Constraints on jet quenching in p–Pb collisions at √sNN = 5.02  TeV measured by the event-activity dependence of semi-inclusive hadron-jet distributions

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Constraints on jet quenching in p–Pb collisions at √

s _NN = ⁵ . 02 TeV measured by the event-activity dependence of semi-inclusive

hadron-jet distributions

.ALICE Collaboration

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

Articlehistory:

Received19December2017

Receivedinrevisedform12March2018 Accepted22May2018

Availableonline24May2018 Editor:M.Doser

TheALICECollaborationreportsthemeasurementofsemi-inclusivedistributionsofcharged-particlejets recoilingfromahigh-transversemomentumtriggerhadroninp–Pbcollisionsat√_s

NN=⁵.02 TeV.Jetsare reconstructedfromcharged-particletracksusingtheanti-kTalgorithmwithresolutionparameterR=⁰.2 and0.4.A data-drivenstatisticalapproachisusedtocorrecttheuncorrelatedbackgroundjetyield.Recoil jetdistributionsarereportedforjettransversemomentum15<p^ch_T,jet<50GeV/cand arecomparedin variousintervalsofp–Pbeventactivity,basedoncharged-particlemultiplicityand zero-degreeneutral energyin theforward (Pb-going)direction. Thesemi-inclusiveobservable is self-normalizedand such comparisonsdonot requiretheinterpretationofp–Pbeventactivityintermsofcollisiongeometry,in contrast to inclusivejet observables.Thesemeasurements provide new constraintsonthe magnitude ofjetquenchinginsmallsystemsattheLHC. Inp–Pbcollisions withhighevent activity,theaverage medium-induced out-of-cone energy transport for jets with R =⁰.4 and 15< p^ch_T,jet<50GeV/c is measuredto beless than0.4 GeV/c at90%confidence, whichis overanorderofmagnitudesmaller than asimilar measurement for central Pb–Pbcollisions at√_s

NN=².76TeV.Comparison ismade to theoretical calculationsofjet quenchinginsmallsystems,and to inclusivejetmeasurements inp–Pb collisionsselectedbyeventactivityattheLHCandind–AucollisionsatRHIC.

©^2018EuropeanOrganizationforNuclearResearch.PublishedbyElsevierB.V.Thisisanopenaccess articleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

The collision of heavy nuclei at high energies generates a Quark–Gluon Plasma (QGP), a dense, highly inviscid, strongly- coupledfluid governed by sub-nucleonicdegrees offreedom [1].

While the structure anddynamical behavior ofthe QGP arise at the microscopic level from the interactions between quarks and gluons that are described by Quantum Chromodynamics (QCD), theQGPalsoexhibitsemergentcollectivebehavior.Currentunder- standing ofthe properties ofthe QGPis based primarily on two phenomena observed in high energynuclear collisions and their comparisonto theoretical calculations:strong collective flow [2], andjet quenching, whicharisesfrominteractionofenergetic jets withthemedium[3].

Jetsinhadroniccollisionsaregeneratedbyhard(highmomen- tum transfer Q²) interactions between quarks and gluons from the projectiles, with outgoing quarks and gluons from the in- teraction observed in detectors as correlated sprays of hadrons (“jets”). Theoretical calculations of jet production based on per-

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

turbative QCD (pQCD) are in excellent agreement over a broad kinematic range with jet measurements in pp collisions at the LargeHadronCollider(LHC) [4–7]. Measurementsinppcollisions of charged-particle jets, whichconsist of the chargedcomponent ofthehadronicjet shower,are alsowell-describedbyQCD-based MonteCarlocalculations [8,9].

Innuclearcollisions,theinteractionofjetswiththeQGPisex- pectedtomodifytheobservedrateofjetproductionandinternal jet structure. Indeed, marked effects due to jet quenching have been observedfor hightransverse momentum (high-pT) hadrons andjets in central Au–Au collisions at the Relativistic Heavy Ion Collider (RHIC) [10–20] and in central Pb–Pb collisions at the LHC [9,21–32].Jetsthereforeprovidewell-calibratedprobesofthe QGP.

Measurementsofasymmetricp–PbcollisionsattheLHCandof lightnucleus–AucollisionsatRHICrevealevidenceofcollectiveef- fectsthataresimilarinmagnitudetothoseobservedinsymmetric collisions ofheavy nuclei[33–50]. Thesemeasurements inasym- metric systems are reproduced both by model calculations that incorporate a locally thermalized hydrodynamic medium in the final state, andby calculations withoutQGP but withlarge fluc- tuations in the initial-state wavefunctions of the projectiles (see https://doi.org/10.1016/j.physletb.2018.05.059

0370-2693/©^2018EuropeanOrganizationforNuclearResearch.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

[51] and references therein). This raises the question whether a QGPisinfactgeneratedinsuchlight asymmetricsystems,which wereinitiallythoughttobetoosmallfortheformationofaquasi- equilibrated fireball of matter in the final state [51]. Additional measurements,inparticulartoexplorejetquenchinginp–Acolli- sions,willhelptoresolvethispictureandtoclarify thenatureof equilibrationinstrongly-interactingmatter.

Thereare severaltheoreticalcalculationscurrentlyavailable of jet quenching effects in p–Pb collisions at the LHC, which dif- ferintheir predictions. Thecalculation in [52] estimates thesize of the region of high energy density to have a radius that is a factor 2 smaller in p–Pb than in central Pb–Pb collisions, with jettransport parameter^q,ˆ ^assumedtobe proportionalto charged multiplicity, to be a factor 7 smaller. Jet energy loss, which is proportional to qˆ and depends on path length of the jet in the medium,is consequentlyexpectedin thiscalculationto bemuch smaller in p–Pb than in central Pb–Pb collisions. In contrast, a modelcalculationbasedonone-dimensionalBjorkenhydrodynam- ics predicts large initial energy density in high multiplicity pp and p–Pb collisions [53]; this energy density corresponds to jet energy loss ofseveral GeV, which is similar inmagnitude to jet energylossmeasuredincentralPb–Pbcollisions [9].A calculation basedonpQCDatnext-to-leadingorder(NLO)findsnegligiblejet quenchingeffectsforinclusivejetproductioninp–Pbcollisions at

√sNN=^{5TeV [54].Finally,aQCD}calculationofinitial-stateenergy lossincoldnuclearmatter (CNM)findssignificantsuppression of inclusivejetproductionforsmall-impactparameterp–Pbcollisions at√

sNN=^{5TeV [55].}

Experimental searchesfor jet quenchingeffects in d–Aucolli- sionsatRHICandinp–PbcollisionsattheLHChavebeencarried out with high-pT hadrons and reconstructed jets. These stud- ies utilizeboth Minimum Bias (MB) eventsandmore-differential event selection, in which events are characterized in terms of

“eventactivity” (EA) based on central charged-particle multiplic- ity(ALICE [56]);forwardcharged-particle multiplicity (STAR [57], PHENIX [58,59], ALICE [56]); forward transverse energy (AT- LAS [60], CMS [61]); or zero-degree neutral energy (STAR [57], ALICE [56]);where“forward”and“zero-degree”refertothedirec- tionoftheheavynuclearprojectile.

