191 2579

UE jet rejection 41 116 2570

Isolation 40 986 2554

Muon rejection 40 525 2523

Inactive area exclusion 39 548 2458

Trigger jet match 39 548 2458

JetswerereconstructedusingthetechniquesdescribedinRef.[14], whicharebrieflysummarizedhere.

Theanti-kt algorithmwasfirstruninfour-momentumrecombi- nationmode,on

η

_×φ=⁰.1×⁰.1 logicaltowersandforthree values of the anti-kt distance parameter, R=⁰.2,0.3, and 0.4.

Thetowerkinematicswereobtainedbysummingelectromagnetic- scale energies of calorimeter cells within the tower boundaries.

Then, an iterative procedure was used to estimate a layer- and

η

-dependent underlyingevent(UE) energy densitywhileexclud- ing actualjetsfromthat estimate. TheUE energywas subtracted fromeachcalorimetercellwithinthetowersincludedintherecon- structedjet.Thecorrectiontakesintoaccount acos 2φmodulation ofthecalorimeterresponseduetoellipticflowofthemedium[23]

whichisestimatedbymeasurementoftheamplitudeofthatmod- ulationinthecalorimeter.Thefinaljetkinematicswerecalculated via a four-momentum sum of all (assumed massless) cells con- tainedwithinthejetsusingsubtractedET values.Acorrectionwas applied to the reconstructed jet to account forjets not excluded oronlypartially excluded fromtheUE estimate. Then,a final jet

η

- and ET-dependenthadronicenergyscalecalibrationfactorwas applied.

Afterthereconstruction, additionalselectionswere appliedfor thepurposesofthisanalysis.“UEjets”generatedbyfluctuationsin theunderlyingevent,wereremovedusingtechniquesdescribedin Ref.[14].

To prevent neighbouring jets from distorting the measure- ment of the fragmentation functions, jets were required to be isolated. The isolation cut required that there be no other jet within R=^{1 having p}T>p^iso_T where p^iso_T ,theisolation thresh- old, is set to half of the analysis threshold for each R value, p^iso_T =⁴².5, 46, and 50 GeV for R=⁰.2, 0.3, and 0.4, respec- tively.To prevent muons fromsemileptonic heavy-flavourdecays from influencing the measured fragmentation functions, all jets with reconstructed muons having p_T>4 GeV within a cone of size R=⁰.4 were excluded fromtheanalysis. To prevent inac- tive regions in the calorimeters from producing artificial high z fragments,jetswere requiredtohavemorethan90%oftheir en- ergy containedwithin fully functionalregions of the calorimeter.

Finally, all jets included in the analysis were required to match HLTjetsreconstructedwithtransversemomenta greaterthanthe triggerthresholdof20 GeV.TheHLTjetswerefoundtobefullyef- ficientforthejetkinematicselectionusedinthisanalysis.Table 1 showstheimpactofthecutson thenumberofmeasuredjetsin central (0–10%)andperipheral (60–80%)collisions. Allthesecuts togetherretainmorethan96%ofalljets.

5. Jetandtrackreconstructionperformance

The performance of the ATLAS detector and analysis proce- duresinmeasuring jetswas evaluatedfromtheMC sampleusing theproceduresdescribedinRef.[14].ReconstructedMC jetswere matchedto“truth”jetsobtainedbyseparatelyrunningtheanti-k_t

Table 2

Therelationshipbetweenthemeantruth-jettransversemomenta,^pTjettrue^,andcor- respondingreconstructedjettransversemomenta,pTjet

rec.Samplevaluesofαandβ obtainedfromlinearfitsto^pTjet

true(^pTjet

rec)(seetext)accordingtoEq.(3)andthe resultingpTjet

trueforpTjet

rec=100 GeV.

