Measurement of charged jet production cross sections and nuclear modification in p-Pb collisions at sNN=5.02 TeV

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Physics Letters B

www.elsevier.com/locate/physletb

Measurement of charged jet production cross sections and nuclear modification in p–Pb collisions at √

s _NN = ⁵ . 02 TeV

.ALICE Collaboration

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

Articlehistory:

Received3March2015

Receivedinrevisedform21July2015 Accepted21July2015

Availableonline26July2015 Editor:L.Rolandi

Chargedjetproductioncrosssectionsinp–Pbcollisions at√_s

NN=⁵.02 TeV measuredwiththe ALICE detectorattheLHCarepresented.Usingtheanti-kTalgorithm,jetshavebeenreconstructedinthecentral rapidityregionfromchargedparticleswithresolutionparametersR=⁰.2 andR=⁰.4.Thereconstructed jets have been corrected for detector effects and the underlying event background. To calculate the nuclear modification factor, RpPb, ofcharged jetsin p–Pb collisions, a pp reference was constructed byscaling previouslymeasuredchargedjetspectraat√

s=^{7 TeV.Inthetransverse momentumrange} 20≤^pT,ch jet≤^{120 GeV}/c, RpPb isfoundtobeconsistentwithunity,indicatingtheabsenceofstrong nuclearmattereffectsonjetproduction.Majormodificationstotheradialjetstructureareprobedvia theratioofjetproductioncrosssectionsreconstructedwiththetwodifferentresolutionparameters.This ratioisfoundtobesimilartothemeasurementinppcollisionsat√

s=^{7 TeV andtothe}expectations fromPYTHIAppsimulationsandNLOpQCDcalculationsat√_s

NN=⁵.02 TeV.

©^{2015CERNforthebenefitoftheALICE}Collaboration.PublishedbyElsevierB.V.Thisisanopen accessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Jetsaretheobservablefinal stateofafragmentingpartonpro- duced e.g. in scattering of partons in nuclei with a large mo- mentum transfer, Q². Atsufficiently large Q²,thejet production cross section is computable since it can be factorized into the non-perturbativeparton distribution andfragmentation functions andthe cross section of partonic scatterings, which iscalculable in perturbative QCD (pQCD) [1]. Jet measurements in p–Pb and their comparison to pp provide a tool to better constrain effects of(cold)nuclearmatteronthesefactors.Inparticular,theycanbe usedtoexamine theroleofa modificationoftheinitialdistribu- tionofquarksandgluons, e.g.shadowing effectsandgluonsatu- ration [2,3], andthe impact ofmultiple scatteringsand hadronic re-interactionsintheinitialandfinalstate[4,5].

In central heavy-ion collisions, the production of jets and high-pT particles is strongly modified: inPb–Pb collisions atthe LHC,theobservedhadronyieldsaresuppressedbyuptoafactorof sevencomparedtoppcollisions,approachingafactoroftwosup- pression athigh pT [6–8]. Asimilar suppressionis alsoobserved forreconstructedjets incentralPb–Pb [9–13].Thisphenomenon, referred toasjetquenching,hasalso beenobserved previouslyin high-pT particle production in central Au–Au collisions at RHIC [14–19]. It isattributed tothe creation ofa quark–gluon plasma (QGP) in the final state, where hard scattered partons radiate

E-mailaddress:[email protected].

gluons in strong interactions withthe medium asfirst predicted in [20,21]. This results in a radiative energy loss of the leading partonandamodifiedfragmentationpattern.

Initially, p–Pb collisions havebeen seenasthe testingground for isolated cold nuclear matter effects, without the formation of a hot and dense medium. However, recent results on low-pT particle productionandlongrangecorrelationsinp–Pb collisions at √

s_NN=⁵.02 TeV [22–25] exhibit features of collective behav- ior, similar to those found in Pb–Pb collisions, where they are attributedtothecreationofaQGP.Athigh pT,resultsonthepro- duction ofunidentifiedchargedparticles[26–29] andjets[30,31]

inp–Pb collisionsat√

sNN=⁵.02 TeV areconsistentwiththeab- sence of a strong final state suppression. The question to what extent other nuclear effects lead to an enhancement of particle productionathighpTisstillopen,apossibleenhancementinp–Pb collisions has beenreportedforsingle charged hadrons[28]. The measurementofjetsinp–Pb collisionscomparedtosinglehadrons tests the parton fragmentation beyond the leading particle with theinclusionoflow-pT andlarge-anglefragments.

Ajetisdefinedexperimentallybythealgorithmthatcombines themeasureddetectorinformationsuchastracksand/orcalorime- tercells into jet objects andby theparameters ofthe algorithm.

Thedesiredpropertiesofsuchalgorithmsinpp(^p¯)collisionsandin thecorresponding theoreticalframework havebeendiscussede.g.

in[32].Ingeneral,jetalgorithmsaimtoreconstructthekinematic properties of the initial parton withas little dependence on the details ofitsfragmentationprocessaspossible,i.e.thealgorithms http://dx.doi.org/10.1016/j.physletb.2015.07.054

0370-2693/©^{2015CERNforthebenefitoftheALICE}Collaboration.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

shouldyieldconsistentresultswhenappliedinatheoreticalcalcu- lationatany stage ofa partonshower andat final state particle level. A particularly well suited class of algorithms in this con- textarethoseusingsequentialrecombinationschemes,whichare infraredandcollinearsafe,incontrastto manyconceptuallysim- plerconealgorithms.Thecomputationallyoptimizedimplementa- tionofsequentialrecombinationalgorithmsintheFastJetpackage [33] facilitates their applicability also in collision systems with highmultiplicity andthereby the comparisonof resultsobtained withthe same jet algorithms in pp, p–Pb,and Pb–Pb collisions.