Inclusivehadron measurementsind–Aucollisions atRHIC[57, 58] exhibit yield enhancement in the region 2<pT<5GeV/c, which is commonly attributed to multiple scattering in the ini- tialstate, withnosignificant yield modificationathigher pT and withno significantdifference observed betweenthe MB andEA- selecteddistributions.Forinclusivehadronmeasurementsinp–Pb collisionsattheLHC,ALICEdoesnotobservesignificantyieldmod- ification for pT>8 GeV/c in both MB and EA-selected events [56,62] whileATLAS andCMSobserve yield enhancement for pT greaterthan ∼^{30 GeV}/c inMBevents [60,63,64],andATLAS ob- servesadditionaldependenceonEA[60].

For inclusive jet production, no significant yield modification hasbeen observed inMB p–Pb collisions atthe LHC andMB d–

Aucollisions at RHIC [59,65–67]. However, measurements by the PHENIXcollaborationatRHIC [59] andtheATLAScollaboration at theLHC [66] findapparentenhancementoftheinclusivejetyield in EA-selected event populations thought to be biased towards large impact parameter in such asymmetric systems (“peripheral collisions”),withcompensating suppressionforeventpopulations assigned small impact parameter (“central collisions”), while the ALICEcollaboration findsnosuchyieldmodificationasafunction ofevent“centrality” [68].

Measurementofjet quenchingeffectswithinclusiveprocesses requires scaling of the inclusive yield from a reference collision system (usually pp) by the nuclear overlap function TaA, with theanglebrackets. . .^{indicatinganaverageovertheeventpop-}

ulation; for current measurements, “aA” denotes d–Au at RHIC andp–PbattheLHC.Foran EA-selectedpopulation,^TaA^{is cal-} culated by correlating EA with collision geometry and applying Glauber modeling [69]. However, the correlation of EAwith col- lisiongeometryinp–Pbcollisionsisobscuredbylargefluctuations intheEAobservables[56],andcanbebiasedbyconservationlaws andbydynamicalcorrelationswhenmeasuringhighQ² processes [70–75].Colorfluctuationsintheprotonwavefunctionmayinduce abiasinsoftparticleproductionforp–Pbeventstaggedbyahard process, thereby biasingthe correlation betweenEAandcollision geometry [76–79]. Amodel calculation showsthat selection bias canmodifythescalingfactorforjetproductioninperipheralA+^A relativetoppcollisions,generatinganapparentsuppressionofjet productioninperipheral A+^{AcollisionsiftheGlauber}calculation doesnot takethiseffectintoaccount [80];similarconsiderations applytoasymmetriccollisionsystems.

WhileGlauber modelingforperipherald–AucollisionsatRHIC hasbeenvalidatedexperimentally formoderate Q² processesus- ing a proton-stripping process and knowledge of the deuteron wavefunction[57],nosuchcheckispossiblewiththeprotonbeam attheLHC.ItisthereforecrucialtomeasuretheEA-dependenceof jetquenchingeffectsinp–PbcollisionsattheLHCwithcorrelation observablesthat do notrequirethe interpretationof EAinterms ofcollisiongeometry.

Acorrelation measurementofdijettransverse-momentumbal- ance in p–Pb collisions at √

sNN=⁵.02 TeV finds no significant difference from a simulated pp reference distribution, indepen- dent of EA [61]. Measurements of dijet acoplanarity, which can be generated by both initial-stateandfinal-state effects,likewise find no significant modification dueto nuclear matter effects in EA-selected p–Pb collisions at √

sNN=⁵.02 TeV, relative to sim- ulated distributions for pp collisions [61,81]. While these mea- surementsprovidequalitativeindications,basedoncomparisonto simulations, that final-state jet quenching effects in high-EA p–

Pbcollisionsaresmall,quantitativemeasurementsorlimitsonjet quenchingeffectsinsuchcollisionsarestilllacking.

Inthispaperwepresentmeasurementssensitivetojetquench- ing in p–Pb collisions at √

sNN=⁵.02 TeV, based on the semi- inclusivedistributionofchargedjetsrecoilingfromahigh-p_T trig- ger hadron [82]. The observable used in this analysis has been measured in pp collisions at √

s=^{7 TeV and compared to cal-} culations based on PYTHIA and on pQCD at NLO, with PYTHIA providing a better description [9]. Ithas alsobeen used tomea- surejet quenchingeffectsin Pb–Pbcollisions at√

sNN=².76 TeV [9] andinAu–Aucollisionsat√

s_NN=^{200 GeV[20].}

The semi-inclusive recoil jet distribution is equivalent to the ratio of inclusive cross sections [9]; comparison of such self- normalized coincidence distributions for p–Pb event populations withdifferentEAthereforedoesnotrequirescalingbythenuclear overlap function

TpPb

. Measurement of this observable in p–Pb collisionsissensitivetojetquenchingeffects,andindeeddoesnot requireinterpretation oftheEAinterms ofp–Pbcollisiongeom- etry. This approach thereby avoids potential bias dueto Glauber modelingwheninterpretingthemeasurement.

We report charged recoil jet distributions reconstructed with theanti-kT algorithm[83] intherange15<p^ch_T,jet<50 GeV/c,for jet resolution parameters R=⁰.2 and 0.4. Correction of the jet yield for background uncorrelated with the triggered hard pro- cess, including multi-partonic interactions (MPI), is carried out statisticallyatthe levelof ensemble-averageddistributions, using the data-drivenmethodfirst applied in[9]. EAinp–Pbcollisions is characterized by two different observables, forward charged- particlemultiplicityandneutralenergyalongthebeamaxis,both measured inthedirectionofthe Pb-beam[56]. Jet quenchingef- fects are quantified by comparing the measured distributions in

differentEAclassesofthep–Pbdataset.Theresultsarecompared to other jet quenchingmeasurements and to theoretical calcula- tionsofjetquenchinginasymmetriccollisionsystems.

