Measurement of jet suppression in central Pb-Pb collisions at √sNN=2.76 TeV

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Physics Letters B

www.elsevier.com/locate/physletb

Measurement of jet suppression in central Pb–Pb collisions at

√ s _NN = ² . 76 TeV

.ALICE Collaboration

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

Articlehistory:

Received6February2015

Receivedinrevisedform25March2015 Accepted20April2015

Availableonline22April2015 Editor:L.Rolandi

Thetransversemomentum (pT)spectrumandnuclearmodificationfactor(RAA)ofreconstructedjetsin 0–10%and10–30%centralPb–Pbcollisionsat√_s

NN=².76 TeV weremeasured.Jetswerereconstructed usingtheanti-kTjetalgorithmwitharesolutionparameterofR=⁰.2 fromchargedandneutralparticles, utilizing theALICEtracking detectorsand ElectromagneticCalorimeter (EMCal).Thejet pTspectraare reported in the pseudorapidity interval of |ηjet|<0.5 for 40<pT,jet<120 GeV/c in 0–10%and for 30<pT,jet<100 GeV/c in10–30% collisions. Reconstructed jets wererequired to contain aleading chargedparticlewithpT>5 GeV/ctosuppressjetsconstructedfromthecombinatorialbackgroundin Pb–Pb collisions.The leading chargedparticle requirementappliedto jetspectraboth inppand Pb–

Pb collisionshad anegligibleeffectonthe RAA.Thenuclear modificationfactorRAA wasfound tobe 0.28±⁰.04 in0–10%and0.35±⁰.04 in10–30%collisions,independentofpT,jetwithintheuncertainties ofthemeasurement.Theobservedsuppressionisinfairagreementwithexpectationsfromtwomodel calculationswithdifferentapproachestojetquenching.

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

1. Introduction

DiscreteformulationsofQuantumChromodynamics (QCD)pre- dict the existence of a cross-over transition from normal nu- clear matter to a new state of matter called the Quark–Gluon Plasma (QGP), where the partonic constituents, quarks and glu- ons,are deconfined.The QGPstateis expectedtoexistatenergy densitiesabove0.5 GeV/fm³andtemperaturesabove160 MeV[1], whichcanbereachedincollisionsofheavy-ionsatultra-relativistic energies. The existence of the QGPis supported by the observa- tionsreportedbyexperimentsattheRelativisticHeavyIonCollider (RHIC)[2–5]andattheLargeHadronCollider(LHC)[6–17].

One way to characterize the properties of the QGP is to use partonsfromthehardscatteringofthepartonicconstituentsinthe collidingnucleons asmediumprobes.Hardscatteringisexpected tooccurearlyinthecollisionevolution,producinghightransverse momentum(pT) partons,whichpropagatethrough theexpanding mediumandeventuallyfragmentintojetsofhadrons.

Dueto interactions ofthe high-pT partons withthe medium, theenergyof thepartons isreducedcompared to proton–proton (pp) collisions due to medium-induced gluon radiation and col- lisionalenergy loss (jetquenching) [18,19]. The productioncross section of the initial hard scattered partons is calculable using

E-mailaddress:[email protected].

perturbative QCD (pQCD), and the contribution from the non- perturbativehadronizationcanbewellcalibratedviajetmeasure- mentsinppcollisions.

Jet quenching has been observed at RHIC [20–29] and at the LHC[8,16,17,30–41]viathemeasurementofinclusivehadronand jet productionathigh pT,di-hadron angularcorrelationsandthe dijet energy imbalance. In all cases, the measured observable is found to be stronglymodified in centralheavy-ion collisions rel- ative to pp collisions, when compared to expectations based on treating heavy-ioncollisions asan incoherentsuperpositionofin- dependentnucleon–nucleoncollisions.

