Measurement of inclusive jet charged-particle fragmentation functions in Pb plus Pb collisions at root S-NN=2.76 TeV with the ATLAS detector

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

r

a

c

t

Articlehistory:

Received11June2014

Receivedinrevisedform27October2014 Accepted30October2014

Availableonline4November2014 Editor:D.F.Geesaman

Measurements ofcharged-particlefragmentationfunctions ofjetsproducedinultra-relativisticnuclear collisionscanprovideinsightintothemodificationofpartonshowersinthehot,densemediumcreated in the collisions. ATLAShas measured jetsin √sNN=2.76 TeV Pb+Pb collisions atthe LHC using a

datasetrecordedin2011withanintegratedluminosityof0.14 nb−1_{.Jetswerereconstructedusingthe}

anti-ktalgorithmwithdistanceparametervalues

R

=0.2,0.3,and 0.4.Distributionsofcharged-particle

transverse momentum and longitudinal momentum fraction are reported for seven bins in collision centralityfor

R

=0.4 jetswith

p

jet

T >100 GeV.Commensurateminimum

p

Tvaluesareusedfortheother

radii.Ratiosoffragmentdistributionsineachcentralitybintothosemeasuredinthemostperipheralbin arepresented.Theseratiosshowareductionoffragmentyieldincentralcollisionsrelativetoperipheral collisionsatintermediate

z values,

0.04z0.2,andanenhancementinfragmentyieldfor

z

0.04. A smaller,lesssignificantenhancementisobservedatlarge

z and

large

p

Tincentralcollisions.

©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 quenching there-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 consistentwiththeoretical

calcu- _{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 areincompletewithout ex-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.Thejetsusedinthe measure-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 (p



ch

T ) and longitudinal momentum fraction (z

≡ 

pch

T

· 

p jet T

/|

p jet T

|

2) distribu-tions, D(pT

)

≡

1 Njet dNch dpch_T

,

(1) D(z)

≡

1 Njet dNch dz

,

(2)

ofchargedparticleswithpch_T

>

2 GeV producedwithinanangular range



R

=

0

.

4 of the reconstructed jet directions forjets with

pjet_T

>

85

,

92

,

and 100 GeV for R

=

0

.

2

,

0

.

3

,

and 0

.

4, respec-tively.Here,



R

=



(φ)

2

_{+ (}

_η

₎

2 _where

_φ

₍

_

_η

_{) isthe} differ-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

)

,calculated us-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

ThemeasurementspresentedinthisLetterwereperformed us-ingtheATLAScalorimeter,innerdetector,muonspectrometer, trig-ger,anddataacquisitionsystems

[20]

.TheATLAScalorimeter sys-temconsistsofaliquidargon(LAr)electromagnetic(EM) calorime-tercovering

|

η

|

<

3

.

2,asteel-scintillatorsamplinghadronic calorime-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 T ax-ial magnetic field. All three detectors are composed of a barrel andtwo symmetricallyplaced end-capsections. The pixel detec-toris composed of3layers of sensors withnominalfeature size 50 μm

×

400 μm.TheSCTbarrelsectioncontains4layersof mod-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).Charged par-ticles with pch_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-handedcoordinatesystemwithitsoriginatthenominal} in-teractionpoint(IP)inthecentreofthedetectorandthez-axisalongthebeampipe.

Thex-axispointsfromtheIPtothecentreoftheLHCring,andthe y axispoints

upward.Cylindricalcoordinates

(

r, φ)areusedinthetransverseplane,

φ

beingthe azimuthalanglearoundthebeampipe.Thepseudorapidityisdefinedintermsof thepolarangle

θ

asη= −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 pch_T

>

0

.

5 GeV.The trackswerereconstructedfromhitsintheinnerdetectorusingthe ATLAS track reconstruction algorithm described inRef. [22] with settingsoptimizedforthehighhitdensityinheavy-ioncollisions

[23].Atotalof14.2millioneventspassedthedescribedselections. ThecentralityofPb

+

Pbcollisionswascharacterizedby



EFCal_T , thetotal transverseenergymeasured inthe forwardcalorimeters

[23].Jet fragmentationfunctionsweremeasuredinseven central-itybinsdefinedaccordingtosuccessivepercentilesofthe



EFCal_T

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



EFCal

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

pT, 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

+

Pbeventstoproduce1.2million over-laideventsforeach p

ˆ

T 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 (z0sin

θ

) impact parameters of thetracks measured with respect to the primary vertex were required to satisfy

|

d0

/

σ

d0

|

<

3 and

|

z0sin

θ/

σ

z

|

<

3, where

σ

d0 and

σ

z are uncertainties on d0 and

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-momentum

recombi-nationmode,on



η

× φ =

0

.