Anadditionalcomplicationinthe contextofjet reconstructionin high-multiplicityeventsarisesfromthe largebackgroundparticle density,i.e.particlesinthe sameaperture asthe jetthat are not relatedtotheinitialhard scattering.Thisbackgroundcan besub- tractedonan event-by-event basis andthe impacton therecon- structedjetobservableneedstobeevaluatedcarefully[12,34,35].

Inthispaper,jetsreconstructedfromchargedparticles(charged jets)withtheanti-kTalgorithmmeasuredwiththeALICEdetector in p–Pb collisions at √

sNN=⁵.02 TeV are reported fordifferent resolutionparameters, R.Section2describesindetailthecorrec- tionstepsneededintheanalysis,includingtheeffectoftheevent backgroundanditsfluctuationsonthejetobservablesandtheun- foldingprocedure to account for background aswell asdetector effects.TheresultsarepresentedanddiscussedinSection3.

2. Dataanalysis

2.1.Eventandtrackselection

ThedatausedforthisanalysisweretakenwiththeALICEde- tector[36]duringthep–Pb runoftheLHCat√

sNN=⁵.02 TeV at thebeginning of 2013. Minimum biasevents havebeen selected requiringatleastonehit inbothofthe scintillatortriggerdetec- tors (V0A andV0C) covering the pseudorapidity 2.8<

η

_lab<5.1 and−³.7<

η

lab<−¹.7,respectively[37].Hereandinthefollow- ing,

η

labdenotesthepseudorapidityintheALICElaboratoryframe.

Comparedto thisframe (with positive

η

in the directionof the V0A),thenucleon–nucleoncenter-of-masssystemmovesinrapid- ityby y_NN= −⁰.465 inthedirectionoftheprotonbeam[38].

The event sample used in the analyses presented in this manuscript was collected exclusively for the beam configura- tion where the proton travels from V0A to V0C (clockwise).

A van der Meer scanwasusedtomeasurethevisiblecrosssection

σ

V0=².09±⁰.07 b for thiscase[39].MonteCarlostudies show that the sample consists mainly of non-single diffractive (NSD) interactions and a negligible contribution from single diffractive andelectromagneticinteractions(formoredetailssee[38,40]).The triggerisnotfullyefficientforNSDevents.Thisinefficiencyaffects onlyevents withouta reconstructed vertex, i.e.withno particles reconstructedwithin theacceptance ofthe SPD. The loss of effi- ciencyisestimatedtobe2.3%withalargesystematicuncertainty of3.1%[38].Inthispaper,thenormalizationtoNSDeventsisonly usedfortheconstructionofthenuclearmodificationfactor.

In addition to the trigger selection, timing andvertex-quality cutsareusedtosuppresspile-upandbadqualityevents.Theanal- ysisrequiresareconstructedvertex,whichisthecasefor98.2%of theevents selected by the trigger. In addition,events witha re- constructedvertex |^z|>10 cm alongthe beamaxis are rejected.

Intotal,about96Meventsareusedfortheanalysis.

ChargedparticlesarereconstructedastracksintheInnerTrack- ing System (ITS) [41] and the Time Projection Chamber (TPC) whichcoverthefullazimuthand|

η

lab|<0.9[42].Fortrackswith reconstructedtrackpointsclosetothevertex(fromthetwoinner SiliconPixelDetector(SPD) layersoftheITS),a momentumreso- lutionof0.8%(3.8%)forp_T=^{1 GeV}/c (50 GeV/c) isreached[36].

Theazimuthaldistributionofthesehighqualitytracksisnotcom- pletely uniform due to inefficient regions in the SPD. This can be compensatedby considering inaddition trackswithout recon- structed track points in the SPD. For those tracks, the primary vertex is used as an additional constraint in the trackfitting to improve the momentum resolution. This approach yields a very uniformtrackingefficiencywithintheacceptance,whichisneeded to avoid geometrical biases of the jet reconstruction algorithm causedbyanon-uniformdensityofreconstructedtracks.Thepro- cedure is described indetail in the context of jet reconstruction withALICE inPb–Pb events[12].Fortheanalyzeddata,theaddi- tional tracks(without SPDtrackpoints) constitute approximately 4.3% ofthe used tracksample. Tracks with pT>0.15 GeV/c and within a pseudorapidityinterval |

η

lab|<0.9 areused asinput to the jet reconstruction. The overall efficiency for charged particle detection,includingtheeffectoftrackingefficiencyaswellasthe geometrical acceptance,is 70% at p_T=⁰.15 GeV/c andincreases to85%at pT=^{1 GeV}/candabove.

2.2. Jetreconstructionandbackgroundcorrections

For thepresent analysis, the anti-kT algorithm fromthe Fast- Jetpackage [43]hasbeenusedtoreconstructjetsfrommeasured trackswithresolutionparameters ofR=⁰.2 andR=⁰.4.Ingen- eral,jetsareonly consideredforfurtheranalysisifthejet-axis is separatedfromtheedgeofthetrackacceptancein

η

labbyatleast theresolutionparameter R usedinthejetfinding,e.g.jetsrecon- structed with R=⁰.4 are acceptedwithin |

η

jet,lab|<0.9−⁰.4= 0.5. The jet transverse momentum is calculated by FastJet using the pT recombinationscheme. Toenable backgroundcorrections, the area A for each jet is determined internally by distributing ghostparticles intothearea that is clustered[44]. Ghostparticles havevanishingmomentumandthereforedonotinfluencethejet finding procedure.Byconstruction,the numberofghostparticles inajet isadirectmeasureforthejetarea. Aghostparticleden- sityof200per unitarea (0.005areaperghost particle)wasused toobtainagoodarearesolutionwithareasonablecomputingtime.