Centrality Jet R α β(GeV) ^pTjettrue(100 GeV) 0–10% 0.2 0.995±⁰.003 −⁷.6±⁰.5 91.9 GeV 60–80% 0.2 0.989±0.002 −6.0±0.3 92.9 GeV 0–10% 0.4 1.027±0.004 −17.7±0.5 85.0 GeV 60–80% 0.4 0.964±0.002 −2.3±0.2 94.1 GeV

algorithm onthe final-statePYTHIAparticles³ forthethreejet R values used in this analysis. For the jet fragmentation measure- ments, the most important aspect of the jet performance is the jet energy resolution (JER). For jet energies ^{100 GeV, the JER} incentral (0–10%)collisionsfor R=⁰.4 jetshascomparablecon- tributions from UE fluctuations and “intrinsic” resolution of the calorimetricjetmeasurement.ForperipheralcollisionsandR=⁰.2 jets, the intrinsic calorimeter resolution dominates the JER. The value of JER evaluated forjetswith pT=^{100 GeV in0–10% col-} lisionsis0.18,0.15,and0.13forR=⁰.4,R=⁰.3,andR=⁰.2 jets, respectively.

ThecombinationofthefiniteJERandthesteeply fallingjet pT spectrumproducesanetmigrationofjetsfromlowerpTtohigher p_T values(hereafterreferredtoas“upfeeding”)suchthatajetre- constructedwithagivenp_T^jet_reccorresponds,onaverage,toalower truth-jet pT, ^pTjet

true^.Therelationship between^pTjet

true^{and p}Tjet rec was evaluated from the MC data set for the different centrality binsandthreeR valuesusedinthisanalysis.Forthejet p_T^jet_recval- ues usedinthisanalysis, that relationship iswell described by a lineardependence,

pTjet true

= α

pTjet

rec

+ β.

(3)

Sample values for

α

and β and the resulting ^pTjet

true ^{values for} R=⁰.2 and R=⁰.4 jets in peripheral andcentral collisions are listed in Table 2. The extracted relationships between pTjet

rec and ^pTjet

true ^{will be used inthe} fragmentationanalysis to correctfor theaverageshiftinthemeasuredjetenergy.

MC studies indicate that the efficiency forPYTHIA jets to be reconstructed andtopassUE jetrejection exceeds98% for p^jet_T >

60 GeV inthe0–10%centralitybin.Forkinematicselectionofjets usedinthisstudy,thejetreconstructionwasfullyefficient.

Theefficiencyforreconstructingchargedparticleswithinjetsin Pb+^{PbcollisionswasevaluatedusingtheMCsample.Fig. 1shows} comparisons of distributions offour importanttrack-quality vari- ables between data and MC simulation for reconstructed tracks over a narrow p^ch_T interval, 5<p^ch_T <7 GeV, to minimize the impact ofdifferences inMC anddatacharged-particle p^ch_T distri- butions. The ratios of the data to MC distributions also shown in the figure indicate better than1% agreementin the

η

depen- denceoftheaveragenumberofpixelandSCThitsassociatedwith the tracks. The distributions of d0 and z0sinθ agree to ^10%

except in the tails of the distributions, which contribute a neg- ligible fraction of the distribution. For the purpose of evaluating the track reconstruction performance and for the evaluation of response matricesthat are used in the unfolding (described be- low), the reference “truth” particles were taken from the set of final-state PYTHIA charged particles. These were matched to re-

3 Final-statePYTHIAparticlesaredefinedasallgeneratedparticleswithlifetimes longerthan0.3·¹⁰⁻¹⁰s originatingfromtheprimaryinteractionorfromsubse- quentdecayofparticleswithshorterlifetimes.