The paper is organized asfollows: Sect. 2 describes the data setand analysis;Sect. 3describes eventselection based on trig- gerhadronsandeventactivity;Sect.4describesjetreconstruction;

Sect.5 discusses the semi-inclusive observable and presents the rawdata; Sect.6 discussescorrections; Sect.7 discusses system- aticuncertainties;Sect.8 presentsresultsanddiscussion; Sect.9 comparesthe resultsto other measurements;andSect.10 isthe summary.

2. Datasetandanalysis

The ALICEdetectorand performance are described in[84,85].

Thedatausedinthisanalysiswererecordedduringthe2013LHC runwithp–Pbcollisions at√

sNN=⁵.02 TeV.ThePb-going direc- tionhasrapidity y>0 andpseudorapidity

η

>0 inthelaboratory frame. The per-nucleonmomenta of thebeams in thisrun were imbalanced in the laboratory frame, with the nucleon–nucleon center-of-massatrapidity yNN= −⁰.465.Theacceptanceoftracks andjetsinthisanalysisarespecifiedintermsof y^∗=^yLAB−^yNN, whereyLABdenotestherapiditymeasuredinthelaboratoryframe.

Events were selected onlineby an MB trigger, whichrequires thecoincidence ofsignals in theV0A andV0C forward scintilla- tor arrays. The V0A array has acceptance 2.8<

η

<5.1 and the V0C array has acceptance −³.7<

η

<−¹.7, both covering the full azimuth. Offlineeventselection also utilizesthe Zero-Degree Calorimeters(ZDC),whichareneutroncalorimetersatzerodegrees relativetothebeamdirection,locatedatadistance112.5 mfrom thenominalinteractionpoint.TheZDCinthePb-goingdirectionis labeledZNA.

Jetreconstruction inthisanalysis usescharged-particle tracks.

TracksaremeasuredbytheInnerTrackingSystem(ITS),asix-layer siliconvertextracker,andtheTimeProjectionChamber(TPC).The trackingsystemacceptancecovers|

η

_|<0.9 overthefullazimuth, withtracksreconstructedintherange0.15<pT<100GeV/c.Pri- mary vertices are reconstructed offline by extrapolation ofthese tracks to the beam axis. Primary tracks are defined as recon- structedtracks withDistance ofClosestApproach tothe primary vertexinthetransverseplaneDCAxy<2.4 cm.

The analysis uses high-quality primary tracks that include at least one track point in the Silicon Pixel Detector (SPD), which comprisesthe two innermost layers of ITS. The azimuthal distri- bution of such high-quality tracks is non-uniform, however, due tothe non-uniformacceptanceofthe SPDinthisrun. Azimuthal uniformityinthetrackingacceptanceisachievedbysupplement- ing the high-quality tracks with complementary tracks that do not have a hit in the SPD, which constitute 4.3% of all primary tracks.The momentumresolutionofcomplementary tracks,with- out an additional constraint, is lower than that of high-quality tracks.Complementarytracksarethereforerefit,includingthere- constructedprimaryvertexasatrackpoint.Trackingefficiencyfor primary tracksis about81% for pT>3GeV/c.Primary-track mo- mentumresolutionis0.7%atpT=^1GeV/c,1.6%atpT=^10GeV/c, and4%atpT=^50GeV/c.Furtherdetailsonthetrackselectionand trackingperformanceinthisanalysisaregivenin[23,68].

TheMBtriggerefficiencyfornon-singlediffractive(NSD)colli- sionsis97.8±³.1%[68,86].Sincethisisacorrelationanalysis,no correctionisappliedforthetriggerinefficiency.Timingcutsonthe V0andZDCsignals, whichareappliedoffline,removebackground eventswith vertices outsideof the nominalp–Pb interaction re- gion that arise frombeam-gas interactions andinteractions with satellitebeambunches [85].

Event pileup, due to multiple interactions in the triggered bunch crossing, is suppressed by rejecting events with multiple primary vertexcandidates. For this procedure, a new set of pri- mary vertexcandidates is constructed from trackletsconstructed solely from SPD hits (“SPD vertices”). SPD vertices have at least fiveSPDtrackletswithinDCA<1 mmandliewithintheexpected envelopeofp–Pbinteractionpoints,withadistancenotmorethan 3

σ

in z or2

σ

inthe xyplane fromthecentroidofthe distribu- tion. The minimum distancein z between SPDvertices is 8 mm.

Events withmultipleSPDverticesarerejectedfromfurtheranal- ysis. The EA-bias of the pileup rejection procedure is negligible, due to the large separation of pileup vertices in z and the re- quirementthateach SPDvertexhaveatleastfivecontributors.In thisdataset,theaverage numberofinteractionsper bunch cross- ingwas

μ

≈⁰.3–0.5%,andthispileuprejectionprocedureremoves lessthan0.15%ofallevents.

Inaddition,acceptedeventsmusthavetheprimaryvertex(de- fined above)with|^zvtx|<10 cmrelativeto thenominalcenterof the ITS along the beam axis. After all event selection cuts, the numberofeventsintheanalysisis96×^106,correspondingtoan integratedluminosityof46 μb⁻¹.

Simulations are usedto correctthe raw dataforinstrumental effects, andto compare the corrected measurements to expecta- tionsfromaneventgenerator.Simulatedeventsweregeneratedfor ppcollisionsat√

s=⁵.02 TeVusingPYTHIA6.425withthePerugia 11tune[87].Theseevents,labeled“particle-level,”includeallpri- marychargedparticlesasdefinedin[88].Followingtheprocedure in[65],instrumentaleffectsarecalculatedbypassingparticle-level events through a detailedmodel of the ALICEdetector based on GEANT3 [89]. Theseeventsare reconstructedwiththe samepro- ceduresthat are used forrealdata; theoutput ofthis process is labeled “detector-level.” Comparison to data also uses a particle- levelsimulation ofpp collisions at√

s=⁵.02 TeV generatedwith PYTHIA 8.215 Tune 4C [90]. All simulations take account of the nucleon–nucleoncenter-of-massrapidityshiftofthep–Pbdata.

3. Eventselection

Thisanalysisisbasedonthesemi-inclusivedistributionofjets recoiling from a high-pT trigger hadron. Event selection requires the presenceof ahigh-pT chargedtrack, calledthe TriggerTrack (TT), in a specified p_T,trig interval. Two exclusive event sets are defined, based on different TT intervals: 12<p_T,trig<50GeV/c, denotedTT{12,50},and6<pT,trig<7GeV/c,denotedTT{6,7}.