InPb–Pb collisions,thebackgroundfromparticlesnotfromthe same hard scattering as the jet has a significant impact on the reconstructed jet momentum [12,35]. The transverse momentum densityofthisbackgroundis estimatedwithastatisticallyrobust methodbyusingthemedianofalljetpT,ch jetperareawithinone eventforjetsreconstructed withthek_T algorithm. Inp–Pb colli- sions,themultiplicity densityistwo ordersofmagnitudesmaller thanincentralPb–Pb collisions[40],soacorrespondingreduction ofthejetbackgroundisexpected.Toobtainareliableestimatefor the more sparse environment ofp–Pb events a modified version oftheapproachdescribedin[45]forppcollisionsisemployed.It usesthesamemethodasinPb–Pb,butcontainsanadditionalcor- rection factor, C, to account forregions without particles, which otherwise wouldnot contribute to the overallarea estimate. The backgrounddensityforeacheventisthengivenby

ρ

ch

=

median

pT,i

Ai

·

C

,

(1)

wherei runsoverallreconstructedkT jetsintheeventwithmo- mentum p_T,i andarea A_i.Cisdefinedby

C

=

jA_j,kT

A_acc

.

(2)

Here,thenumeratoristheareaofallk_T jetscontainingtracksand the denominator, Aacc,is theacceptance inwhich chargedparti- clesareconsideredasinputtothejetfinding(2×⁰.9ײ

π

).The probabilitydistributionforthebackgrounddensityinthismethod,

Fig. 1.(Coloronline.)Left:Probabilitydistributionoftheevent-by-eventtransversemomentumbackgrounddensity(seeEq.(1)).Themeanandvariancefortwoeventclasses areindicatedinthefigure.p^raw_{T,ch jet}representsuncorrectedjetpT.Right:Probabilitydistributionofbackgroundfluctuationscalculatedwiththerandomconeapproachand definedviaEq.(4)(resolutionparameterR=0.4).

withthesametrackselectioncriteriaasthesignaljetreconstruc- tionandaradiusof0.4,isshowninFig. 1(left).The background densityobtainedwith R=⁰.4 is used both forthe correction of signaljetswith R=⁰.4 and R=⁰.2 toavoidevent-by-eventfluc- tuationsinthedifferenceofthemomentaforthetworadii.

Theprobabilitydistributionof

ρ

chdecreasesapproximatelyex- ponentially. It is smaller than 4 GeV/c for 98.6% of all events.

The mean background density and its variance for all events is

ρ

ch=¹.02 GeV/c (with negligible statistical uncertainty) and

σ

(

ρ

ch)=⁰.91±⁰.01 GeV/c.Foreventscontaining a jetwithun- correctedtransversemomentum pT,ch jet>20 GeV/c,itis

ρ

ch= 2.2±⁰.01 GeV/cand

σ

(

ρ

ch)=¹.47±⁰.09 GeV/c,respectively.The observedincrease oftheunderlyingeventactivityforeventsthat containahigh-pT jetisexpected. Thisincreaseisalreadypresent inpp collisions andhasbeen quantifiedin detailandwithmore differentialobservablesthanthebackgrounddensity,e.g.in[46].

The background density estimate provides an event-by-event correction for each jet withreconstructed transverse momentum p_{T,ch jet} andjetarea A_{ch jet}:

p_{T,ch jet}

=

^praw_{T,ch jet}

−

^Ach jet

· ρ

ch

.

(3) However, thisapproach neglects that the backgroundfor a given eventisnot uniformlydistributed inthe (

η

lab,

ϕ

)-planebutfluc- tuatesfrom region to region.These fluctuationsare mainly Pois- sonian, but also encode correlated region-to-region variations of theparticlemultiplicityandthemean pT [35].Theeffectofthese fluctuations can be accounted for on a statistical basis in the unfoldingofthe measuredjet p_{T,ch jet}-distributions.Thedistribu- tionofregion-to-regiondensityfluctuationsaroundtheevent-wise background densityestimate can be evaluated for the full event sample by a Random Cone (RC) approach as described in [35].

Coneswitharadius R corresponding totheresolutionparameter of the jet finding algorithm are placed randomly in the (

η

lab,

ϕ

) jet-acceptanceandthetransversemomentaforalltracks(charged particles)fallingintothisconeare summedandcomparedtothe backgroundestimate:

δ

p_T,ch

=

i

p_T,i

− ρ

_chA

,

A

= π

R²

.

(4)

Thedistributionoftheresiduals,δpT,ch,asshowninFig. 1(right) for R=⁰.4,is adirect measureforall intra-eventfluctuationsof the background and can be used directly in the unfolding pro- cedure. In Fig. 1(right), a clearasymmetry of the distributionis visible.Itiscausedbythefactthattheδp_T,ch distributionofsin- gleparticlessampledintheconeisasymmetric.Sincethenumber ofparticles within a cone increaseswith its size, statisticalfluc- tuationsof thebackgroundestimate also increase(see also[35]).

Furthermore,therandomlyplacedconescanalsooverlapwithjets.