Measurementsof the jet kinematics are expectedto be more closely correlated to the initial partonkinematics than measure- mentsofhigh-pThadrons.Jetsareusuallyreconstructedbygroup- ing measured particles within a given distance,e.g. a cone with radius R.Theinteraction withthemedium canresultinabroad- ening of the jet shape, a softening of the jet fragmentation [42]

leadingtoanincreaseofout-of-conegluonradiation[43]withre- spect to jets reconstructed in pp collisions [17]. Therefore, for a givenjetresolutionparameter R andafixedinitialpartonenergy, theenergyofjetsreconstructedinheavy-ioncollisionsisexpected tobesmallerthanthosereconstructedinppcollisions.

Jetmeasurementsinheavy-ioncollisionsarechallengingsincea singleeventcanhavemultiple,possiblyoverlapping,jetsfromin- dependentnucleon–nucleonscatters,aswellascombinatoric“jets”

fromthe large,partially correlatedandfluctuatingbackground of http://dx.doi.org/10.1016/j.physletb.2015.04.039

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

lowtransversemomentumparticles.Consequently,jetreconstruc- tioninheavy-ion collisionsrequires arobust jet-signaldefinition, and a procedure to correct for the presence of the large back- groundanditsassociatedregion-to-regionfluctuations[44].

The resultsreported in thisletter are fromlead–lead (Pb–Pb) collision data atan energy per nucleon pairof √

sNN=2.76 TeV recordedby theALICEdetectorin2011. Chargedparticles are re- constructed with the Inner Tracking System (ITS) and the Time ProjectionChamber (TPC)downto pT of0.15 GeV/c.Neutralpar- ticles, excluding neutrons and K_L⁰s, are reconstructed with the Electromagnetic Calorimeter (EMCal) down to a transverse en- ergy ofthe EMCalclustersof 0.3 GeV.Forjet reconstruction, we followed the approach applied in Refs. [45,46], where the aver- age energy density of the event was subtracted from the signal jets on a jet-by-jet basis, and the detector and background ef- fectswerecorrectedonanensemblebasisviaanunfoldingproce- dure.Thesignaljetswereobtainedusingtheanti-kTjetalgorithm [47] with a resolutionparameter of R=⁰.2 inthe pseudorapid- ity range of |

η

jet|<0.5. Signal jets were required to contain at least one charged particle with pT>5 GeV/c. The corrected jet pT spectraandnuclearmodificationfactors(RAA)arereportedfor 40<p_T,jet<120 GeV/cin0–10%andfor30<p_T,jet<100 GeV/c in10–30%centralPb–Pb collisionsandthecorrectedjet pT spec- trumfor20<pT,jet<120 GeV/cinppcollisionsat√

s=².76 TeV from13.6 nb⁻¹ recordedin 2011.The RAAiscompared toexpec- tationsfrom two jet quenchingmodelcalculationswith different approaches, described later, inorderto test thesensitivityofthe observable to the energy density via the centrality dependence, andtothepartonenergyscaleviathemomentumdependence.

2. Experimentalsetup

ForacompletedescriptionoftheALICEdetectoranditsperfor- manceseeRefs. [48]and[49],respectively.Theanalysispresented herereliesmainlyon theALICEtrackingsystemandEMCal,both of which are located inside a large solenoidal magnetwith field strength0.5 T.

The tracking system consists of the ITS, a high-precision six- layer silicondetector system withthe inner layer at 3.9 cm and theouter at43 cm fromthecenter ofthe detector,andthe TPC witha radial extent of85–247 cm, provides up to 159 indepen- dent spacepoints per track.The two innermostlayers ofthe ITS consistoftheSiliconPixelDetector(SPD),whichprovidestwolay- ersof silicon pixel sensors at radii 3.9 cm and7.6 cm fromthe beamaxisandcoversthefullazimuthover|

η

|<2 and|

η

|<1.4, respectively. The combined information of the ITS and TPC can determine the momenta of charged particles from low momen- tum (pT≈⁰.15 GeV/c) to highmomentum (pT≈^{100 GeV}/c) in

|

η

_|<0.9 andfullazimuth.