1

×

0

.

1 logicaltowersandforthree values of the anti-kt distance parameter, R

=

0

.

2

,

0

.

3, and 0.4.

Thetowerkinematicswereobtainedbysumming electromagnetic-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 densitywhile exclud-ing actualjetsfromthat estimate. TheUE energywas subtracted fromeachcalorimetercellwithinthetowersincludedinthe recon-structedjet.Thecorrectiontakesintoaccount acos 2

φ

modulation ofthecalorimeterresponseduetoellipticflowofthemedium

[23]

whichisestimatedbymeasurementoftheamplitudeofthat mod-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 pT

>

pisoT where pisoT ,theisolation thresh-old, is set to half of the analysis threshold for each R value, piso

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 pT

>

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.TheHLTjetswerefoundtobefully ef-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-kt

Table 2

Therelationshipbetweenthemeantruth-jettransversemomenta,pTjettrue,and cor-respondingreconstructedjettransversemomenta,pTjetrec.Samplevaluesofαand

β

obtainedfromlinearfitstopTjettrue(pTjetrec)(seetext)accordingtoEq.(3)andthe resultingpTjettrueforpTjetrec=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 jetshascomparable con-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

pT values(hereafterreferredtoas“upfeeding”)suchthatajet re-constructedwithagivenpTjetreccorresponds,onaverage,toalower truth-jet pT,



pTjettrue



.Therelationship between



pTjettrue



and pTjetrec was evaluated from the MC data set for the different centrality binsandthreeR valuesusedinthisanalysis.Forthejet pTjetrec val-ues usedinthisanalysis, that relationship iswell described by a lineardependence,



pTjettrue



=

α

pTjetrec

+ β.

(3)

Sample values for

α

and

β

and the resulting



pTjettrue



values for

R

=

0

.

2 and R

=

0

.

4 jets in peripheral andcentral collisions are listed in Table 2. The extracted relationships between pTjetrec and



pTjettrue



will be used inthe fragmentationanalysis to correctfor theaverageshiftinthemeasuredjetenergy.

MC studies indicate that the efficiency forPYTHIA jets to be reconstructed andtopassUE jetrejection exceeds98% for pjet_T

>

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

Theefficiencyforreconstructingchargedparticleswithinjetsin Pb

+

PbcollisionswasevaluatedusingtheMCsample.

Fig. 1

shows comparisons of distributions offour importanttrack-quality vari-ables between data and MC simulation for reconstructed tracks over a narrow pch_T interval, 5

<

pch_T

<

7 GeV, to minimize the impact ofdifferences inMC anddatacharged-particle pch_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 z0sin

θ

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} longerthan0.3·10−10_{s originatingfromtheprimaryinteractionorfrom} subse-quentdecayofparticleswithshorterlifetimes.

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

Fig. 1. ComparisonbetweendataandMCdistributionsforfourdifferentcharged-particlereconstructionselectionparameters.Thedistributionsareshownforthe0–10% centralitybinandfor charged-particletransversemomentaintherange5

<

pchT <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 pTjettrue

>

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.Anexampleoftheresulting param-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,the system-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 the tran-sitionbetweentheSCTbarrelandend-capandthe detectoredge respectively. Toaccount forthisand other localizedvariations of thehigh pT reconstructionefficiencywithpseudorapidity,the pa-rameterizations in Fig. 2 for pT

>

8 GeV are multiplied by an

η

-dependent factorevaluated in intervalsof0.1 units to produce

ε

(

pT

,

η

)

.

6. Fragmentationfunctionsandunfolding

Jetsused forthe fragmentationmeasurements presented here were required to have pjet_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.The re-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.Theshadedbandsshowthesystematic un-certaintyintheparameterizedefficiencies(seetext).(Forinterpretationofthe ref-erencestocolorinthisfigurelegend,thereaderisreferredtothewebversionof thisarticle.)

notsignificantlychangetheresultofthemeasurement,itreduces thesystematicuncertaintiesatlarge z orpch_T .

Thefragmentationfunctionsweremeasured forcharged parti-cleswithpch

T

>

2 GeV withinanangularrange



R

=

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,wascalculated accord-ingto

z

=

p ch T

pjet_T cos

R

,

(4)

where



R hererepresentstheanglebetweenthechargedparticle andjetdirections.4

ChargedparticlesfromtheUEcontributea pch_T- and centrality-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 pT thresholdsusingagridof



R

=

0

.

4 conesthatspanned the full coverage of the inner detector. Any such cone having a chargedparticlewith pch_T

>

6 GeV was assumedto beassociated

4 _The

_

_{R isaboost-invariantreplacementforthepolarangle}

_θ

_.

witha realjet intheeventandwas excludedfromthe UE back-ground determination.The threshold of6 GeV was chosen to be highenoughtoavoidbiasoftheUE pch_T distribution.