ThechoiceoftheupperTTintervallimitsisdrivenbytwocom- peting factors: the hardening of the recoil jet p_T-spectrum with increasing pT,trig, and the decrease of the inclusive hadron pro- ductioncrosssectionforincreasing pT,trig.ThechoiceofTT{12,50}

providesthe optimumkinematicreachandstatisticalprecision of thenormalizedrecoiljetspectrumforthisdataset.Thecriteriafor the lower TT interval, TT{6,7}, are that it be significantly lower in p_T,trig, with correspondingly softer recoil jet spectrum, while still in the region in which inclusive hadron production can be well-described perturbatively using collinear fragmentationfunc- tions [91,92].

ThefractionofsucheventsintheMBpopulationis6.9×¹⁰⁻⁴ forTT{12,50}and6.4×^{10−3 forTT{6,7}.However,an eventmay} satisfyboththeTT{6,7}andTT{12,50}selectioncriteria,sincefrag- mentation of an energetic jet can generate hadrons in both TT selectionintervals.A procedureisrequiredtoensureexclusive,sta- tisticallyindependentdatasetsforthetwoTT-selectedpopulations.

In addition,optimization ofthe statisticalprecision of theanaly- sis requires similar number ofevents in the two TT classes.The MB population was thereforedivided randomly intotwo subsets, whose sizes are inverselyproportional to the relative rateof the

Fig. 1.DistributionofeventactivityEAindecilebinsmeasuredinZNA(left)andV0A(right),fortheMBeventpopulationandforeventpopulationsselectedwiththe requirementofahigh-pTtriggerhadronintheintervals6<pT,trig<7GeV/c(TT{6,7})and12<pT,trig<50GeV/c(TT{12,50}).LargeEAistotheleft,withthe0–10%bin representingthelargestEA,orhighestamplitudesignalinZNAorV0A.

twoTTselections:90%ofMBeventsareassignedtotheTT{12,50}

analysis,withtheremaining10%assignedtotheTT{6,7}analysis.

Aneventcanalsocontainmultiplehadronswithinasingle TT interval,likewisearisingfromjetfragmentation.Foreventswithat leastonehadronsatisfyingTT{6,7},therelativerateoftwoormore hadronsinan eventsatisfying TT{6,7}is2.3%; the corresponding relativerateofmultiplehadronssatisfyingTT{12,50}is5.3%.Ifan event contains more than one track in the assignedTT interval, thetriggerhadronischosenasthecandidatewiththehighestpT. The resulting p_T-distribution of trigger tracks is consistent with theshapeoftheinclusivehadrondistributionwithin2%.Afterthe TT event selection procedure there are 63k eventsaccepted that satisfyTT{6,7}and60keventsacceptedthatsatisfyTT{12,50}.

Adifferentprocedurewasemployedin [9] forthecaseofmul- tiple trigger candidates in a TT interval, where the trigger track waschosenrandomlyamongst thecandidates.However,theanal- ysisreportedherehasawiderrangein p_T fortheupperTTclass, andrandomselectionresultsinreducedlevelofagreement(∼^10%) ofthetriggertrackpT-distributionwiththeinclusivehadronspec- trumshape.The full analysiswas alsocarriedout forthischoice ofprocedurefortrigger selection,andall resultingphysicsdistri- butionsagreewiththoseoftheprimaryanalysiswithintheuncer- tainties.

MeasurementofEAusessignalsfromV0AandZNA.Classifica- tion of events in percentile intervals ofthe V0Aand ZNA signal distributionsisdiscussedin[56].

The ZNAthresholdis setso that the detectorisfullyefficient for single neutrons. About 5% of accepted events do not have a ZNAsignalabovethedetectorthreshold.Theseeventscorrespond top–PbcollisionsinwhichthePb-nucleusremnantisnotaccom- paniedby any beam-rapiditysingle neutrons. The distributionof mid-rapidity trackmultiplicity forthese eventsresembles closely that for events with low but observable ZNA signal, and these events are therefore assigned to the bin with lowest ZNA sig- nal.

Fig.1showsthedistributionofEAmeasuredbyZNAandV0A, in decile bins of signal amplitude. The decilebin limitsare de- terminedfromtheir distributions intheMB population,withMB events therefore distributeduniformly in this projection by con- struction. The figure also shows V0A and ZNA distributions for eventpopulationsselectedbytheTT{6,7}andtheTT{12,50}crite- ria.Requiringthepresenceofahigh-p_Thadrontriggerinanevent isseentoinduceabiastowardslargerEA,correspondingtolarger amplitude in both ZNA andV0A. A small dependenceon the TT class (i.e. on p_T,trig) is also observed, with magnitude less than

10%oftheoverallbias,andwiththeTT-dependenceslightlylarger forV0AthanforZNA.Fig.1showssignificantcorrelationbetween EAandthepresenceofahardprocessinthecentralregion.

For furtheranalysis, eventswere assigned to wider percentile bins in ZNA or V0A, based on their MB distributions: 20%

of the MB population with largest signal (“0–20%”), the next 30% (“20–50%”), and the remaining 50% with the lowest signal (“50–100%”). The bias imposed by TT selection, shown in Fig. 1, corresponds to different fractions of the TT-biased population:

the nominal0–20%ZNAinterval correspondsto 0–35%oftheTT- biasedpopulation; thenominal 20–50%ZNAinterval corresponds to 35–74% of TT-biased; and the nominal 50–100% ZNA interval corresponds to74–100%ofTT-biased.Similarmodificationofper- centilefractionsduetoTTbiasisobservedfortheV0Asignal.

The sameevents are usedforthe ZNAand V0Aselections, so thattheanalysesusingthetwodifferentEAmetricsarenotstatis- ticallyindependent.

4. Jetreconstruction

Severaltypesof jetare usedin theanalysis, whichwe distin- guishbythenotationforjet pT: p^raw_T,jet^,chreferstotheoutputofthe jetreconstructionalgorithm; p^reco_T,jet^,chis p^raw_T,jet^,chaftersubtractionof an estimated contribution to jet pT of uncorrelated background;

and p^ch_T,jet refers to the fully corrected jet spectrum. For simu- lations, p^part_T,jet refers to reconstructed charged-particle jets at the particle-level, and p^det_T,jet refers to reconstructed charged-particle jetsatthedetector-level.