TheEMCalisaPb-scintillatorsamplingcalorimeter,whichcov- ers107 degreesinazimuthand|

η

|<0.7.Itconsistsof10 super- moduleswithatotalof11520 individualtowerseachcoveringan angularregion

η

_×

ϕ

₌0.014×⁰.014 which are read out by avalanchephotodiodes.

Thedatawererecordedin2011forPb–Pbcollisionsat√ sNN= 2.76 TeV using a set of triggers based on the hit multiplicity recordedbytheVZEROdetector,whichconsistsofsegmentedscin- tillators covering the full azimuth over 2.8<

η

<5.1 (VZERO-A) and−³.7<

η

<−¹.7 (VZERO-C).

3. Dataanalysis

A total of 11.5M (15 μb⁻¹) and5.7M (3.7 μb⁻¹) events with VZERO multiplicities corresponding to 0–10% and 10–30% most centraleventswereselectedusingthecentralitydeterminationas

described inRef. [50]. The accepted events,reconstructed asde- scribedinRef.[51],wererequiredtohaveaprimaryreconstructed vertexwithin10 cmofthecenterofthedetector.

Reconstructedtrackswererequiredtohaveatleast3hitsinthe ITSusedinthefittoensureadequatetrackmomentumresolution for jet reconstruction.For trackswithout anyhit in the SPD, the primary vertex location was usedin addition tothe TPCandITS hits forthe momentum determinationof thetrack. Thisreduced the azimuthal dependence of the track reconstruction efficiency duetothenon-uniformSPDresponse,withoutcreatingtrackcol- lectionswithdrasticallydifferingmomentumresolutions.Accepted trackswere requiredtobemeasured with0.15<p_T<100 GeV/c in|

η

|<0.9,andtohaveatleast70TPCspace-pointsandnoless than80%ofthegeometricallyfindablespace-pointsintheTPC.The trackingefficiencywasestimatedfromsimulationsofthedetector response using GEANT3 [52] with the HIJING [53] event genera- tor asinput. In 0–10% collisions, it is about56% at 0.15 GeV/c, about83%at1.5 GeV/candthendecreasesto81%at3 GeV/c,after whichitincreasesandlevelsofftoabout83%atabove 6.5 GeV/c.

In 10–30% collisions, the tracking efficiency follows a similar pT dependence pattern, with absolute values of the efficiency that are 1 to 2% higher compared to 0–10% collisions. The momen- tum resolutionδpT/pT,estimated ona track-by-track basis using the covariance matrix of the track fit, is about 1% at 1.0 GeV/c andabout3% at50 GeV/c.Trackswith pT>50 GeV/c were only a smallcontributionto theinclusivejet populationconsidered in this analysis, for example only 20% of the jetswith pT,jet larger than100 GeV/c werefoundtocontainatrackabove50 GeV/c.

EMCal cells witha calibrated response of more than 50MeV were clusteredprior toinclusion inthe jet finderby aclustering algorithm whichrequiredeach cluster toonlyhavea single local maximum [49]. Interactions of slow neutrons or highly ionizing particles in the avalanche photodiodes createclusters with large apparent energy, but anomalously small number of contributing cells, and are removed from theanalysis. Anon-linearity correc- tion,derivedfromelectrontestbeamdata,ofabout7%at0.5 GeV andnegligibleabove3 GeV,was appliedtotheclusters’ energies.

The energy resolution obtained from electron test beam data is about15%at0.5 GeVandbetterthan5%above3 GeV.

Unlike electrons and photons, which deposittheir full energy intheEMCalvia electromagneticshowering, chargedhadronsde- posit energy in the EMCal, mostly via minimum ionization, but also via nuclear interactions which generate hadronic showers.