ATLAS Collaboration / Physics Letters B 739 (2014) 320–342 323

Fig. 1. ComparisonbetweendataandMCdistributionsforfourdifferentcharged-particlereconstructionselectionparameters.Thedistributionsareshownforthe0–10%

centralitybinandfor charged-particletransversemomentaintherange5<p^ch_T <7 GeV.Top:averagenumberofpixel (left)andSCT(right) hitspertrack.Bottom:

distributionoftrackimpactparameterswithrespecttothereconstructedprimaryvertex;bothtransverse,d0(left),andlongitudinal,z0sinθ(right),impactparametersare shown.RatiosofdistributionsindatatothoseinMCsimulationareshownforeachquantity.

constructedchargedparticlesusingassociations betweendetector hitsandtruth tracksrecorded by the ATLAS Geant4simulations.

Truthparticles forwhich nomatchingreconstructed particlewas foundwereconsideredlostduetoinefficiency.

The charged-particle reconstruction efficiency,

ε

(pT,

η

), was evaluated separately in each of the seven centrality bins used in this analysis for truth particles within R=⁰.4 of R=⁰.4 truth jets having pTjet

true>100 GeV. Fig. 2 shows the efficiency asa functionoftruth-particle pT averagedover |

η

_|<1 (top) and 1<|

η

|<2.5 (bottom) forthe 0–10% and60–80% centralitybins.

ForpT<8 GeV,

ε

(pT,

η

)wasdirectlyevaluated usingfinebinsin pT and

η

.For pT>8 GeV the pT dependence ofthe efficiencies wereparameterizedseparatelyinthetwopseudorapidityintervals shownin Fig. 2using a functional form that describestrends at low pT aswell asathighpT.Anexampleoftheresultingparam- eterizations is shownby the solid curves in Fig. 2. A centrality- dependent systematic uncertainty in the parameterized efficien- cies,shown by the shaded bands inFig. 2, was evaluated based onboththeuncertaintiesintheparameterizationandonobserved variationsoftheefficiencywithpT,whichlargelyresultfromloss ofhitsintheSCTathigherdetectoroccupancy.Thus,thesystem- aticuncertaintyin the60–80% centrality binissmall becauseno significant variation ofthe efficiency is observed atlow detector occupancy,while theuncertainties arelargestforthe0–10% cen- tralitybinwiththelargestdetectoroccupancies.

The efficiencies shown in Fig. 2 decrease by about 12% be- tween the |

η

|<1 interval covered by the SCT barrel and the 1<|

η

_|<2.5 intervalcoveredprimarilybytheSCTend-cap. More significantlocalizeddropsinefficiencyofabout20%areobserved over 1<|

η

|<1.2 and 2.3<|

η

|<2.5 correspondingto thetran- sitionbetweentheSCTbarrelandend-capandthe detectoredge respectively. Toaccount forthisand other localizedvariations of thehigh p_T reconstructionefficiencywithpseudorapidity,thepa- rameterizations in Fig. 2 for pT>8 GeV are multiplied by an

η

-dependent factorevaluated in intervalsof0.1 units to produce

ε

(p_T,

η

).

6. Fragmentationfunctionsandunfolding

Jetsused forthe fragmentationmeasurements presented here were required to have p^jet_T >85, 92 and 100 GeV for R=⁰.2, 0.3, and 0.4 jets,respectively. Thejet thresholdsfor R=⁰.3 and R =⁰.2 jets represent the typical energy measured with the smallerjet radii foran R=⁰.4 jetwith pT=^{100 GeV.Jetswere} alsorequiredtohaveeither0<|

η

|<1 or1.2<|

η

|<1.9.There- strictionofthemeasurementto|

η

_|<1.9 avoidstheregionatthe detectoredgewithreducedefficiency(|

η

_|>2.3).Theexclusionof therange1<|

η

|<1.2 removesfromthemeasurementjetswhose large-z fragments,which are typically collinearwiththe jet axis, would be detected in thelower-efficiency

η

region spanning the gap between SCT barrel and end-cap. While this exclusion does

Fig. 2. Charged-particlereconstructionefficiencyasafunctionoftruthpT,for0–10%

(red)and60–80%(blue)centralitybinsintheregion|η|<1 (top)and1<|η|<2.5 (bottom).ThepTvaluesforthe0–10%pointsareshiftedforclarity.Thesolidcurves showparameterizationsofefficiencies.Theshadedbandsshowthesystematicun- certaintyintheparameterizedefficiencies(seetext).(Forinterpretationoftheref- erencestocolorinthisfigurelegend,thereaderisreferredtothewebversionof thisarticle.)

notsignificantlychangetheresultofthemeasurement,itreduces thesystematicuncertaintiesatlarge z orp^ch_T .