The resulting per-jet UE charged-particle yields, dnUE_ch

/

dpch_T were evaluated over2

<

pch_T

<

6 GeV as a function of pch_T , pjet_T , and

η

jet_{,averagedoverall conesinalleventswithinagiven} cen-tralitybinaccordingto:

dnUE_ch dpch_T

=

1 Ncone

N

_chcone

(p

ch_T

,

pjet_T

,

η

jet

₎



pch_T

.

(5)

Here Ncone represents thenumberof backgroundcones having a jet of agiven radiusabove the corresponding pjet_T threshold,and



Ncone_ch representsthenumberofchargedparticlesinagiven pch_T

bininallsuch conesevaluatedforjetswithagiven pjet_T and

η

jet_. Not shown in Eq. (5) is a correction factor that was applied to each backgroundconetocorrectforthe differenceintheaverage UE-particleyieldatagivenpch_T betweenthe

η

positionofthecone and

η

jet_{,andaseparatecorrectionfactortoaccountforthe} differ-ence inthe elliptic flow modulation atthe

φ

position of the UE coneand

φ

jet.Thatcorrectionwasbasedonaparameterizationof the pch_T andcentralitydependenceofpreviously measuredelliptic flowcoefficients, v2[23].

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

/

dpch_T isobserved tobe independentof pjet_T both inthe dataandMCsimulation.Thatobservationexcludesthepossibility that the upfeeding ofjets in pjet_T dueto the finite JER could in-duce adependenceoftheUEonjet pT.However,such upfeeding was observedtoinduce inthe MCeventsa pjet_T -independent,but centrality-dependent mismatchbetween the extracted dnUE

ch

/

dpchT and the actual UE contribution to reconstructed jets. That mis-matchwasfoundtoresultfromintrinsiccorrelationsbetweenthe charged-particle densityintheUE andthe MC pjet_T error,



pjet_T

=

pTjetrec

−

pTjettrue.Inparticular,jetswithpositive(negative)



p

jet T are found to have an UE contribution larger(smaller) than jetswith



pjet_T

∼

0.Duetothenetupfeedingonthefallingjetspectrum,the selectionofjetsaboveagivenpjet_T thresholdcausestheUE contri-bution tobelarger thanthatestimatedfromtheabove-described procedure. The average fractional mismatchin the estimated UE backgroundwasfoundtobeindependentof pch_T andtovarywith centralitybyfactorsbetween1.04–1.08,1.07–1.10,and1.12–1.15for

R

=

0

.

2

,

0

.

3

,

and 0

.

4,respectively.The measureddnUE

ch

/

dpchT val-uesinthedatawerecorrectedbythesesamefactorsbeforebeing subtracted.

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

Dmeas

(p

T

)

≡

1

ε



1 Njet

N

ch

p

ch_T

−

dnUE_ch dpT



,

(6) and Dmeas

(z)

≡

1

ε



1 Njet

N

ch

z

−

dnUE_ch dpT





pch_T=zpjet_T



,

(7)

where Njetrepresentsthetotalnumberofjetspassingthe above-describedselectioncutsinagivencentralitybin,and



Nch repre-sentsthenumberofmeasuredchargedparticleswithin



R

=

0

.

4 ofthe jetsingivenbinsof pch_T andz,respectively. Theefficiency correction, 1

/

ε

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

ε

(

pT

,

η

)

,assumingpTchtrue

=

pTchrec.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 Dmeas_{(z)and D(z)} distributions,bottomleft:ratiosofmeasuredtounfoldedR=0.4 D(z)distributionswiththe0–10%shiftedby+1 forclarity.Topmiddleandright:central-to-peripheral ratiosofmeasured(Rmeas

D(z))andunfolded(RD(z))distributionsforR=0.4 andR=0.2,respectively.Bottommiddleandright:ratioofRmeasD(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 Dmeas(pT)andD(pT) distributions,bottomleft:ratiosofmeasuredtounfoldedR=0.4 D(pT)distributionswiththe0–10%shiftedby+1 forclarity.Topmiddleandright:central-to-peripheral ratiosofmeasured(Rmeas

D(pT))andunfolded(RD(pT))distributionsforR=0.4 andR=0.2,respectively.Bottommiddleandright:ratioofRmeasD(pT) toRD(pT)forR=0.4 and

R=0.2,respectively.

that assumption is not strictly valid, the efficiency varies suffi-ciently slowly with pTchtrue that the error introduced by this as-sumptionis



1% everywhere.