Jet reconstruction is carried out using the kT and anti-kT al- gorithms [83] withthe boost-invariant pT recombinationscheme [93], usingall accepted charged tracks with p_T>0.15GeV/c. Jet area A_jet iscalculatedusingtheFastjetalgorithm[94] with ghost area0.005.

Two jet reconstruction passes are carried out for each event.

The firstpass estimatesthe levelofuncorrelatedbackgrounden- ergy inthe event, whilethe second passgenerates the setofjet candidates used inthephysics analysis, withadjustment oftheir pT usingtheestimatedbackgroundlevelfromthefirstpass.

In the first pass,the p^raw_T,jet^,ch distribution reconstructed by the kT algorithmwithR=⁰.4 isusedtoestimate

ρ

,themagnitudeof backgroundenergyperunitarea [95],

Table 1

Contributionstotherelativesystematicuncertaintyoftherecoildistributionfor R=⁰.2 and0.4inEA- biasedeventsbasedonZNA.

recoilsyst. uncert. (%) ZNA 0–20%

recoilsyst. uncert. (%) ZNA 50–100%

p^ch_T,jet 15–20 GeV/c 40–50 GeV/c 15–20 GeV/c 40–50 GeV/c

R 0.2 0.4 0.2 0.4 0.2 0.4 0.2 0.4

Unfolding algorithm <1 1.7 1.8 4.8 1.4 1.4 1.1 <1

Unfolding prior 0.5 0.2 1.7 0.5 0.2 1.2 1.5 1.2

Binning of raw spectrum 1.1 2.4 0.5 1.2 1.0 1.2 2.1 2.2

ρestimator 0.2 2.7 0.9 0.2 0.8 2.8 2.0 4.4

cRef 2.3 3.6 1.7 0.5 1.4 0.9 1.7 1.3

Track reconstruction efficiency 4.7 3.3 9.0 11 4.8 4.2 10 11

TrackpTresolution 0.6 0.6 1.0 1.7 0.6 0.6 1.0 1.7

Weak decays <1 <1 <1 <1 <1 <1 <1 <1

Cumulative 5.4 6.3 9.6 12 5.4 5.6 11 12

ρ =

^mediankTjets

⎧ ⎨

⎩

p^raw_T,jet^,ch

A_jet

⎫ ⎬

⎭ ,

(1) where the median is calculated by excluding the jet which has thetriggerhadronasaconstituent.A different

ρ

estimator [96] is utilizedtoassessthesystematicuncertaintiesofthisprocedure.

The second jet reconstruction pass is carried out using the anti-kT algorithm with R=⁰.2 and 0.4. The value of p^raw_T,jet^,ch for eachjetcandidatefromthisstepisthenadjustedfortheestimated backgroundenergydensity [95],

p^reco_T,jet^,ch

=

p^raw_T,jet^,ch

−

Ajet

· ρ .

(2) Ajetcandidatefromthesecondpassisacceptedforfurtheranal- ysisifits area satisfies Ajet>0.6

π

R² [9,23],and its jet axislies within|

η

jet|<0.9−^{R andanazimuthalintervalsituatedback-to-} backwithrespecttotheTT,

ϕ

>

π

₋0.6,where

ϕ

₌

ϕ

TT−

ϕ

_jet

and0<

ϕ

<

π

.Aneventmayhavemultipleacceptedjetcandi- dates.

For further analysis we follow the procedure used in [9], in whichnorejectionofindividualjetcandidatesiscarriedout.Recoil jet distributions are accumulated for the selected event popula- tions,andcorrectionsfor uncorrelatedjetyield andforsmearing andresidualshiftofp^ch_T,jetduetouncorrelatedbackgroundarecar- ried out at the level of the ensemble-averaged distributions, as discussedbelow.

Jetenergy resolutiondueto instrumental effects(JER) andjet energyscale(JES)uncertaintyaresimilartothosein [9].TheJERis determinedbycomparingsimulatedjetsattheparticleanddetec- torlevels. The distributionof (p^det_T,jet−^ppart_T,jet^)/ppart_T,jet ^isasymmetric, with a sharp peak centered at zero and a tail to negative val- ues [20]. Fit ofa Gaussian function to thesharp peak gives

σ

2–3%,whilethefulldistributionhasRMS^{25%,withbothquan-} tities having no significant dependence on p^part_T,jet and R. The JES uncertainty,whichisduepredominantlytouncertaintyintracking efficiency,is4%,likewise withnosignificantdependenceon p^ch_T,jet and R. However, these values of JER and JES uncertainty, while helpfulto characterize the jet measurement, are not usedin the analysis.Correctionsarecarriedoututilizingthefullresponsema- trix,which incorporatesdetaileddistributions ofall contributions toJERandJESuncertainty. Thesystematicuncertainties (Table 1) likewisetakesuchfactorsfullyintoaccount.

5. Observableandrawdata

Thesemi-inclusiveh+jetdistributioncorrespondstothep_T-dif- ferential distribution of recoil jets normalized by the number of triggerhadrons, N_trig,

1 N_trig

d²Njets

dp^ch_T,jetd

η

jet

p_T,trig∈^TT ϕ∈^recoil

=

¹

σ

^pPb→h+X

d²

σ

^{pPb→h+jet+X}

dp^ch_T,jetd

η

jet

h∈^TT ϕ∈^recoil

(3)

All accepted jets contribute to the distribution on the LHS. This distributionisequivalenttomeasurementoftheratiooftwocross sections,asshownon the RHS:the coincidencecross section for bothtriggerhadronandrecoiljettobeintheacceptance,divided bythe inclusiveproductioncrosssection fortriggerhadrons. This expressionappliesto boththeMBeventpopulation,andtoevent subsetsselectedbyEA.Thefeaturesofthisobservableanditsthe- oreticalcalculationsarediscussedindetailinRefs. [9,20].Herewe considertwospecificaspectsofthisdistribution.

Thefirstaspectisthebiasimposedbythehigh-pT hadrontrig- ger.Forcollisionsystemsinwhichjetquenchingoccurs,selection of high-p_T hadrons is thought to bias towards the fragments of jet that have experienced little quenching, due to the combined effect ofjet energyloss andthe shapes ofthe inclusive jet pro- ductionandthejetfragmentationdistributions [97–104].Ifthatis thecase,thenthehadrontriggerbiasinthismeasurementwould beindependentofEA.ThisconjectureissupportedbyALICEmea- surements ofinclusive hadron production inp–Pb collisions that find no significant yield modification in the trigger p_T-range of thismeasurement, forboth the MB andEA-selectedeventpopu- lations [56,62]. The picture provided by current ATLAS and CMS hadron productionmeasurements [60,63] is morecomplex, how- ever.Furtherstudyofthisconjecturerequiresadditionalmeasure- ments ofinclusive hadron productionin pp andp–Pb collisions, together withtheoretical calculationsincorporatingjet quenching thataccuratelyreproducethesemeasurements.