Thefragmentationfunctionsweremeasured forchargedparti- cleswithp^ch_T >2 GeV withinanangularrangeR=⁰.4 ofthejet directionforall three R values usedin thejet reconstruction. To reduce the effectsof theUE broadeningof thejet position mea- surement,forR=⁰.3 andR=⁰.4 jets,thejetdirectionwastaken from that of the closest matching R=⁰.2 jet within R=⁰.3 when such a matching jet was found. For each charged particle, thelongitudinaljetmomentumfraction, z,wascalculatedaccord- ingto

z

=

^pchT

p^jet_T cos

R

,

(4)

whereR hererepresentstheanglebetweenthechargedparticle andjetdirections.⁴

ChargedparticlesfromtheUEcontributea p^ch_T- andcentrality- dependent background to the measurement that must be sub- tracted to obtain the true fragmentation functions. The contri- bution of the UE background was separately evaluated for R= 0.2, 0.3, and 0.4 jetsineventshavingatleastonesuchjetabove thejet p_T thresholdsusingagridofR=⁰.4 conesthatspanned the full coverage of the inner detector. Any such cone having a chargedparticlewith p^ch_T >6 GeV was assumedto beassociated

4 TheR isaboost-invariantreplacementforthepolarangleθ.

witha realjet intheeventandwas excludedfromthe UEback- ground determination.The threshold of6 GeV was chosen to be highenoughtoavoidbiasoftheUE p^ch_T distribution.

The resulting per-jet UE charged-particle yields, dn^UE_ch/dp^ch_T were evaluated over2<p^ch_T <6 GeV as a function of p^ch_T , p^jet_T , and

η

^jet,averagedoverall conesinalleventswithinagivencen- tralitybinaccordingto:

dn^UE_ch dp^ch_T

=

¹

Ncone

N_ch^cone

(

p^ch_T

,

p^jet_T

, η

^jet

)

p^ch_T

.

(5)

Here Ncone represents thenumberof backgroundcones having a jet of agiven radiusabove the corresponding p^jet_T threshold,and N^cone_ch representsthenumberofchargedparticlesinagiven p^ch_T bininallsuch conesevaluatedforjetswithagiven p^jet_T and

η

^jet. Not shown in Eq. (5) is a correction factor that was applied to each backgroundconetocorrectforthe differenceintheaverage UE-particleyieldatagivenp^ch_T betweenthe

η

positionofthecone and

η

^jet,andaseparatecorrectionfactortoaccountforthediffer- ence inthe elliptic flow modulation atthe φ position of the UE coneandφ^jet.Thatcorrectionwasbasedonaparameterizationof the p^ch_T andcentralitydependenceofpreviously measuredelliptic flowcoefficients, v2[23].

By evaluating the UE contribution only from events contain- ingjetsincludedintheanalysis,thebackgroundautomaticallyhas thecorrectdistributionofcentralitieswithinagivencentralitybin.