The measured Dmeas

(

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 Dmeas

₍

_z

₎

be-tweencentral(0–10%)andperipheral(60–80%)collisions, Rmeas

D(z)

≡

Dmeas

(

z

)

|

0–10

/

Dmeas

(

z

)

|

60–80.Forcomparison,the Dmeas

(

z

)

ratiois shownon the top right panel for R

=

0

.

2 jets.Similar plots are shownin Fig. 4 but for Dmeas

(

pT

)

. The Dmeas

(

z

)

ratios for both

R

=

0

.

2 and R

=

0

.

4 indicatean enhanced fragment yield atlow

z, z



0

.

04,in jets in the 0–10% centrality bincompared to jets inthe60–80%centralitybinanda suppressedyieldoffragments withz

∼

0

.

1.Similar resultsareobservedin the Dmeas

₍

_p

T

)

ratios overthe corresponding pT ranges.The R

=

0

.

2 Dmeas

(

z

)

andthe

R

=

0

.

2 and R

=

0

.

4 Dmeas

₍

_p

T

)

ratios rise above one for z



0

.

2

or pT



25 GeV. However, the ratios differ from one by only 1–2

σ

(

stat

)

.NosuchvariationsoftheDmeas

(

z

)

andDmeas

(

pT

)

dis-tributions withcentralityasseen inthedataare observedinthe MCsimulation.Thecentral-to-peripheralratiosofMCDmeas

(

z

)

and

Dmeas

(

pT

)

distributions for R

=

0

.

4 and R

=

0

.

2 jets(not shown) arewithin3%ofoneforallz andpT.

The Dmeas

(

pT

)

and Dmeas

(

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

(

pT

)

, the unfolding accounts only for the charged-particle pT resolution and uses a response matrix derived from the MC data set that describes the

distri-bution of reconstructed pch_T as a function of MC truth pch_T . The responsematrix A

(

pTchrec

,

pTchtrue

)

isfilledusingtheprocedures de-scribedin Section5. The D

(

z

)

unfoldingsimultaneously accounts forbothchargedparticleandjetresolutionusinga response ma-trix A

(

zrec

,

ztrue

)

with ztrue (zrec) calculated using purely truth (fully reconstructed) quantities. A cross-check was performed for the D

(

z

)

unfoldingthatincludedonlythejetenergyresolutionto ensurethatthecombinationofthetwosourcesofresolutioninthe one-dimensionalunfolding didnot distort theresult. Becausethe

Dmeas

(

z

)

and Dmeas

(

pT

)

distributions were already corrected for thecharged-particle reconstructionefficiency,theresponse matri-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 pTjettrue or ztrue 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 wastakentobethestatisticaluncertaintyintheunfolded result.

Unfolded fragmentationfunctions, D

(

z

)

, are showninthe top left panel in Fig. 3and compared to thecorresponding Dmeas

(

z

)

distributions for R

=

0

.

4 jets in central (0–10%) and peripheral (60–80%)collisions.Similar resultsfor D

(

pT

)

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(pT)

≡

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,themiddleandbottomrightpanelsin

Fig. 3

(Fig. 4) show theratio of Rmeas

D(z) (RmeasD(pT)) to RD(z)

(

RD(pT)

)

.Except forthelowestz point,theratioisconsistentwithoneoverthe en-tirez range.Thus,thefeaturesobservedin Rmeas

D(z)

(

R

meas

D(pT)

)

,namely

theenhancementatlowz (pT)incentralcollisionsrelativeto pe-ripheralcollisions,thesuppressionatintermediatez (pT),andthe riseaboveoneatlargez (pT)arerobustwithrespecttotheeffects ofthechargedparticleandjet pT 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,fromsystematicuncertaintiesinthe un-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].The typ-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 systematic uncer-taintyfromJERandcentrality-dependentJESontheratiosreaches 6% athigh pT 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.Theuncertaintyduetothechoiceof regular-izationparameterwasevaluatedbyvaryingk overtherange5–12. The typicalsystematicuncertaintyisfound tobesmallerthan3% or 2% for the D

(

z

)

or D

(

pT

)

, respectively. The systematic uncer-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.

Theestimateofsystematicuncertaintyduetothetracking effi-ciencyfollowsmethodsoftheinclusivechargedparticle measure-ment [23].Theuncertaintyisquantified usingtheerrorofthefit oftrackingefficiencyandbyvaryingthetrackingselectioncriteria. In the intermediate-pT 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.Sincethereisnojetquenching em-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 (pT)rangesz

=

0

.

02–0

.

06 (pT

=

2–6 GeV),z

=

0

.

06–0

.

3 (pT

=

6–30 GeV),andz

>

0

.