To avoiddouble counting, the energy depositedin the EMCalby charged particles that were already reconstructed as tracks, the clusters’ energieswerecorrectedbythefollowingprocedure[54]:

All tracks with p_T>0.15 GeV/c were propagated to the aver- age cluster depthwithin the EMCal,andthen associatedto clus- ters with E_T>0.15 GeV within the window |

η

|<0.015 and

|

ϕ

|<0.025. Trackswere always matched to their nearest clus- ter, while clusters were allowed to havemultiple track matches.

Clusters withmatched tracks were correctedforcharged particle contamination by removing the fraction f =^{100% of the sumof} the momenta of all matched tracks from the cluster energy, as done in [54]. Clusters with ET>0.30 GeV after this correction wereusedinthisanalysis.

ThecollectionoftracksandcorrectedEMCalclusterswas then assembled intojetsusing theanti-kT or thekT algorithms inthe FastJetpackage [55] witha resolutionparameterof R=⁰.2.Only those jetsthat were at least R away fromthe EMCalboundaries of|

η

_|<0.7 and1.4< φ <

π

,andthusfullycontainedwithin the EMCal acceptance,were kept intheanalysis whichlimitsthe ef- fect ofthe acceptanceboundarieson themeasured jet spectrum.

Jetsreconstructedby theanti-k_T algorithmwere usedtoquantify

signaljets,whilejetsreconstructedbythekT algorithmwereused toquantifythecontributionfromtheunderlyingevent.

Thesignal spectrum formedfromthe reconstructed jetsisaf- fected by the contribution from the underlying event. In order to suppress the contribution of the background to the measure- ment of the jet energy, we followed the approach described in Refs. [45,46], which addresses the average additive contribution tothe jet momentum ona jet-by-jetbasis. The underlyingback- ground momentum density was estimated event-by-event using themedianof p^raw_T,jet/A_jet,where p^raw_T,jet is theuncorrected energy and Ajet is the area of jets reconstructed withthe kT algorithm.

Due to the limited acceptanceof the EMCal,

ρ

ch, the medianof theevent-by-eventmomentumdensitydistributionobtainedfrom chargedjets(i.e.jetsreconstructedfromtracksonly)in

η

jet<0.5 and full azimuthal acceptance was used. Then,

ρ

scaled was de- terminedby scaling

ρ

ch usinga centrality-dependent factor.This factorisobtained fromaparametrization ofthemeasurement of the charged-to-neutral energy ratio, using tracks and corrected clusters in the EMCal acceptance. In 0–10% central Pb–Pb colli- sions, the average charged background momentum density was

ρ

ch≈^{110 GeV}/c.Afterscalingtoincludetheneutralcomponent weobtained

ρ

scaled≈^{190 GeV}/c,whichcorrespondstoan aver- agecontribution ofthe underlyingevent ofabout24 GeV/c in a cone of R=⁰.2. In 10–30%central Pb–Pb collisions

ρ

scaled ^de- creases to ≈^{130 GeV}/c. For every signal jet reconstructed with theanti-k_T algorithm, the backgrounddensityscaled by the area of the reconstructed signal jet was subtracted from the recon- structed transverse momentum of the signal jet according to p^reco_T,jet=^praw_T,jet−

ρ

_scaled·A_jet.

Region-to-regionbackgroundfluctuationsleadtoasmearingof the reconstructed jet energy. Their magnitude was estimated as described in Refs. [45,46] in two different ways: (1) by taking the scalar sum of the pT of all particles found in a cone ran- domly placed in the event, referred to as random-cone method, and(2) embedding a single particle in the eventand inspecting theanti-k_Tjetthatcontainsthatembeddedparticle,referredtoas embedded track method. The first method does not rely on any assumptionsaboutthestructureofthebackgrounditselfandgives approximately the same background fluctuation as embedding a trackwithinfinitemomentumforanti-kT jets.Thesecondmethod shouldbeabletoreproducethebackgroundasseenbytheanti-kT algorithmmore directly.The background fluctuationswere quan- tifiedbyδpT=^pconeT −

ρ

scaled·

π

R² fortherandom-conemethod, andδpT=^preco_T,jet−^pprobeT forthe embedded-trackmethod witha minimumof p^probe_T =^{10 GeV}/c forthe pT oftheembedded track.