The dn^UE_ch/dp^ch_T isobserved tobe independentof p^jet_T both inthe dataandMCsimulation.Thatobservationexcludesthepossibility that the upfeeding ofjets in p^jet_T dueto the finite JER could in- duce adependenceoftheUEonjet p_T.However,such upfeeding was observedtoinduce inthe MCeventsa p^jet_T -independent,but centrality-dependent mismatchbetween the extracted dn^UE_ch/dp^ch_T and the actual UE contribution to reconstructed jets. That mis- matchwasfoundtoresultfromintrinsiccorrelationsbetweenthe charged-particle densityintheUE andthe MC p^jet_T error,p^jet_T = p_T^jet_rec−^pTjet

true.Inparticular,jetswithpositive(negative)p^jet_T are found to have an UE contribution larger(smaller) than jetswith p^jet_T ∼^{0.Duetothenetupfeedingonthefallingjetspectrum,the} selectionofjetsaboveagivenp^jet_T thresholdcausestheUEcontri- bution tobelarger thanthatestimatedfromtheabove-described procedure. The average fractional mismatchin the estimated UE backgroundwasfoundtobeindependentof p^ch_T andtovarywith centralitybyfactorsbetween1.04–1.08,1.07–1.10,and1.12–1.15for R=⁰.2, 0.3, and 0.4,respectively.The measureddn^UE_ch/dp^ch_T val- uesinthedatawerecorrectedbythesesamefactorsbeforebeing subtracted.

Two different sets of charged-particle fragmentation distribu- tionsweremeasuredforeachcentralitybinandR value:

D^meas

(

pT

) ≡

¹

ε

1 N_jet

N_ch

p^ch_T

−

^dn

UE ch

dpT

,

(6)

and

D^meas

(

z

) ≡

¹

ε

1 N_jet

Nch

z

−

^dnUEch dp_T

p^ch_T=zp^jet_T

,

(7)

where Njetrepresentsthetotalnumberofjetspassingtheabove- describedselectioncutsinagivencentralitybin,andNch repre- sentsthenumberofmeasuredchargedparticleswithinR=⁰.4 ofthe jetsingivenbinsof p^ch_T andz,respectively. Theefficiency correction, 1/

ε

,was applied ona per-particlebasis usingthe pa- rameterizedMCefficiency,

ε

(p_T,

η

),assumingp_T^ch_true=^pTch

rec.While

ATLAS Collaboration / Physics Letters B 739 (2014) 320–342 325

Fig. 3. Measuredandunfolded D(z)distributionsforR=0.4 and R=0.2 jetsincentral(0–10%)andperipheral(60–80%)collisions.Topleft:R=0.4 D^meas(z)and D(z) distributions,bottomleft:ratiosofmeasuredtounfoldedR=0.4 D(z)distributionswiththe0–10%shiftedby+1 forclarity.Topmiddleandright:central-to-peripheral ratiosofmeasured(R^meas_D(z))andunfolded(RD(z))distributionsforR=⁰.4 andR=⁰.2,respectively.Bottommiddleandright:ratioofR^meas_D(z) toRD(z)forR=⁰.4 andR=⁰.2, respectively.

Fig. 4. MeasuredandunfoldedD(pT)distributionsforR=0.4 andR=0.2 jetsincentral(0–10%)andperipheral(60–80%)collisions.Topleft:R=0.4 D^meas(pT)andD(pT) distributions,bottomleft:ratiosofmeasuredtounfoldedR=0.4 D(pT)distributionswiththe0–10%shiftedby+1 forclarity.Topmiddleandright:central-to-peripheral ratiosofmeasured(R^meas_D(p

T))andunfolded(RD(pT))distributionsforR=⁰.4 andR=⁰.2,respectively.Bottommiddleandright:ratioofR^meas_D(p

T) toRD(pT)forR=⁰.4 and R=⁰.2,respectively.

that assumption is not strictly valid, the efficiency varies suffi- ciently slowly with pTch

true that the error introduced by this as- sumptionis1% everywhere.