In p–Pb collisions, thereis thepossibilityformultiple hard colli- sions withinonep–Pb event, soajetcan alsobethebackground to ajet fromanotherhard collisionandcontribute asanupward fluctuation. Therefore, an overlap of random cones with possible signal jetsshouldnot be a prioriexcludedin thefluctuationesti- mate,butispartofitssystematicuncertainty.

2.3. Detectoreffectsandunfolding

The main detector-related effects on the reconstructedjet are the reconstruction efficiency and the momentum resolution for single charged particles. To determine the correction for these, a fulldetectorsimulationofppjeteventsgeneratedwithPYTHIA6 (Perugia 2011, version 6.425) [47] and GEANT3 particle trans- port [48] isperformed. Inthe simulation, two jet collectionsare matchedgeometrically(closenessin(

η

lab,

ϕ

)-plane)withaone-to- onecorrespondence[12]:jetsreconstructedatthechargedparticle level (part) without detector effects and jets reconstructed from tracksafterparticletransport throughtheALICEdetector(det).In the simulation, the particlelevel reconstruction includes charged primary particlesproducedinthecollisionwith pT>0.15 GeV/c.

Charged decay products from primary particle decays, excluding those from weak decays of strange particles, are included with the same pT threshold. The response matrix is populated with matched particle- and detector-level jets. It relates the particle- level to the detector-level charged jet momentum and encodes theeffectsofsingle-particlemomentumresolutionandreconstruc- tion efficiency on the reconstructed jet momentum. A correction for the missing energyof neutral jet-constituents is not applied.

The response isshown on a logarithmic scale in Fig. 2 (left) for chargedjetswith R=⁰.4 andparticle-level momentumbetween 45<p^part_{T,ch jet}<50 GeV/c.It can be seen that the mostprobable value for the reconstructed momentum is the particle-level mo- mentum,butthedistributionhaslargetailstotheleftandright.It ismoreprobablethatjetsarereconstructedwithalowermomen- tumthan thetruth,which isduetothe dominatingeffectofthe single-particle reconstruction efficiency that reduces the number of reconstructedparticles ina jet.The tailtothe right-hand side ismainly duetothesingle-particle momentumresolution,where a fractionoftracksisreconstructedwithhighermomentum than thetruth,causinganupwardshiftofthejetmomentum.

In addition, Fig. 2 (left) shows the effect of the background fluctuationsonthereconstructedjetmomentumandthecombina- tion ofdetectoreffectsandbackgroundfluctuations. Eventhough the background fluctuationsshow a strongtail to theright-hand side, itis seenthat inthecombined unfoldingmatrixthe effects

Fig. 2.(Coloronline.)Left:Projectionofthecombinedunfoldingmatrixforjetswithparticle-levelmomentum45<p^part_{T,ch jet}<50 GeV/c.The matrixisobtainedfromthe combinationofthedetectorresponseandbackgroundfluctuationmatrices,whicharealsoshownasprojections(seetextfordetails).Right:Probabilitydistributionofthe relativedifferencebetweenparticle-level(generatedtrue)anddetector-levelchargedjettransversemomentumforjetswithdifferentmomenta.Theeffectofbackground fluctuationsisincludedforthejetsreconstructedatdetectorlevel.CharacteristicvaluesofthedistributionsaresummarizedinTable 1.

Table 1

Characteristicvaluesforthedistributionofresidualsofthetotalchargedjet re- sponseshowninFig. 2(right),includingtheeffectofbackgroundfluctuationsand without:mostprobablevalue(MPV)determinedviaaGaussianfittothecentral peakregion,firstandsecondmoment(meanandwidthσ),andquartiles.Thepre- cisionofthequartilesislimitedbythefinitebinwidthof0.01.

p^part_{T,ch jet} 20–25 GeV/c 45–50 GeV/c 80–90 GeV/c MPV (Gaussian fit) 0.006±0.002 −0.001±0.002 −0.010±0.004 id. w/o bkg. fluct. 0.007±^0.001 −^0.003±^0.002 −^0.013±^0.004 Mean 0.149±^0.030 −^0.181±^0.030 −^0.222±^0.030 id. w/o bkg. fluct. −^0.163±^0.030 −^0.188±^0.030 −^0.226±^0.030 Widthσ 0.238±^{0.030 0.246}±^{0.030 0.259}±^0.030 id. w/o bkg. fluct. 0.233±0.009 0.245±0.005 0.258±0.003 Quartile, 25% above 0.01±0.01 −0.01±0.02 −0.01±0.02 id. w/o bkg. fluct. 0.01±0.01 −0.01±0.02 −0.03±0.02 Quartile, 50% above −^0.05±^0.04 −^0.09±^0.01 −^0.13±^0.04 id. w/o bkg. fluct. −^0.07±^0.04 −^0.09±^0.04 −^0.13±^0.04 Quartile, 75% above −^0.25±^0.06 −^0.29±^0.05 −^0.37±^0.04 id. w/o bkg. fluct. −^0.27±^0.04 −^0.29±^0.06 −^0.37±^0.04

ofsingle-particlemomentumresolutionplaythedominantrolein reconstructing a jet with momentum higher than the truth. The defaultalgorithm fortheunfoldingofthe measuredjet spectrum isbasedontheSingularValueDecomposition(SVD)approach[49]as implementedinthe RooUnfoldpackage [50]. Thedefaultprior in theunfoldingprocedureisasmoothedversionoftheuncorrected jet spectrum itself. In addition to the SVD unfolding approach, Bayesian [51,52] and

χ

² [53] unfolding havebeen used for sys- tematiccomparisons and validity checks.The unfolded spectrum isalsocorrectedforunmatched jetsusingajetreconstruction ef- ficiencyobtained from generated–reconstructed comparison. This jet reconstruction efficiencyis larger than 96% in the considered momentumrange.