Above10 GeV/ctheresultingδpTdistributiondoesnotdependon thep_Toftheembeddedparticle.Theδp_Tdistributionsforthetwo methodsinthe10%mostcentralcollisionsareshowninFig. 1 for p^probe_T =^{60 GeV}/c.The twomethods appeartoprovide thesame quantitative response to the background fluctuations, with only marginal differencesmainly due to smalljet area fluctuationsin theembeddingtrackmethod.ThewidthsoftheδpT distributions areabout6 GeV/c.The left-handside (LHS)ofthe distributionis Gaussian-likeandisdominatedbysoftparticleproduction.Tode- termine its width, the distributions were fitted recursively with a Gaussian function in the range [

μ

^LHS−³

σ

^LHS,

μ

^LHS+ ¹₂

σ

^LHS] usingthemeanandwidthofthe δpT distributionasstartingval- uesfor

σ

and

μ

.The LHSwidthis about5 GeV/c in0–10% and about3.5 GeV/c in10–30%events.Theright-hand sidehasaddi- tionalcontributionsfromhardscatteringprocesses,andtheresult- ing non-Gaussian tailathigh δpT isdueto overlapping jets. The random-conemethodwasusedasthebaselineinthisanalysisfor creatingthe response matrix used in unfolding, while the single

Fig. 1.TheδpTdistributionforR=⁰.2 withtherandom-coneandtheembedded- track methods inthe 10% mostcentral events, with p^probe_T =60 GeV/c for the embedded-trackmethod.

particle embedding method was used to study the sensitivity of theresultstothemethod.

Additionally, signal jets were required to contain a charged trackwithatransversemomentumofatleast5 GeV/candamin- imumbackgroundsubtracted p^reco_T,jet of30 GeV/c for0–10%andof 20 GeV/c for 10–30% most central events, which roughly corre- spondsto5

σ

oftheδpTdistribution,inordertosuppressthecon- tributionofcombinatorialjets, i.e.fromjetsreconstructedmainly fromupwardfluctuationsofthesoft-particlebackground.

Both the averagebackground andthe backgroundfluctuations are averaged over all possible orientations of the event plane, namely it is assumed that the signal jet sample being analyzed is isotropicallydistributedwithrespect to theeventplane. How- ever, the jet sample may show some degree of correlation with theeventplane,bothforphysicalreasons(e.g. pathlengthdepen- denceofjetenergyloss) orasaresultofthecutsappliedinthe analysis(mostnotablytherequirementontheleadinghadron p_T).

Sincethe backgroundisalsocorrelatedwiththeeventplane due to flow (v2) [10],a question mayarise aboutthe validity ofthis approach. Upper limits on the magnitude of these effects have beenestimatedby usingrandom cones biasedtowardsthe event plane, either by requiringthe presence ofa 5 GeV/c trackorby weighting the distribution using an upper limit on the jet v2 of 0.1. Inboth cases,the upperlimitson theshiftof thejet energy scale (JES)werefoundtobesmallerthan0.1 GeV/c.

4. Unfolding

The measuredjet spectraare distortedby theresponseofthe detectors used in the measurement and the background fluctu- ations in the underlying event. To correct for these effects we usedan “unfolding”procedure,asdescribed inRef.[46].Thecor- recteddistribution p^true_T,jetandthemeasured distribution p^reco_T,jetare related by a convolution through the response matrix RM_tot= RM_bkg×^RMdet, where RM_det parametrizes the detectorresponse and RM_bkg the backgroundfluctuations. The unfoldingprocedure operates under the assumption that p^reco_T,jet=^RMtot×^ptrue_T,jet^{. Both} backgroundfluctuationsandthedetectorresponsetojetsareuni- formwithinthe

η

and

ϕ

acceptances,whichisa preconditionfor thefactorizedapproachusedinbuildingRMtot.