The measured D^meas(z) distributions for R=⁰.4 jets in the 0–10% and60–80%centralitybinsareshowninthetopleftpanel in Fig. 3. The top middle panel shows the ratio of D^meas(z) be- tweencentral(0–10%)andperipheral(60–80%)collisions, R^meas_D(z) ≡ D^meas(z)|0–10/D^meas(z)|60–80.Forcomparison,the D^meas(z)ratiois shownon the top right panel for R=⁰.2 jets.Similar plots are shownin Fig. 4 but for D^meas(pT). The D^meas(z) ratios for both R=⁰.2 and R=⁰.4 indicatean enhanced fragment yield atlow z, z⁰.04,in jets in the 0–10% centrality bincompared to jets inthe60–80%centralitybinanda suppressedyieldoffragments withz∼⁰.1.Similar resultsareobservedin the D^meas(p_T)ratios overthe corresponding p_T ranges.The R=⁰.2 D^meas(z) andthe R=⁰.2 and R=⁰.4 D^meas(p_T) ratios rise above one for z⁰.2

or pT^{25 GeV. However, the ratios differ from one by only} 1–2

σ

(stat).NosuchvariationsoftheD^meas(z)andD^meas(pT)dis- tributions withcentralityasseen inthedataare observedinthe MCsimulation.Thecentral-to-peripheralratiosofMCD^meas(z)and D^meas(pT)distributions for R=⁰.4 and R=⁰.2 jets(not shown) arewithin3%ofoneforallz andpT.

The D^meas(pT)and D^meas(z) distributionswereunfolded using a one-dimensional Singular Value Decomposition (SVD) method [27] implemented in RooUnfold [28] to remove the effects of charged particle and jet pT resolution. The SVD method imple- ments aregularized matrix-basedunfolding that attemptsto “in- vert” the equation b=^{Ax, where x, is a true spectrum, b is an} observedspectrum,and A isthe“responsematrix”thatdescribes the transformation of x to b. For D(p_T), the unfolding accounts only for the charged-particle p_T resolution and uses a response matrix derived from the MC data set that describes the distri-

bution of reconstructed p^ch_T as a function of MC truth p^ch_T . The responsematrix A(pTch

rec,pTch

true) isfilledusingtheproceduresde- scribedin Section5. The D(z) unfoldingsimultaneously accounts forbothchargedparticleandjetresolutionusinga responsema- trix A(z^rec,z^true) with z^true (z^rec) calculated using purely truth (fully reconstructed) quantities. A cross-check was performed for the D(z)unfoldingthatincludedonlythejetenergyresolutionto ensurethatthecombinationofthetwosourcesofresolutioninthe one-dimensionalunfolding didnot distort theresult. Becausethe D^meas(z) and D^meas(pT) distributions were already corrected for thecharged-particle reconstructionefficiency,theresponsematri- ces were only populated with truth particles for which a recon- structed particle was obtainedand each entry was corrected for reconstructionefficiencysoastonotdistort theshapeofthetrue distributions.

Toensurethat statisticalfluctuationsin theMC pTjet

true or z^true distributionsdonotdistorttheunfolding,thosedistributionswere smoothed by fitting them to appropriate functional forms. The truth D(pT) distributions were fit to polynomials in ln(pT). The truth D(z)distributionswereparameterizedusinganextension of astandardfunctionalform[29],

D

(

z

) =

^a

·

^zd1

(

1

+

^c

−

^z

)

^d2

·

¹

+

^b

· (

1

−

^z

)

^d3

,

(8)

wherea,b,c,di werefreeparameters ofthefit.Thenon-standard additionalparameter“c”wasaddedtoimprovethedescriptionof thetruthdistributionatlargez.Whenfillingthetruthspectraand response matrices, theentries were weighted tomatch thetruth spectratothefitfunctions.

The SVD unfolding was performed using a regularization pa- rameter obtained from the ninth singular value (k=^{9) of the} unfoldingmatrix.Systematicuncertainties intheunfoldingdueto regularizationwereevaluatedbyvaryingk overtherange5–12for which the unfolding was observed to be neither significantly bi- asedbyregularizationnorunstable.Thestatisticaluncertaintiesin theunfolded spectrawere obtainedusingthepseudo-experiment method [27]. The largest absoluteuncertainty obtained over 5≤ k≤^{12 wastakentobethe}statisticaluncertaintyintheunfolded result.