Theinfluenceofthesedetectoreffectsandbackgroundfluctua- tionsonthejetmomentumisshownforthreetransversemomen- tumintervalsinFig. 2(right)viatheprobabilitydistributionofthe relativedifference ofthe detector-levelandparticle-levelcharged jettransversemomentum.Forallmomentumbinsthedistribution isasymmetric.Themostprobableresponsewasdeterminedusing Gaussianfitstothepeakregion.ItcanbeseeninTable 1thatitis closetozero(≤^{1%)withamild p}T dependence.Tofurtherquan- tifythedistributions, numericalvalues fortheir meanandwidth are also given in Table 1. Since the width is not a well-defined measure of the jet momentum resolution for these asymmetric distributions,thequartiles ofthedistribution areprovided inad- dition. Approximately, 25% of the jets have a larger momentum than the generated. The 50% (median) correction is only 5% for p^part_{T,ch jet}=^{20–25 GeV}/candincreasestowardslargerjetmomenta.

InTable 1thevaluesfortherespectivedistributionswithoutback- ground fluctuationsare also given (notshown in Fig. 2). Clearly, the instrumental response dominates thejet responseas already seeninFig. 2(left).Themaineffectofthebackgroundfluctuations isabroadeningofthejetresponseandanupwardshiftoftheaver- agereconstructedenergyduetotheasymmetricshapeofthefluc- tuationsasseeninFig. 1(right).Themostprobablevalueremains unaffectedwithin theuncertaintieswhenbackgroundfluctuations areincluded.

2.4. Nuclearmodificationfactor

ThenuclearmodificationfactorcomparesapT-differentialyield inp–Pb collisionstothedifferentialproductioncrosssectioninpp collisionsatthesame√

s_NN toquantifynucleareffects:

R_pPb

=

^d2NpPb

/

d

η

dp_T

T_pPb

·

^d2

σ

pp

/

d

η

dp_T

.

(5) Here,

TpPb

is the nuclear overlap function which accounts for the increased parton flux in p–Pb compared to pp collisions. It isrelatedtothe numberofbinarynucleon–nucleoncollisions via TpPb

= ^Ncoll/

σ

_INEL^pp andhasbeencalculatedinaGlauber Monte Carlo,asdescribedin[38].Here,

σ

_INEL^pp representsthetotalinelas- ticcrosssectioninppcollisions.Forminimumbiasp–Pb collisions, the nuclear overlap function is

T_pPb

=(0.0983±⁰.0034)mb⁻¹ and Ncoll =6.87±⁰.56. In this paper, the reference differen- tialproduction crosssection in ppis constructedfrom theALICE chargedjetmeasurementat7 TeV[54]byapQCDbasedscaling.In thenuclearmodificationfactor,theinvariant yieldforNSDevents in p–Pb is compared to inelastic pp collisions. Hence, the addi- tionalcorrectionof(2.3±³.1)% isappliedasdiscussedabove.

2.5. NLOcalculationsandppreference

Perturbative QCD calculations are used for two purposes in this paper: for comparison to the measurement of jet produc- tion in p–Pb, and as additional input to the construction of the pp reference. The calculations have been performed within the POWHEGboxframework[55,56],whichfacilitatesnext-to-leading order (NLO) precision in calculating parton scattering cross sec- tions in an event-by-event Monte Carlo. Event-by-eventthe out- going partons from POWHEG are passed to PYTHIA8[57] where the subsequent parton shower is handled. For this, a POWHEG version matched to the PYTHIA8fragmentation is used to avoid doublecountingofNLOeffectsalreadyconsideredinthePYTHIA8 code.TheMonte Carloapproachhastheadvantagethat thesame

Table 2

Summaryofsystematicuncertaintiesonthefullycorrectedjetspectrum,thecorrespondingnuclearmodificationfactor,andthejetproductioncrosssectionratioforthe resolutionparametersR=0.2 andR=0.4.Thepercentagesaregivenforthewholeshowntransversemomentumrange20–120 GeV/c.

Observable Jet cross section RpPb R

Resolution parameter R=⁰.2 R=⁰.4 R=⁰.2 R=⁰.4 0.2/0.4

Uncertainty source

Single-particle efficiency (%) 7.9–12.8 10.2–14.2 4.1–5.9 4.9–6.3 2.1–2.1

Unfolding (%) 2.2 1.7 2.8 2.2 1.5

Unfolding prior steepness (%) 1.4–4.8 0.5–4.0 2.9–8.0 0.9–4.4 1.1–1.5

Regularization strength (%) 3.1–3.9 2.3–4.4 3.6–5.8 2.3–5.6 1.1–4.7

MinimumpTcut-off (%) 1.1–0.3 2.3–0.1 1.3–1.4 2.8–4.1 1.2–0.4

Background estimate (%) 1.8–0.6 3.7–1.5 1.8–0.6 3.7–1.5 2.0–0.9

δpT,chestimate (%) 0.0–0.0 0.1–0.0 0.0–0.0 0.1–0.0 0.1–0.0

Combined uncertainty (%) 9.2–14.4 11.5–15.5 7.1–11.9 7.5–10.7 3.8–5.7

TpPb

(%) – – 3.4 3.4 –

pp cross section (%) – – 3.5 3.5 –

Reference scaling pp 7 TeV (%) – – 10.0 10.0 –

NSD selection efficiency p–Pb (%) – – 3.1 3.1 –

Combined scaling uncertainty (%) – – 11.6 11.6 –

selection criteria and jet finding algorithm can be used on final state particlelevel,asintheanalysisofthe realdata,inparticu- lar,the limitation to chargedconstituents ofa jet. The dominant uncertaintyin theparton levelcalculation isgiven by thechoice ofrenormalizationscale,