The detectorresponse for jet reconstruction was obtainedus- ing pp eventssimulated withthePYTHIA 6[56] event generator

(tune A [57]). Jets were reconstructed both at “generator level”

andat“detectorlevel”usingtheanti-kT algorithm.Generator-level simulationsutilizedonlypromptparticlesoriginatingfromthecol- lision(withc

τ

<1 cm),directlyfromtheeventgeneratoroutput, withoutaccountingfordetectoreffects;detector-levelsimulations also includeda detailedparticle transport and detectorresponse simulationbasedonGEANT3[52]withthedetectorresponsesetto the Pb–Pb configuration. During detector-level jet reconstruction, an additional pT-dependent tracking inefficiency was introduced inordertoaccountforthelargerinefficiencyduetothelargeroc- cupancy effects in central Pb–Pb events compared to pp events.

Occupancy effects have been estimated comparing the tracking performance in PYTHIA and HIJING simulations, which represent ppandPb–Pbevents[53].TheoccupancyeffectsincentralHIJING eventsarelargerfor pT<0.5 GeV/cwheretheefficiencyisabout 4% lower compared to PYTHIA, and then levels off to about 2%

lowerfor pT>2 GeV/c.Insemi-centralHIJINGevents,occupancy effects onthe tracking efficiencyamount to no morethan 2% at low pT andabout1% for pT>2 GeV/c.Other than thistracking efficiencycorrection,thedetectorresponsetojetswasassumedto bethesameinPb–PbeventsasinthePYTHIAsimulatedpp colli- sions.

Thegenerator-levelanddetector-leveljetswerematchedbased onthe Euclideandistancebetweentheirjet axes inpseudorapid- ityandazimuthal angle.It wasensured thatthematchingopera- tionis bijective:each generator-leveljet was matchedto atmost onedetector-leveljet [46]. Everymatchedjet paircorrespondsto an entryin the detector response matrix, RM_det. An unmatched generator-leveljetrepresentsajetthatwasnotreconstructed,and thisdistributionwasusedtodeterminethejetreconstructioneffi- ciency.In0–10%Pb–Pbevents,thedetectorjetreconstructioneffi- ciencywasfoundtobe90%at40 GeV/cand95%above70 GeV/c, limitedmainlybythetrackreconstructionefficiencyoftheleading charged particle. As described above, at detector level the con- stituentcut was 150 MeV/c fortracks,and300 MeV forclusters after the cluster energy is corrected for charged particle energy contamination.However,atgeneratorlevelnosuchcutisapplied, and hence the reconstructed jets are corrected to a constituent chargedparticlemomentumof0 MeV/candtoaconstituentclus- terenergyof0 MeVintheunfoldingprocess.Anetnegative shift oftheJESatdetectorlevelwasobtained, whichoriginatesmainly from tracking inefficiency and unreconstructed particles, such as neutronsandK_L⁰,thoughthesubtractionprocedureforenergyde- posits by charged particles in the EMCal and missing secondary particles from weak decays contribute to the shift [54]. The JES correction applied through the response matrix is about 23% at p^true_T,jet of40 GeV/c and29%at120 GeV/c independentofcentral- ity.

The RM_bkg matrix was constructed row-by-row by takingthe δpTdistributionandshiftingitalongthep^reco_T,jetaxisbytheamount p^true_T,jet corresponding to each row (Toeplitz matrix). This matrix construction method assumes that the response of the jet spec- trumtobackgroundfluctuationsisindependentofthejetmomen- tum.

The pT-dependenceofthejetmomentumresolution

σ

(p^reco_T,jet)/

p^true_T,jet is different for the background and detector contributions [46]. The contributionfrom background fluctuations is dominant atlow p^true_T,jetandisproportionalto1/p^true_T,jet,whereasthecontribu- tionfromdetectoreffectsisfairlyconstant withp^true_T,jet.The cross- overbetweenthetwocontributionshappensatp^true_T,jet≈^{30 GeV}/c.