3 (pT

>

30 GeV)withparameters con-strained such that the linear functions matchat the boundaries. Theresultingfitsareusedasestimatesofthesystematic uncertain-tiesonallmeasured RD(z) andRD(pT)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 intheanalysiswiththedistributionsfordifferentcentralities mul-tipliedby successivevaluesoftwoforpresentationpurposes.The shadederrorbandsindicate systematicuncertainties asdiscussed in the previous section. The D

(

pT

)

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

Fig. 7. RatiosofunfoldedD(pT)distributionsforsixbinsincollisioncentralitytothoseinperipheral(60–80%)collisions,D(pT)|cent/D(pT)|60–80,forR=0.4 jets.Theerror barsonthedatapointsindicatestatisticaluncertaintieswhiletheyellowshadedbandsindicatesystematicuncertainties.(Forinterpretationofthereferencestocolorinthis figurelegend,thereaderisreferredtothewebversionofthisarticle.)

intermediate z values in more central collisions relative to the 60–80%centrality bin.Forthe 0–10% centralitybin,the yield of fragmentsat z

=

0

.

02 is enhanced relativeto that inthe60–80% centralitybinby 25% whiletheyield at z

=

0

.

1 is suppressedby about 10%. The size of the observed modifications at low, inter-mediate,andhighz decreasesgraduallyfromcentraltoperipheral collisions.

The statistical and systematic uncertainties on RD(z) grow as z

→

1 duetothestatisticalfluctuationsonthe D

(

z

)

distributions at large z and due to the sensitivity of the steeply falling D

(

z

)

distributions to JER andJES systematic uncertainties. The results in

Fig. 6

showcentralvaluesforRD(z)aboveoneathighz forthe

0–10% throughthe30–40%centralitybinsbuttheRD(z)values

dif-ferfromone by typically1

σ

(

stat

)

.

Fig. 7

showsratiosof R

=

0

.

4

D

(

pT

)

distributionsfromnon-peripheralcentralitybinstothosein theperipheral,60–80%centralitybin.Theratiosinthefigureshow thesame features asthe D

(

z

)

ratios, namelyan enhancement at low pT, asuppression atintermediate pT, andan increase above one atlarge pT that is more significant than that seen for D

(

z

)

. Themagnitudesofthedeviationsfromoneinthe D

(

z

)

andD

(

pT

)

ratiosare similarinthelow,intermediate,andhighz and pT re-gions.Thisdemonstratesthatthemodificationsobservedin

Fig. 6

do not result fromdistortions ofthe z measurement dueto JER andJES.

Tofurtherdemonstratethatthecentrality-dependent modifica-tionsobservedin D

(

z

)

andD

(

pT

)

donotresultfromunknownUE effects not includedin thesystematic uncertainties, Fig. 8shows ratios of D

(

z

)

and D

(

pT

)

distributions between central (0–10%) and peripheral (60–80%) collisions for R

=

0

.

2 and R

=

0

.

3 jets. ThefluctuationsintheUEareafactorofapproximately100%(30%) smallerfor R

=

0

.

2 (R

=

0

.

3) jetsthan they are for R

=

0

.

4 jets. Nonetheless,thefeaturesseenintheR

=

0

.

4 D

(

z

)

orD

(

pT

)

ratios arealsopresentinthe R

=

0

.

2 and R

=

0

.

3 ratios withthe same magnitudes.Duetothe reducedsystematicuncertainties on D

(

z

)

andD

(

pT

)

for R

=

0

.

2 andR

=

0

.

3 jetscomparedto R

=

0

.

4 jets,

the enhancementin thefragmentationfunctionsatlarge z or pT incentralcollisionsismoresignificantforthesmallerjetsizes. 9. Discussion

To quantifytheeffects ofthe modifications observedin Fig. 8

on theactual distributionoffragmentswithin the measuredjets, the differences in fragmentation functions,



D

(

z

)

=

D

(

z

)|

cent

−

D

(

z

)

|

60–80 were calculated and integrals of these distributions,





D

(

z

)

dz takenoverthreez rangeschosentomatchthe observa-tions:0.02–0.04,0.04–0.2,and0.4–1.Thelast intervalwaschosen to focus on theregion where RD(z)

>

1. The results are givenin Tables 3 and 4 for R

=

0

.

3 and R

=

0

.

2 jets,respectively. Similar results were obtainedfor R

=

0

.

4 jets butwithlarger uncertain-ties.Theresultspresentedinthetablesindicateanincreaseinthe numberofparticleswith0

.

02

<

z

<

0

.

04 oflessthanoneparticle per jetinthe0–10%centralitybinrelativetothe60–80% central-ity bin. A decrease of about1.5 particles per jet is observed for 0

.

04

<

z

<

0

.

2.The differencesbetweentheintegralsofthe frag-mentationfunctionsover0

.