Unfolded fragmentationfunctions, D(z), are showninthe top left panel in Fig. 3and compared to thecorresponding D^meas(z) distributions for R=⁰.4 jets in central (0–10%) and peripheral (60–80%)collisions.Similar resultsfor D(p_T)are showninFig. 4.

Forbothfigures, the ratiosofunfolded tomeasured distributions areshowninthebottomleftpanel withtheratiofor0–10%cen- tralitybinoffsetby +^{1.Thoseratiosshow thattheunfoldinghas} minimalimpactonthefragmentationfunctionsinbothperipheral andcentral collisions. Onlythe largest z point in the 0–10% bin changesbymorethan20%.

The middle and top right panels in Fig. 3 (Fig. 4) show for R=⁰.4 and R =⁰.2 jets, respectively the ratios of unfolded D(z)(D(pT)) distributions, RD(z)≡^D(z)|0–10/D(z)|60–80 (RD(p_T)≡ D(pT)|0–10/D(pT)|60–80),compared tothe ratiosbeforeunfolding.

The unfoldingreducesthe D(z) ratioslightlyatlow z but other- wise leavestheshapesunchanged. Toevaluate theimpact ofthe unfolding on thedifference between central andperipheral frag- mentationfunctions,themiddleandbottomrightpanelsinFig. 3 (Fig. 4) show theratio of R^meas_D(z) (R^meas_D(p

T)) to R_D(z)(R_D(pT)).Except forthelowestz point,theratioisconsistentwithoneovertheen- tirez range.Thus,thefeaturesobservedin R^meas_D(z) (R^meas_D(p

T)),namely theenhancementatlowz (pT)incentralcollisionsrelativetope- ripheralcollisions,thesuppressionatintermediatez (pT),andthe riseaboveoneatlargez (pT)arerobustwithrespecttotheeffects ofthechargedparticleandjet p_T resolution.

7. Systematicuncertainties

Systematic uncertainties in theunfolded D(z) and D(pT) dis- tributions can arise due to uncertainties in the jet energy scale andjetenergyresolution,fromsystematicuncertaintiesintheun- foldingprocedureincludinguncertaintiesintheshapeofthetruth distributions, uncertainties inthe chargedparticle reconstruction, andfromtheUEsubtractionprocedure.

Thesystematicuncertaintyduetothejetenergyscale(JES)has two contributions,anabsoluteJESuncertaintyandanuncertainty in the variation ofthe JESfrom peripheralto more central colli- sions.TheabsoluteJESuncertaintywasdeterminedbyshiftingthe transverse momentum of the reconstructed jetsaccording to the evaluationofthejetenergyscaleuncertaintyinRef.[30].Thetyp- icalsizeoftheJESuncertaintyforjetsusedinthisstudyis2%.The shiftintheJEShasnegligibleimpactontheratiosbetweencentral andperipheraleventsof D(pT) andD(z) distributionswhereas it has a clearimpact on the D(pT) and D(z) distributions. At high pT or z theresulting uncertainty reaches15%. The evaluation of centrality-dependent uncertainty on JES uses the estimates from Ref. [14]. The centrality-dependent JES uncertainty is largest for themostcentralcollisionswhereitreaches1.5%.Theevaluationof the jet energy resolution(JER) uncertaintyfollows the procedure applied inproton–proton jetmeasurements [31].The typical size ofJER uncertaintyforjetsused inthestudyislessthan 2%.This uncertainty is centrality independent since the dijets in MC are overlayed to real data.The resulting combined systematicuncer- taintyfromJERandcentrality-dependentJESontheratiosreaches 6% athigh p_T and10% athighz and ithas asimilar size inthe caseof D(pT)orD(z)distributionsasinthecaseoftheirratios.

The systematic uncertainty associated with the unfolding is connected withthe sensitivity ofthe unfolding procedure to the choice ofregularizationparameterandtotheparameterizationof thetruthdistribution.Theuncertaintyduetothechoiceofregular- izationparameterwasevaluatedbyvaryingk overtherange5–12.