Thecombinedjet momentumresolution isabout23% at p^true_T,jet of 40 GeV/c and20% at 120 GeV/c for0–10% collisions, while itis 24%atp^true_T,jetof30 GeV/c and20%at100 GeV/cfor10–30%.

Two unfolding algorithms withdifferent regularization proce- dureswereusedforcorrectingthemeasuredjetspectrum:the

χ

²

minimization method [58] with a log–log-regularization and the generalized Singular Value Decomposition (SVD) method [59],as implemented in RooUnfold [60], which was used for the default value ofthe data points. The measured spectrum usedas an in- put to the unfolding was in the range 30< p_T,jet<120 GeV/c for 0–10% and 20< p_T,jet<100 GeV/c for 10–30% collisions.

A smoothed version of the measured spectrum was used as the prior, sothat thestatisticalfluctuationswithin thedatawere not magnified inthe unfolding process. The regularization parameter used for SVD unfolding is k=^{5. The value of k is chosen such} that it corresponds to the d vector magnitude of 1, and Pearson coefficientswhichdonotshowalargevariationinthecorrelation betweenneighboring pTbins.

The corrected jet spectra are reported for 40 < p_T,jet <

120 GeV/c in 0–10%,and for30<pT,jet<100 GeV/c in 10–30%

wherethe efficiencyduetothesekinematiccutsishigh, approx- imately 90%. Itwas verifiedthat thecut on thereconstructedjet pT hasanegligibleeffectinthereportedpT regionofthefinalre- sult,aslongastherequirementontheleadingchargedtrackp_Tis atleast5 GeV/c.Ifthisthresholdisreduced,thecutonthemini- mumreconstructedjetp_Tbecomescrucialforunfoldingstability.

Theanalysisproceduresinthe10%mostcentralcollisionswere testedwithtwodifferentMonte Carlo(MC)models,whereevents were constructedby embedding jetsinto a softbackground.The first testverifiedthe robustnessoftheunfolding frameworkwith the inclusionof fake“jets”that are clusteredfromthesoftback- ground, whichdid notoriginate froma hardprocess. Thesecond modeltestedtheassumptionthatthebackgroundanddetectorre- sponsescanbefactorized.

In the first model, the soft background of both charged and neutral particles was modeled with3100<N_tracks<5150 where theparticletransversemomentaweretakenfromaBoltzmanndis- tribution with a temperature of 550 MeV. This model created a fluctuating background similar to that ofthe 0–10% Pb–Pb data;

e.g. thebackground fluctuations, asestimated via the δpT distri- butions, coincide within few percent. Jets were reconstructed at generator levelin PYTHIA-onlyeventsandatdetectorlevel,with the added background.The first model validatedthe background subtractiontechnique,andinparticularthestabilityoftheunfold- ingmethodagainstthecontributionfromtheresidualcombinato- rial background.In the second model,the backgroundwas taken fromreal0–10%Pb–Pbevents.Thechargedparticlecorrectionfor the EMCal clusters was applied after embedding. Only jets with at least 1 GeV/c of transverse momentum coming from the em- bedded PYTHIAevent were selected for the test. This is needed to reject the signal from hard scatterings in the data, but also removes mostofthe combinatorialjets fromthePb–Pb underly- ing event. The secondmodel was usedto testthe validityof the charged particlecorrection applied to theEMCal clusters, inpar- ticularintheinterplaybetweentheunderlyingeventandthejets.

It alsovalidatescertain aspects ofthecorrectionsapplied forthe backgroundfluctuations, e.g. theunsmearing ofthejet pT dueto backgroundfluctuationsortheoverlapwithlow momentumjets.

Backgroundtracksandclusterscouldbematchedtojettracksand clusters orvice versa, so that the correction forcharged particle contamination could potentially causean over-subtraction that is not corrected forin the unfolding procedure. These Monte Carlo testsshowedthat theanalysisprocedures outlinedabove,includ- ing unfolding,recovered theinput spectrumwithin thestatistical andsystematicuncertaintiesofthemodels.