μ

R,andfactorization scale,

μ

F.The de- faultvaluehasbeenchosentobe

μ

R=

μ

F=^pT andindependent variationsby afactoroftwoaround thecentralvalueare consid- eredasthesystematicuncertainty.Inaddition,theuncertaintyon theparton distributionfunctionshas beentakeninto account by thevariationofthefinalresultsfortherespectiveerrorsetsofthe partondensityfunctions(PDFs).

Forthecomparisonwiththemeasuredp–Pb data,protonPDFs correctedfornucleareffects (CTEQ6.6[58] withEPS09[59]) have beenused. Priorto passing thescatteredpartons to PYTHIA8for showering,they canbe boostedinto thesamereferenceframe as thep–Pb reactionby yNN=⁰.465.

The construction of the pp reference at √

sNN=⁵.02 TeV is basedontheALICEmeasurementofchargedjetsinppcollisionsat 7 TeV,describedindetailin[54].Forthepurposeofthereference scaling, the sameanalysis chain has beenused as forp–Pb. The samebinninginpseudorapidityandtransversemomentumallows for a partial cancellation of common systematic uncertainties in theppandp–Pb datasets.Inaddition,thesamebackgroundsub- tractionapproachasinthep–Pb analysisisused forthepp data.

In the present analysis, the scaling is done with a factor which isdeterminedforeach p_{T,ch jet} binbythe NLOpQCD calculations (POWHEG+^{PYTHIA8) atthe two energies. For the pp reference} scalingthe partondistributionfunctionsin thePOWHEGcalcula- tionhavebeenreplacedbythefreeprotonPDFfromCTEQ6.6.The scalingfactorisgivenby

F

(

p_T

) =

^yield

(

p_{T,ch jet}

)

^{5.02 TeV,boosted}

pp,NLO

yield

(

p_{T,ch jet}

)

^{7 TeV}

pp,NLO

.

(6)

The factordecreases monotonically from F≈⁰.65 to 0.45 in the reported pT range. As already described above, the laboratory frame is not the center-of-mass frame of the collision as is the caseforppcollisions.Therefore,thenumeratorofthescalingfac- tor F in Eq.(6) is determined in theNLO calculation wherethe additional Lorentz-boost is applied to the hard scatteredpartons prior to fragmentation. The resulting reduction of the observed jetsfor|

η

lab|<0.5 issmallerthan5%intherelevantmomentum range.

2.6. Jetproductioncrosssectionratio

Thebroadeningornarrowingofthepartonshowerwithrespect to the original partondirection can have a direct impact on the jet production cross section reconstructed with different resolu- tionparameters.Thiscanbetestedviatheratioofyieldsorcross sectionsincommonrapidityinterval,here|

η

lab|<0.5 forR=⁰.2 and0.4:

R

(

0

.

2

,

0

.

4

) =

^d

σ

_pPb,R=0.2

/

dp_T

d

σ

pPb,R=⁰.4

/

dp_T

.

(7) Considering the extreme scenario that all fragments are already containedwithin R=⁰.2 thisratioisunity. Inthiscase, alsothe statistical uncertainties between R=⁰.2 and R=⁰.4 are fully correlated andcancel completely in the ratio, when the jets are reconstructedfromthesamedataset.Inthecasethejetsareless collimated,theratiodecreasesandthestatisticaluncertaintiesonly cancelpartially. Forthe analysispresentedinthispaper,thecon- ditionalprobability forreconstructing an R=⁰.2 jetin thesame pT-binasageometricallyclose R=⁰.4 jetis25–50%, whichleads to a reductionof thestatisticaluncertaintyof theratioof 5–10%

comparedtothecaseofnocorrelation.

2.7. Systematicuncertainties

ThevarioussourcesofsystematicuncertaintiesarelistedinTa- ble 2 for the full pT-rangeof thethree observablespresented in thispaper:jet productioncross section,nuclear modificationfac- tor, and cross section ratio. The most important sources will be discussedinthefollowing.

The dominant sourceof uncertaintyfor the pT-differential jet productioncrosssectionistheimperfectknowledgeofthesingle- particletrackingefficiencythathasadirectimpactonthecorrec- tion of the jet momentum in the unfolding, asdiscussed above.

In p–Pb collisions, the single-particle efficiency is known with a relative accuracy of 4%, which is equivalent to a 4% uncertainty onthejetmomentumscale.Toestimatetheeffectofthetracking efficiencyuncertaintyonthejetyield,thetrackingefficiencyisar- tificiallyloweredby randomlydiscardingacertain fraction(4%in p–Pb)oftracksusedasinputforthejetfinding.Dependingonthe shape ofthespectrum,theuncertaintyonthesingleparticleeffi- ciency(jetmomentumscale)translatesintoanuncertaintyof8to 15%ontheyield.

To estimate the uncertaintyon the p–Pb nuclearmodification factor, the uncertainty on the single-particle tracking efficiency

inthe two collision systems (ppand p–Pb) has to be evaluated.