The secondaspect istheeffectof triggerhadronefficiencyon the equalityin Eq. (3). As noted inSect. 3,the analysis requires selection of a single trigger hadron ineach event. However, in a fewpercentofeventstherearemultiplehadronssatisfyingtheTT selection criteria, ofwhich only one is chosen as trigger. Conse- quently,notallhadronsthatwouldcontribute tomeasurementof theinclusivehadroncrosssection(firsttermontheRHSofEq. (3)) alsocontributetoN_trig(firsttermontheLHSofEq. (3)).However, asnotedabove,theshapeofthetriggerhadron p_T-distributionis consistentwiththatoftheinclusivehadronspectrumwithin 2%.In other words,thetriggerdistributionusedinpracticesamplesthe inclusive hadron distribution with efficiency less than unity but without pT-dependent bias, within a precision of 2%. This same inefficiency also applies to the h+jet coincidence process in the second termontheLHS ofEq. (3), anditthereforecancelsiden-

ticallyintheratio.Equation (3) thereforeremainsvalidfortrigger selectionefficiencylessthanunity.

Thestudyofjetquenchingusinginclusiveyieldsrequirescom- parison oftheinclusivedistribution measured inheavy ioncolli- sions to a reference distribution measured in a systemin which quenching effects are not expected, usually pp collisions at the same√

sNN.Suchcomparisonsmustaccountfortheeffectofmul- tiplenucleon–nucleon collisionsin eachcollision ofheavy nuclei, whicharisesduetonucleargeometry.Forinclusivedistributionsin p–Pbcollisionsthisisaccomplishedbyscalinginclusivecrosssec- tions forpp collisions by

TpPb

, whichis calculatedby modeling basedon Glauber theory under theassumption that EAis corre- latedwiththecollisiongeometry [56–60,62,63,65,66,68,69].

Forthesemi-inclusivedistributioninEq. (3),thereferencedis- tributionwithoutnucleareffectsis

1

σ

_ref^pPb→h+X

d²

σ

_ref^{pPb→h+jet+X}

dp^ch_T,jetd

η

jet

h∈^TT ϕ∈^recoil

=

¹

T_pPb

· σ

^pp→h+X

T_pPb

·

^d2

σ

^pp→h+jet+X

dp^ch_T,jetd

η

jet

h∈TT ϕ∈recoil

=

¹

σ

^pp→h+X

d²

σ

^pp→h+jet+X

dp^ch_T,jetd

η

_jet

h∈^TT ϕ∈recoil

.

(4)

Since the scaling factors T_pPb

in the numeratorand denomina- torcancelidentically,thereferencedistributionforthisobservable hasno dependenceon

T_pPb

.In other words,this distributionis self-normalized,andmeasurementofjetquenchingusingthisob- servabledoesnotrequireGlaubermodelingforthereferencespec- trum.Inparticular,theassumptionthateventactivityiscorrelated withthecollisiongeometryisnotrequired.

Asimilar approach,utilizingacoincidence observable tomea- surejetquenchinginhigh-multiplicity ppcollisions,was recently proposedin [105].

Fig. 2, left panels, show recoil-jet distributions for R=⁰.4 in p–Pbcollisions withthe 50–100%ZNA selection, andfor R=⁰.2 and0.4 withthe 0–20%ZNA selection. Distributions inEA inter- vals selected with V0A andwith 20–50% ZNA are similar [106].

Thedistributions havenon-zeroyieldfor p^reco_T,jet^,ch<0,becausere- gions ofan eventcan haveenergydensitylessthan

ρ

[9]. These distributions are significantly narrower in the region p^reco_T,jet^,ch<0 thanthoseobservedincentralPb–Pbcollisions, wheretheuncor- relatedcomponentoftheeventissignificantlylarger [9].

Fig. 2, right panels, show ratios of the distributions for the twoTTclasses.Therightpanelsalsoshowthecorrespondingratio forpp collisions at√

s=⁵.02 TeV,using simulated detector-level eventsgeneratedwithPYTHIAPerugia11.Forp^reco_T,jet^,ch∼^{0 thetwo} distributions agreewithin ∼^{10% forboth valuesof R,consistent} withtheexpectationthatyieldinthisregionarisespredominantly fromprocessesthat are uncorrelatedwiththetriggerhadron [9].

At larger p^reco_T,jet^,ch, the distribution for TT{12,50} exceeds that for TT{6,7}.Thisdependenceoftherecoildistributionon p_T,trigisex- pectedfromQCD-based considerations, since higher p_T,trig biases towardshardprocesseswithhigher Q² onaverage.Indeed,hard- eningof thesemi-inclusive recoiljet distribution withincreasing pT,trig isalsoseeninthePYTHIA-generatedratiosforppcollisions at√

s=⁵.02 TeV showninthefigure, andhas beenmeasuredin ppcollisionsat√

s=^{7 TeVandobservedin}theoreticalcalculations basedonNLOpQCDandonPYTHIA [9].

The PYTHIA-generated ratio for pp collisions reproduces well theratiomeasuredforlow-EAp–Pbcollisions(ZNA50–100%,Fig.2 upperrightpanel),whilethelevelofagreementbetweenthesim-

ulation and measurements is not as good for high-EA p–Pb col- lisions (ZNA 0–20%, Fig.2,middle andbottomright panels).This occursbecausethereislargeruncorrelatedbackgroundinhigh-EA thaninlow-EAp–Pbcollisions.

Thedistributionofjetcandidatesthatareuncorrelatedwiththe trigger isindependent of p_T,trig,by definition.The distributionof correlated recoiljetscan thereforebe measured usingthe recoil observable, which is the difference of the two normalized recoil distributions[9],

_recoil

p^ch_T,jet

=

¹

Ntrig

d²Njets

dp^ch_T,jet

p_T,trig∈^TTSig

−

c_Ref

·

¹ Ntrig

d²Njets

dp^ch_T,jet

p_T,trig∈^TTRef

,

(5)

whereTT_Sig andTT_RefrefertoSignalandReferenceTTintervals,in this analysiscorresponding to TT{12,50}andTT{6,7} respectively.

recoil isnormalizedperunit

η

jet,notationnotshown.