4

<

z

<

1 arenotsignificantrelativeto theuncertainties.Theresultsfor





D

(

z

)

dz showninthetwo ta-bles indicate that in the mostcentral collisions a small fraction,

<

2%, of the jet transverse momentum is carried by the excess particles in0

.

02

<

z

<

0

.

04 forcentralcollisions, butthatthe de-pletioninfragmentyieldin0

.

04

<

z

<

0

.

2 accountsonaveragefor about14%ofpjet_T .

To better evaluate the significance of the increase in RD(z)

and RD(pT) above one atlarge z or pT,average RD(z) and RD(pT) ratios were calculated by summing the central and peripheral

D

(

z

)

or D

(

pT

)

distributions over different regions corresponding

to the last n points in the measured distributions, n

=

2–6. For

each resulting average ratio, RD(z) or RD(pT), the significance of the deviation from one was evaluated as

(

RD(z)

−

1

)/

σ

(

RD(z)

)

ATLAS Collaboration / Physics Letters B 739 (2014) 320–342 329

Fig. 8. Ratiosofunfoldedfragmentationfunctions,D(z)(top)andD(pT)(bottom),forcentral(0–10%)collisionstothoseinperipheral(60–80%)collisionsforR=0.2 (left) andR=0.3 (right)jets.Thefragmentationfunctionswereevaluatedusingchargedhadronswithin



R=0.4 ofthejetaxis.Theerrorbarsonthedatapointsindicate statisticaluncertaintieswhiletheyellowshadedbandsindicatesystematicuncertainties.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderis referredtothewebversionofthisarticle.)

Table 3

DifferencesofD(z)distributionsindifferentcentralitieswithrespecttoperipheraleventsforR=0.3 jets.Theerrorsrepresentcombinedstatisticalandsystematic uncer-tainties. Centrality z=0.02–0.04 z=0.04–0.2 z=0.4–1.0  D(z)dz zD(z)dz D(z)dz zD(z)dz D(z)dz zD(z)dz 0–10% 0.79+₋00..1925 0.020+ 0.005 −0.007 −1.7+ 0.6 −0.8 −0.14+ 0.04 −0.06 0.06+ 0.05 −0.04 0.033+ 0.026 −0.021 10–20% 0.66+₋00..1718 0.016+ 0.005 −0.005 −1.6+ 0.7 −0.8 −0.12+ 0.05 −0.06 0.05+ 0.05 −0.04 0.029+ 0.026 −0.021 20–30% 0.52+₋00..1318 0.013+ 0.004 −0.005 −1.3+ 0.6 −0.6 −0.12+ 0.04 −0.04 0.04+ 0.04 −0.04 0.025+ 0.024 −0.020 30–40% 0.39+₋00..1217 0.009+ 0.004 −0.005 −1.3+ 0.6 −0.7 −0.10+ 0.04 −0.05 0.06+ 0.04 −0.04 0.036+ 0.020 −0.019 40–50% 0.38+₋00..1115 0.009+ 0.003 −0.004 −0.6+ 0.6 −0.8 −0.07+ 0.04 −0.06 −0.01+ 0.04 −0.04 −0.005+ 0.024 −0.021 50–60% 0.28+₋00..1521 0.006+ 0.004 −0.006 −1.2+ 0.9 −0.7 −0.08+ 0.06 −0.06 0.04+ 0.04 −0.04 0.025+ 0.021 −0.021 Table 4

DifferencesofD(z)distributionsindifferentcentralitieswithrespecttoperipheraleventsforR=0.2 jets.Theerrorsrepresentcombinedstatisticalandsystematic uncer-tainties. Centrality z=0.02–0.04 z=0.04–0.2 z=0.4–1.0  D(z)dz zD(z)dz D(z)dz zD(z)dz D(z)dz zD(z)dz 0–10% 0.65+₋00..2120 0.017+ 0.006 −0.005 −1.7+ 0.5 −0.6 −0.14+ 0.04 −0.05 0.07+ 0.05 −0.04 0.037+ 0.030 −0.022 10–20% 0.60+₋00..1616 0.016+ 0.005 −0.004 −1.6+ 0.7 −0.7 −0.12+ 0.05 −0.05 0.08+ 0.05 −0.04 0.046+ 0.029 −0.025 20–30% 0.48+₋00..1114 0.013+ 0.003 −0.004 −1.6+ 0.6 −0.5 −0.13+ 0.04 −0.04 0.04+ 0.05 −0.04 0.026+ 0.029 −0.024 30–40% 0.44+₋00..1115 0.011+ 0.003 −0.004 −1.4+ 0.6 −0.7 −0.11+ 0.05 −0.05 0.07+ 0.04 −0.05 0.044+ 0.021 −0.028 40–50% 0.33+₋00..0914 0.009+ 0.003 −0.004 −1.0+ 0.6 −0.8 −0.09+ 0.04 −0.06 −0.03+ 0.05 −0.04 −0.011+ 0.030 −0.020 50–60% 0.27+₋00..1218 0.007+ 0.003 −0.005 −1.0+ 0.8 −0.7 −0.07+ 0.06 −0.06 0.04+ 0.04 −0.05 0.027+ 0.024 −0.029

statistical andsystematic uncertainty. Because there issignificant cancellation of systematic uncertainties in the ratios, this analy-sisprovides amoresensitiveevaluationofthesignificanceofthe large-z excess.ForR

=

0

.