The typicalsystematicuncertaintyisfound tobesmallerthan3%

or 2% for the D(z) or D(pT), respectively. The systematicuncer- tainty due to the parameterization of the truth distribution was determined from the statistical uncertainties of the fits to these distributions.Thissystematicuncertaintyisbelow1%or2%forthe D(z)orD(pT),respectively.

Theestimateofsystematicuncertaintyduetothetrackingeffi- ciencyfollowsmethodsoftheinclusivechargedparticlemeasure- ment [23].Theuncertaintyisquantified usingtheerrorofthefit oftrackingefficiencyandbyvaryingthetrackingselectioncriteria.

In the intermediate-p_T region the systematic uncertainty is less than 2%.InthelowandhighpT regionthesystematicuncertainty islarger,butlessthan 8%.

Anindependentevaluationofpotentialsystematicuncertainties in the central-to-peripheral ratios of D(z) and D(pT), dueto all aspects of theanalysis, was obtained by evaluatingthe deviation fromunityoftheMCcentral(0–10%)toperipheral(60–80%)ratios ofthefragmentationfunctions.Sincethereisnojetquenchingem- ployedinMCsimulation,theratiosareexpectednottoshowany deviationfromunity.Nodeviationfromunityisindeedobserved, the largestlocalizeddeviationis^{4%.Toquantify thedeviations} from unity, the MC RD(z) and RD(pT) ratios were fit by piece- wise continuous functions composed of linear functions defined overthez (p_T)rangesz=⁰.02–0.06 (p_T=^{2–6 GeV),z}=⁰.06–0.3 (pT=^{6–30 GeV),andz}>0.3 (pT>30 GeV)withparameterscon- strained such that the linear functions matchat the boundaries.

Theresultingfitsareusedasestimatesofthesystematicuncertain- tiesonallmeasured RD(z) andRD(p_T)ratiosreportedinSection8.

This systematic uncertainty is certainly correlated with andmay overlapwithothersystematicuncertaintiesdescribedabove.

ATLAS Collaboration / Physics Letters B 739 (2014) 320–342 327

Fig. 5. UnfoldedR=0.4 longitudinalchargedparticlefragmentationfunction,D(z)andthechargedparticletransversemomentumdistribution,D(pT),forthesevencentrality binsincludedinthisanalysis.Thestatisticaluncertaintiesareeverywheresmallerthanthepoints.Theyellowshadederrorbarsindicatesystematicuncertainties.Greylines connectingthecentralvaluesofdistributionsaretoguidetheeye.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversion ofthisarticle.)

Fig. 6. RatiosofD(z)forsixbinsincollisioncentralitytothoseinperipheral(60–80%)collisions,D(z)|cent/D(z)|60–80,forR=⁰.4 jets.Theerrorbarsonthedatapoints indicatestatisticaluncertaintieswhiletheyellowshadedbandsindicatesystematicuncertainties.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereader isreferredtothewebversionofthisarticle.)

8. Results

Theunfoldedfragmentationfunctions,D(z)andD(pT),forR= 0.4 jetsareshowninFig. 5forthesevencentralitybinsincluded intheanalysiswiththedistributionsfordifferentcentralitiesmul- tipliedby successivevaluesoftwoforpresentationpurposes.The shadederrorbandsindicate systematicuncertainties asdiscussed in the previous section. The D(p_T) and D(z) distributions have

similar shapes that are characteristic of fragmentation functions withasteepdropattheendpoint.

To evaluate the centrality dependence of the fragmentation functions,ratioswere calculatedofthe R=⁰.4 D(z)distributions for all centrality bins excluding the peripheral bin to the D(z) measuredintheperipheral,60–80%centralitybin.Theresultsare shownin Fig. 6. The ratios forall centralities show an enhanced yield oflow z fragments anda suppressed yield offragments at