Thisuncertaintyon the efficiencyis correlatedbetweenthe data sets, since the correction is determined with the same underly- ingMonteCarlodescriptionofthe ALICEdetectorandforsimilar trackqualitycuts. Onlyvariations ofdetectorconditionsbetween runperiodsmayreducethedegreeofcorrelation.Theuncorrelated uncertaintyhasbeenestimatedtobe 2%,andtheuncertaintyfor thenuclearmodificationfactorhasbeendeterminedbyartificially introducing such a difference in the tracking efficiency between thetwocollisionsystems.

The uncertainty on the spectra induced by the underlying event subtraction has been estimated by comparing the results with various methods for background subtraction; ranging from purely track-based to jet-based density estimates, including an

η

lab-dependent correction. As seen inFig. 1, a typical correction

π

R²

ρ

ch forajet with R=0.4 is about1 GeV/c. Theuncertainty on this correction can be treated similar to an uncertainty on thejet momentumscale. For thefinal spectrum, theuncertainty ontheyields fromthebackgroundcorrection methodisapproxi- mately 2%.

Inthedeterminationofthefluctuationsoftheunderlyingevent, the main uncertainty is given by the exclusion of reconstructed jetsintherandomconesamplingoftheevent.Theprobabilityfor a random coneto overlap withreconstructed jets ishigher than forthejetsitself.Onaverage,ajetcanoverlapwithNcoll−^{1 jets} inone event.TherandomconecanoverlapwithN_coll jets. Toac- countforthis,theδp_T,chcalculationcanbemodifiedtodiscardon astatisticalbasisrandom conesthatoverlapwithsignal jets.This lowerstheaverageoverlap probability.However,since thismodi- fiedδp_T,chcalculationstronglydependsonthesignaljetdefinition andalso onhow an overlap is defined, it is not usedby default butconsideredforsystematicuncertainties.Theeffectofthispar- tialsignalexclusionapproachonthefullycorrectedjetyieldsisof theorderof0.1%.

The uncertainty of the scaling procedure to obtain the ref- erencespectrum is estimated by determining the scaling factors F(pT) after varying the scales

μ

R and

μ

F in the POWHEG NLO generation,andbyusingdifferenttunes intheoutgoingfragmen- tationhandled by PYTHIA8. Furthermore,standalone calculations with PYTHIA6 and PYTHIA8 using different generator tunes and with HERWIG at the two energies have been performed to ob- tainscaling factorsaccordingtoEq.(6).Ageneraluncertaintyfor how well LO generators and NLO calculations can describe the

√s-dependenceofparticleproductionisalsoconsidered:inALICE measurements ofthe

π

⁰ productioninpp collisions, it hasbeen observedthatpQCDcalculationspredictastrongerincreaseofthe productioncrosssection whengoingfrom0.9 to7 TeVthan sup- portedbythe data[60].A similareffectis alsoseeninunidenti- fiedchargedhadronsmeasuredwithALICE at0.9,2.76,and7 TeV [61].Furthermore,the√

s-dependenceofthejetproductioncross sectionhasbeencrosscheckedinternallywithaninterpolationbe- tween7and2.76 TeV,usingpreliminaryALICEresultsoncharged jetsat√

s=².76 TeV.Intotal,thesestudiesyieldanadditionalun- certaintyonthepp referenceof10% forthe extrapolationfrom7 to5.02 TeV.Itisreportedasanindependentnormalizationuncer- tainty,similartotheuncertaintyonthenuclearoverlapfunction.

3. Results

The pT-differential production cross sections for jets recon- structed fromcharged particles inminimum bias p–Pb collisions at√

s_NN=⁵.02 TeV areshowninFigs. 3 and 4fortheresolution parameters R=⁰.4 and R=⁰.2.The spectra are found to agree wellwithscaledNLOpQCDcalculations(POWHEG+^PYTHIA8)us- ingnuclearPDFs(CTEQ6.6+^{EPS09)asseenbestintheratiodata}

Fig. 3.(Coloronline.)Toppanel:pT-differentialproductioncrosssectionofcharged jetproductioninp–Pb collisionsat5.02 TeV forR=⁰.4.Bottompanel:Ratioof dataandNLOpQCDcalculations.Theglobaluncertaintyfromthemeasurementof thevisiblecrosssectionof3.5% isnotshown.TheuncertaintiesonthepQCDcal- culationareonlyshownintheratioplotasdashedlines.ThepQCDcalculations takeintoaccounttherapidityshiftofthenucleon–nucleoncenter-of-masssystem inp–Pb withaboostedpartonsystem.

Fig. 4.(Coloronline.)Toppanel:pT-differentialproductioncrosssectionofcharged jetproductioninp–Pb collisionsat5.02 TeV forR=⁰.2.Bottompanel:Ratioof dataandNLOpQCDcalculations.Theglobaluncertaintyfromthemeasurementof thevisiblecrosssectionof3.5% isnotshown.TheuncertaintiesonthepQCDcal- culationareonlyshownintheratioplotasdashedlines.ThepQCDcalculations takeintoaccounttherapidityshiftofthenucleon–nucleoncenter-of-masssystem inp–Pb withaboostedpartonsystem.

overcalculationinthelowerpanels.However,theeffectofthenu- clearPDFsonthejetproductioninthereportedkinematicregime isalmostnegligible,asseeninthecomparisontocalculationswith onlyprotonPDFs(CTEQ6.6).