4 jetsthecombinedRD(z)(RD(pT)),differs fromonebyapproximately1

σ

(1

.

5

σ

) foranyofthen values.For

R

=

0

.

2 jets, RD(z) differs from 1 by approximately 1

.

5

σ

for all n values, while RD(pT) differs from one by 2

σ

for n

=

3–6 cor-responding to pT

>

47

.

5 GeV through pT

>

20 GeV. The greater significanceofthedeviationsofthe R

=

0

.

2 RD(pT)relative tothe

R

=

0

.

2 RD(z) andthe R

=

0

.

4 RD(z)and RD(pT) canbeattributed tothereducedrole ofthejetenergyresolutionininfluencingthe measurement of the central-to-peripheral ratios for large hadron momenta.

Theoretical predictions for medium modifications of fragmen-tationfunctionsbasedonradiativeenergyloss

[32–35]

have gen-erally predictedsubstantial reduction inthe yield of high pT, or large-z fragments and an enhancement at low pT or low z.The predictedreductionatlargez genericallyresultsfromtheradiative energyloss ofthe leading partons inthe shower andthe result-ing redistribution of the jet energy to lower z hadrons. Instead ofa reduction, an enhanced yieldof highz fragments is seen in thedata.However, the differencebetweenobserved behaviour at large z and expectations fromtheoretical calculations maybe at leastpartially attributedto the fact that the fragmentation func-tions presentedin thispaperwere evaluated withrespect tothe energies ofquenchedjets. In contrast,theoretical analyses ofthe fragmentation functions of quenched jets are typically evaluated in terms of the initial, unquenched jet energies. However, some recent theoretical analyses [36,37] of jet fragmentation functions usingquenchedjetenergieshaveshownthatjetquenching calcu-lationscanreproducethegeneralfeaturesobservedintheresults presentedinthisLetter.Inadditionto directmodificationsofthe fragmentationfunctionduetoquenching,thequenchingmay indi-rectlyalterthefragmentationfunctionofinclusivejetsbyaltering therelativefractionofquarksandgluons.

The simultaneous effects of quenching on the hadron con-stituents of jets and the measured jet energies may explain a relative increase of experimental fragmentationfunctionsin cen-tral collisions atlarge z as suggestedby the data. Jetsthat frag-ment to large-z hadrons may lose less energy than typical jets duetoreducedformationorcolour-neutralizationtime

[38]

.Thus, the fragmentationfunction measured forinclusive jetsmayhave a higher proportion of jets with large-z hadrons. The results in Ref.[36]indicatesuchan effectthatisqualitativelysimilartothe data.

10. Conclusions

ThisLetterhaspresentedmeasurements byATLAS of charged-particle fragmentation functions in jets produced in

√

sNN

=

2

.

76 TeV Pb

+

Pb collisions at the LHC. The measurements were performedusing a data set recorded in2011 withan integrated luminosity of0.14 nb−1_{.Jets werereconstructed withtheanti-k}

t

algorithm for distance parameters R

=

0

.

2

,

0

.

3, and 0.4, andthe contributions of the underlying event to the jet kinematics and thejetfragment distributionsweresubtracted.Jetfragmentswere measured within an angular range



R

=

0

.

4 from the jet axes for all three jet sizes. Distributions of per-jet charged-particle transverse momentum, D

(

pT

)

, and longitudinal momentum frac-tion, D

(

z

)

, were presented for seven bins in collision central-ity for jet pT

>

85

,

92

,

and 100 GeV, respectively, for R

=

0

.

2,

R

=

0

.

3, and R

=

0

.

4 jets. Ratios of fragmentation functions in the different centrality bins to the 60–80% bin were presented and used to evaluate the medium modifications of jet fragmen-tation. Those ratios show an enhancement in fragment yield in

central collisions for z



0

.

04, a reduction in fragment yield for 0

.

04



z



0

.

2 and an enhancement in the fragment yield for

z

>

0

.