The Referencespectrum in _recoil is scaled by the factor c_Ref to account for the invariance ofthe jet density withTT-class, as indicated by comparison of the spectrum integrals in Fig. 2 and thelargeryieldofSignalspectrumathighp^reco_T,jet^,ch[9].Thevalueof c_RefinthisanalysisistakenastheratiooftheSignalandReference spectrainthebin0<p^reco_T,jet^,ch<1 GeV/c,asshownbythearrowin Fig. 2,right panels.The value ofc_Ref lies between0.92and0.99 for the various spectra. Additional variation in the value of cRef wasusedtoassesssystematicuncertainties.

WenotethattheTT_Refdistributionincludescorrelatedrecoiljet yield,so thatthe subtractioninEq. (5) removesboth thetrigger- uncorrelated yield andthe TT_Ref-correlated yield. The recoil ob- servable is thereforea differential, not absolute, measurement of the recoil spectrum [9], though the TTRef component is signifi- cantlysmallerthanthat inthe TT_Sig componentovermostofthe p^reco_T,jet^,chrange.Therecoil distributionsinFig.2liesignificantlybe- low the TT-specific distributions for p^reco_T,jet^,ch<5 GeV/c butagree withtheTT{12,50}distributionwithin15%forp^reco_T,jet^,ch>15 GeV/c.

Thesefeaturesindicatethat theregionofnegative andsmallpos- itive p^reco_T,jet^,ch isdominatedby uncorrelatedjet yield,whilethere- gionforlargepositive p^reco_T,jet^,chisdominatedbyrecoiljetyieldthat iscorrelatedwithTT_Sig.

Onecontributiontouncorrelatedbackgroundisjetyielddueto Multiple Partonic Interactions (MPI), which can occur when two independenthigh-Q²interactionsinthesamep–Pbcollisiongen- erate thetrigger hadron andajet in therecoilacceptance. Since the two interactions are independent, the recoil jet distribution generatedbyMPIwillbeindependentofpT,trig,bydefinition,and will beremoved fromrecoil by thesubtraction. No correctionof recoil forthecontributionofMPIisthereforeneededintheanal- ysis.

Therawrecoil distributions,such asthoseinFig.2,muststill be correctedforjetmomentum smearingduetoinstrumental ef- fectsandlocalbackgroundfluctuations, andforjetreconstruction efficiency. Jet quenching effects are measured by comparing the corrected _recoil distributionsfor differentEAclasses,andatdif- ferent R.

6. Corrections

Corrections forinstrumental effectsandlocalbackgroundfluc- tuations are carried out usingunfolding methods [107–109].The measured distribution ^M_recoil is related to the true distribution ^T_recoil byalineartransformation,

Fig. 2.Uncorrectedsemi-inclusivedistributionsofchargedjetsrecoilingfromahigh-pThadrontriggerinp–Pbcollisionsat√_s

NN=⁵.02 TeVwiththeEAselectionof50–100%

inZNAforR=⁰.4 (toppanels),andwiththeEAselectionof0–20%inZNAforR=⁰.2 (middlepanels)andR=⁰.4 (bottompanels).TheacceptanceforTTandrecoiljets intheCMframearedenoted y^∗_TTand y^∗_jet,respectively.Leftpanels:rawdistributionsforTT{12,50}(redcircles)andTT{6,7}(blueboxes),andthecorrespondingrecoil distribution(Eq. (5),blackcircles).Rightpanels:ratioofyieldsforTT{12,50}/TT{6,7}measuredbyALICEinp–PbcollisionsandcalculatedusingdetectorlevelPYTHIAPerugia 11simulationofppcollisionsat√

s=5.02 TeV.ThePYTHIA-generatedratiosinthetoprightandbottomrightpanelsarethesame.Thearrowindicatesthe0–1 GeV/cbin whichisusedtocalculatecRef.Theuncertaintiesarestatisticalonly.(Forinterpretationofthecolorsinthefigure(s),thereaderisreferredtothewebversionofthisarticle.)

^M_recoil

(

p^reco_T,jet^,ch

)

=

^Rfull

(

p^reco_T,jet^,ch

,

p^part_T,jet

) ⊗

eff

(

p^part_T,jet

) ·

^T_recoil

(

p^part_T,jet

)

,

(6)

whereeff(p^part_T,jet)isthejetreconstructionefficiencyandR_fullisthe cumulativeresponsematrixexcludingjetreconstructionefficiency.

Theexplicitspecificationofjetreconstructionefficiencyinthisex- pression,distinctfromtheunfoldingstep,makesinterpretationof the unfolding procedure more transparent. R_full(p^reco_T,jet^,ch,p^part_T,jet) is

further assumedto factorizeasthe product ofseparate response matricesforbackgroundfluctuationsandinstrumentalresponse, R_full

(

p^reco_T,jet^,ch

,

p^part_T,jet

) =

^Rbkgd

(

p^reco_T,jet^,ch

,

p^det_T,jet

) ⊗

^Rinstr

(

p^det_T,jet

,

p^part_T,jet

).

(7) ThematrixR_fullcanbeclosetosingular,inwhichcasethesolution ofEq. (6) viadirectinversionofRfullgenerateslargefluctuationsin centralvaluesandlargevarianceduetothestatisticalvariationin

^M_recoil(p^reco_T,jet^,ch)and R_full[107].AnapproximatesolutionofEq. (6) thatisphysicallymoremeaningfulisobtainedbyregularized un- folding, which imposes a smoothness constrainton the solution.

Unfoldinginthisanalysisiscarriedoutusingapproachesbasedon SingularValueDecomposition(SVD)[108] andonBayes’Theorem [109],asimplementedintheRooUnfoldpackage [110].

The instrumental response matrix, R_instr, is calculated from the simulated detector response applied to events generated by PYTHIAforppcollisionsat√

s=⁵.02 TeV.Jetsattheparticle-level and detector-level are matched in (

η

,φ) space by selecting the detector-leveljet that is closest tothe particle-leveljet, andvice versa.AnentryinRinstr ismadeforeverymatchedpair.TheRinstr matrixisnormalizedsuchthat,foreachbininp^part_T,jet,thesumover allbinsin p^det_T,jet isunity.Inpractice,however,thematchingprob- abilityislessthan unity,whichisaccountedforinEq. (6) bythe efficiencyfactor eff(p^part_T,jet). No dependence of Rinstr on EAofthe p–Pbeventpopulationwasobserved.