Fig. 4alsoshowsthejetspectrafor−⁰.65<

η

lab<−⁰.25 and 0.25<

η

lab<0.65 comparedtotheresultsfromthesymmetricse- lection |

η

lab|<0.5. Here,

η

lab denotes the pseudorapidity of the jet axis. The first selection roughly corresponds to a small win- dowaround mid-rapidityforthe nucleon–nucleoncenter-of-mass

Fig. 5.(Coloronline.)NuclearmodificationfactorsRpPbofchargedjetsforR=0.2 (left)andR=0.4 (right).Thecombinedglobalnormalizationuncertaintyfrom TpPb

,the correctiontoNSDevents,themeasuredppcrosssection,andthereferencescalingisdepictedbytheboxaroundunity.

system, while thesecond isseparated fromit by aboutone unit inrapidity.Nosignificantchangeofthejetspectraisobservedfor thesetwo

η

lab regions centeredat−⁰.45 and 0.45.Thus, thejet measurement has no strong sensitivity to the rapidity shift and thepseudorapiditydependentvariationofthemultiplicity(under- lying event)within the statisticalandsystematicuncertainties of themeasurement.

The nuclear modification factor R_pPb is constructed based on thepT-differentialyieldsandtheextrapolatedppproductioncross section at 5.02 TeV for R=⁰.2 and 0.4. It is shown in the left and rightpanel of Fig. 5, respectively. In the reported pT-range, itisconsistentwithunity,indicatingtheabsenceofalarge mod- ification of the initial partondistributions ora strongfinal state effect on jet production. Before comparing these results to the measuredsingle-particleresultsfor R_pPb,onehastoconsiderthat the samereconstructed pT corresponds to a differentunderlying parton transverse momentum. Assuming that all spectra should obey the samepower law behaviorat high pT,an effective con- versionbetweenthespectracanbe derivedata givenenergyvia thePOWHEG+^PYTHIA8simulationsdescribedabove.Tomatchthe single charged particle spectra in the simulation to charged jets with R=⁰.4, a transformation p^h_T^±→².28p^h_T^± is needed. Thus, the reported nuclear modification factor for charged jets probes roughly thesameparton p_T-region astheALICEmeasurement of single charged particles that shows a nuclear modificationfactor in agreement with unity in the measured high-pT range up to 50 GeV/c[27].

Since the jet measurements integrate the final state particles, theyhaveasmallersensitivitytothefragmentationpatternofpar- tonsthansingleparticles.Differencesbetweenthenuclearmodifi- cationfactorforjetsandsinglehigh-p_T particles,assuggestedby measurementsin[28,29],couldpointtoamodified fragmentation patternordifferentlybiasedjetselectioninp–Pb collisions.

Amodifiedfragmentationpatternmaybealsoreflectedinthe collimationor transverse structure ofjets. The first step in test- ing possible cold nuclear matter effects on the jet structure is the ratio of jet production cross sections for two different reso- lution parameters. It is shownfor R=⁰.2 and R=⁰.4 in p–Pb in Fig. 6 and compared to PYTHIA6 (Tune Perugia 2011) and POWHEG+^PYTHIA8at √

s_NN=⁵.02 TeV and to ALICEresults in pp collisions at √

s=^{7 TeV [54]. All datashow the expected in-} creaseoftheratiofromtheincreasingcollimationofjetsforhigher transversemomentumandagreewellwithintheuncertainties.No significant energydependenceorchangewith collisionspeciesis observed. The data for p–Pb collisions is well described by the NLOcalculationaswellasby thesimulationofppcollisions with PYTHIA6atthesameenergy.Itshouldbe notedthattheratiofor

Fig. 6.(Coloronline.)Chargedjetproductioncrosssectionratiofordifferentres- olutionparametersasdefinedinEq.(7). Thedatainp–Pb collisionsat √

sNN= 5.02 TeV arecomparedtoPYTHIA6(tune:Perugia2011,nouncertaintiesshown) andPOWHEG+PYTHIA8(combinedstat.andsyst.uncertaintiesshown)atthesame energy,andtoppcollisionsat7 TeV(onlystat.uncertaintiesshown).

chargedjetsis,ingeneral,abovetheratioobtainedforfullyrecon- structedjets,containingchargedandneutralconstituents.Thiscan beunderstoodfromthecontributionfromneutralpionsthatdecay alreadyatthecollisionvertexandleadtoan effectivebroadening ofthejetprofilewhenincludingtheneutralcomponentinthejet reconstruction,mainlyintheformofdecayphotons.Forthesame reason, theinclusion ofthe hadronization in the NLO pQCD cal- culation is essential to describe the ratio of jet production cross sectionasalsodiscussedin[62].

4. Summary

In thispaper, pT-differential chargedjet productioncross sec- tions inp–Pb collisionsat√

sNN=⁵.02 TeV havebeen shownup to pT,ch jet of 120 GeV/c for resolution parameters R=⁰.2 and R=⁰.4.Thechargedjetproductionisfoundtobecompatiblewith scaled pQCD calculationsatthe sameenergyusing nuclearPDFs.

At the same time, the nuclear modification factor R_pPb (using a scaledmeasurementofjetsinppcollisionsat√

s=^{7 TeV asaref-} erence)doesnotshowstrongnucleareffectsonjetproductionand isconsistent withunity forR=⁰.4 and R=⁰.2 inthe measured pT-rangebetween20and120 GeV/c.Thejetcrosssectionratioof R=⁰.2/0.4 is compatiblewith7 TeV pp dataandalso withthe predictions fromPYTHIA6Perugia 2011andPOWHEG+^PYTHIA8 calculationsat 5.02 TeV. No indication ofa strong nuclearmodi- fication ofthe jet radial profileis observed, comparing jetswith differentresolutionparameters R=⁰.2 and R=⁰.4.