4.Themodificationsdecreasemonotonicallywithdecreasing collisioncentralityfrom0–10%to50–60%.Asimilarsetof modifi-cations isobservedinthe D

(

pT

)

distributionsovercorresponding

pT ranges.

Acknowledgements

We thank CERN forthe very successful operation ofthe LHC, as well asthe supportstaff fromour institutions withoutwhom ATLAScouldnotbeoperatedefficiently.

We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia;BMWFW andFWF, Austria; ANAS, Azer-baijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF, DNSRC and Lundbeck Foundation, Den-mark; EPLANET, ERC and NSRF, European Union; IN2P3-CNRS, CEA-DSM/IRFU,France; GNSF,Georgia;BMBF,DFG,HGF, MPGand AvHFoundation,Germany;GSRTandNSRF,Greece;ISF,MINERVA, GIF, I-CORE and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; FOM and NWO, Netherlands; BRF and RCN, Norway; MNiSW and NCN, Poland; GRICES and FCT, Portugal; MNE/IFA, Romania; MES of Russia and ROSATOM, Rus-sian Federation; JINR; MSTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, South Africa; MINECO, Spain; SRC and Wallenberg Foundation, Sweden; SER, SNSF and Cantons of Bern and Geneva, Switzerland; NSC, Taiwan; TAEK, Turkey; STFC, the Royal Society and Leverhulme Trust, United Kingdom; DOE and NSF,UnitedStatesofAmerica.

The crucial computing supportfrom all WLCG partnersis ac-knowledgedgratefully,inparticularfromCERNandtheATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Swe-den),CC-IN2P3(France),KIT/GridKA(Germany),INFN-CNAF(Italy), NL-T1(Netherlands),PIC(Spain),ASGC(Taiwan),RAL(UK)andBNL (USA)andintheTier-2facilitiesworldwide.

References

[1]A. Majumder, M. Van Leeuwen, Prog. Part. Nucl. Phys. 66 (2011) 41–92, arXiv:1002.2206.

[2]Y. Mehtar-Tani, J.G. Milhano, K. Tywoniuk, Int.J. Mod. Phys. A 28 (2013) 1340013,arXiv:1302.2579.

[3]N.Armesto,B.Cole,C.Gale,W.A.Horowitz,P.Jacobs,et al.,Phys.Rev.C86 (2012)064904,arXiv:1106.1106.

[4]G.-Y.Qin,B.Muller,Phys.Rev.Lett.106(2011)162302,arXiv:1012.5280. [5]G.Ovanesyan,I.Vitev,Phys.Lett.B706(2012)371–378,arXiv:1109.5619. [6]J.Casalderrey-Solana,J.Milhano,U.Wiedemann,J.Phys.G38(2011)124086,

arXiv:1107.1964.

[7]J.Casalderrey-Solana,Y.Mehtar-Tani,C.A.Salgado,K.Tywoniuk,Phys.Lett.B 725(2013)357–360,arXiv:1210.7765.

[8]J.-P. Blaizot, E. Iancu, Y. Mehtar-Tani, Phys. Rev. Lett. 111 (2013) 052001, arXiv:1301.6102.

[9]J.Casalderrey-Solana,D.C.Gulhan,J.G.Milhano,D.Pablos,K.Rajagopal,J.High EnergyPhys.1410(2014)19,arXiv:1405.3864.

[10]ATLASCollaboration,Phys.Rev.Lett.105(2010)252303,arXiv:1011.6182. [11]CMSCollaboration,Phys.Rev.C84(2011)024906,arXiv:1102.1957. [12]CMSCollaboration,Phys.Lett.B712(2012)176–197,arXiv:1202.5022. [13]CMSCollaboration,Phys.Lett.B718(2013)773,arXiv:1205.0206. [14]ATLASCollaboration,Phys.Lett.B719(2013)220–241,arXiv:1208.1967. [15]ALICECollaboration,J.HighEnergyPhys.1403(2014)013,arXiv:1311.0633. [16]T.Renk,Phys.Rev.C85(2012)064908,arXiv:1202.4579.

[17]M.Cacciari,G.P.Salam,G.Soyez,J.HighEnergyPhys.0804(2008)063,arXiv: 0802.1189.

[18]CMSCollaboration,J.HighEnergyPhys.1210(2012)087,arXiv:1205.5872. [19]CMSCollaboration,Phys.Rev.C90(2014)024908,arXiv:1406.0932. [20]ATLASCollaboration,J.Instrum.3(2008)S08003.

[21]ATLASCollaboration,J.HighEnergyPhys.1009(2010)056,arXiv:1005.5254. [22]ATLASCollaboration,Phys.Lett.B688(2010)21–42,arXiv:1003.3124. [23]ATLASCollaboration,Phys.Lett.B707(2012)330–348,arXiv:1108.6018.