The background response matrix, Rbkgd, is calculated by em- beddingsingle trackswithtransversemomentum p^embed_T intoreal p–PbeventsthatcontainaTT [9].Therelativeazimuthalanglebe- tweentheembeddedtrackandtheTTisintherange[

π

/4,3

π

/4], tominimize overlapofthe embeddedtrackwiththe jetcontain- ingTTandwithtruerecoiljets.Thesehybrideventsareanalyzed withthesameprocedures usedforrealdata,andthejetcontain- ingtheembeddedtrackisidentified.Smearingofjetcandidatep_T duetobackgroundfluctuationsisquantifiedbythedistributionof

δ

pT

=

^preco_T,jet^,ch

−

^pembedT

,

(8)

where p^reco_T,jet^,ch refers to the jet containing the embedded track.

R_bkgd, theprobability distribution ofδpT,iscalculated separately forthe MB population andfor thevarious event populations se- lected by EA. Embedding of PYTHIA-generated jets rather than singletracksyieldsverysimilarδp_T distributions.

Unfoldingfollowstheproceduredescribedin[23].Theinputto unfoldingisthemeasureddistribution^M_recoil(p^reco_T,jet^,ch)intherange 1<p^reco_T,jet^,ch<90 GeV/c. Theunfolding procedure requiresspecifi- cation ofa prior distribution.For the primary analysis, the prior istherecoildistributioncalculatedwithPYTHIA8tune4C[90] for ppcollisionsat√

s=⁵.02 TeV.RegularizationofSVDunfoldinguti- lizesastatisticaltesttodeterminethetransitionbetweenrandom fluctuationsandstatisticallysignificantcomponentsofthed-vector [108], which is achieved typically with regularization parameter k=^4.ForregularizationofBayesianunfolding,convergenceisde- termined by the stability of the unfolded solution forsuccessive iterations,whichisachievedtypicallybytheseconditeration.

For both unfolding approaches, consistency of the solution is checked by backfolding, i.e. smearing the unfolded distribution with R_full andcomparing theresult withthe ^M_recoil distribution.

Sinceregularizationsuppressesoscillatingcomponentsofthesolu- tion,thebackfoldedand^M_recoildistributionswillingeneralnotbe identical.Consistencyofunfoldingisimposedbyrequiringthatthe differencebetweenthebackfoldedand^M_recoil distributionsineach binbelessthan3

σ

,basedon^M_recoil statisticalerrors;otherwise, thesolutionisrejected.

Closure of the unfolding procedure was verified by a test in which the response matrix, the recoil distribution, and the prior weregeneratedby statisticallyindependentsets ofPYTHIA- generatedeventsforppcollisions at√

s=⁵.02 TeV.Theresponse matrixandthespectrumwere generatedusingPYTHIA6Perugia- 11, while the prior was generated using PYTHIA8 tune 4C. The recoil distribution fromthis test agrees withthe input particle- leveldistributiontobetterthan 5%.

Correction forjetreconstruction efficiencyis applied afterthe unfolding step by scaling the unfolded _recoil distribution by 1/eff(p^ch_T,jet).Thevalueofeff(p^ch_T,jet)is0.96atp^ch_T,jet=^{15 GeV}/cand 0.98atp^ch_T,jet=^{60 GeV}/c.

7. Systematicuncertainties

The systematicuncertainties of therecoil distribution areas- sessedbyvaryingthecomponentsofthecorrectionprocedure.The mostsignificantsystematicuncertaintiesareduetothefollowing:

– Regularization ofunfolding:forSVD,varyk by±^{2 relativeto} its value in theprimary analysis; forBayesian unfolding,use thefirstthreeiterations;

– Unfoldingprior:generatepriordistributionswithPYTHIA6and PYTHIA8;foradditionalvariation takethedifferencebetween the priors from the two PYTHIAversions and vary them by its magnitude but with opposite sign; use the unfolded so- lution based on the iterative Bayesian approach as prior for SVD-basedunfolding;

– Binningofdistributions:usethreedifferentchoicesofbinning, withcorrespondingvariationinspectrumlimits;

– Calculationof

ρ

: utilizeamodified procedure[65,81,96] that accountsforsparse regions oftheevent, insteadofthearea- basedapproach(Eq. (1));

– cRef variation: useas upper limit cRef=1, in which the ref- erence recoiljet spectrum is not scaled. For the lower limit, doublethevalue of(1−^cRef) fromtheprimary analysis, giv- ing cRef=⁰.95 for R=⁰.2 and cRef=⁰.90 for R=⁰.4. The systematicuncertaintybandcorrespondsto thelargestdevia- tionfromallsuchvariationsoftheunfoldedspectrum,relative tothespectrumresultingfromthec_Ref choiceoftheprimary analysis;

– Trackingefficiency:vary±^{4%relativetonominalvalue[65];}

– Trackmomentumresolution:extractsystematicuncertaintyof momentum resolution fromazimuthal variation ofthe inclu- sivecharged-trackdistribution;vary Rinstraccordingly.

The correction for secondary vertex tracks due to weak decays makes a smaller contribution to the systematic uncertainty than theabovesources.

There is a difference in the response matrix fordifferent se- lections of EA, due to the different magnitude of uncorrelated backgroundinducedbysuchaselection.Thecorrectionprocedure accountsforthisdifference.However,theremaybearesidualcor- relationbetweentheEA-biasandTT-biasinthecalculationofthe response.Thiscorrelationwasexploredbycalculatingtheresponse matrixwiththeappropriateEA-selecteddata,bothwithandwith- outTT-bias.Thecorrectedspectraresultingfromthetworesponse matricesdiffer by lessthan 2% forall p^ch_T,jet, R,andEA-selection.

This is however a check, not a systematicuncertainty, since the response matrix for the analysisis properly calculated using the TT-bias,anditdoesnotcontributetothesystematicuncertaintyof themeasurement.

TheEA-biasinducedbytheTT{6,7}andTT{12,50}requirements are similar, and the δp_T distributions generated for events with thetwoTTrequirementsarelikewisesimilar.Thisvariationinthe δpTdistributiongeneratesvariationoflessthat1%inthecorrected spectrum,afterunfolding.

Statistical fluctuations ofthe raw datainfluence the quantita- tive assessmentofthesystematicuncertaintiesarising fromthese sources. We utilizethefollowing procedureto minimize such ef- fects.Foreachsourceofuncertainty,severalrandomizedinstances of theraw recoil spectrum are generatedby variation aboutthe