Fig. 2.ThespectraofR=0.2 jetswithaleadingtrackrequirementof5 GeV/cin 0–10%and10–30%mostcentralPb–Pbcollisionsscaledby1/Ncollandininelastic ppcollisionsat√_s

NN=².76 TeV.Theuncertaintiesonthenormalizationareabout 11%forthePb–PbdatafromtheuncertaintyonNcollandabout8%fortheppdata fromthetotalinelasticcrosssection.

Table 1

Summaryofsystematicuncertaintiesfor0–10%mostcentralcollisions.Thefirstcol- umnistheuncertaintyattheminimump^min_T,jetof40 GeV/c,thesecondcolumnis theuncertaintyatthemaximump^max_T,jetof120 GeV/c.The minimumandmaximum columnsgivetheextreme,andthelastcolumngivestheaveragesystematicuncer- taintyovertheentirepTrange.Thetotalcorrelateduncertaintywascalculatedby addingthecomponentsinquadrature,whiletheshapeuncertaintywascalculated astheσ ofthedifferentvariations(seetextfordetails).

Category Relative uncertainty (%)

p^min_T,jet p^max_T,jet Min. Max. Avg.

Tracking efficiency 7.7 11.3 7.3 11.3 8.8 Track momentum resolution 1.0 1.0 1.0 1.0 1.0 Charged particle correction 0.7 2.7 0.7 6.4 3.7

EMCal clusterizer 3.2 1.8 0.1 3.2 1.4

EMCal response 4.4 4.4 4.4 4.4 4.4

Background fluctuations 3.9 2.7 2.3 3.9 2.8

Jet rawpTcuts 2.6 6.7 1.5 6.7 3.6

Combinatorial jets 0.3 0.5 0.0 0.5 0.2

Total correlated uncertainty 10.6 14.5 10.6 14.5 12.0

Unfolding method 0.1 10.0 0.1 15.5 6.6

SVD reg. param.k=^{4 3}.6 11.7 2.4 11.7 6.0 SVD reg. param.k=^{6 7}.2 2.7 1.5 8.8 5.3

Prior choice 1 1.9 4.0 0.2 4.0 1.6

Prior choice 2 2.1 1.4 0.1 2.1 0.9

Total shape uncertainty 3.8 7.2 2.7 7.4 5.3

5. Results

Theunfoldedjetspectrain0–10%and10–30%centralcollisions aredisplayedinFig. 2.Tocomparethespectrawiththespectrum measuredinppcollisions,theyieldisdividedbythenumberofbi- narycollisions,whichisN_coll=¹⁵⁰¹±^{167 for0–10%and743}±⁷⁹ for 10–30% collisions, as estimated from a Glauber MC calcula- tion[50].

Thesystematic uncertainties on thejet spectrum are summa- rized in Table 1 for the 0–10% centrality class. For the 10–30%

centralityclassthecorresponding uncertainties differ,onaverage, by2%orless. Thesystematicuncertaintieswere dividedintotwo categories: correlated uncertainties and shape uncertainties. The correlated uncertainties result dominantly from uncertainties on theJES,suchastheuncertaintyofthetrackingefficiency,thatwill shifttheentirejet spectrum inone direction, whereasthe shape

uncertaintiesarerelatedtotheunfoldingandcandistorttheslope ofthespectrum.

The dominant correlated uncertainty on the jet spectrum of about 9% arises from the uncertainty on the tracking efficiency.

It is estimatedby varying the trackingefficiency by 5% in deter- mining RMdet and unfolding the spectrum. The uncertainty due tothecorrectionprocedureforthechargedparticledoublecount- ing intheEMCalofabout4% wasdetermined byvarying f from 100% to30% inboth the measured spectrumandthe RMdet.The determinationoftheuncertaintiesfromother EMCalresponse re- lateduncertaintiesasEMCalenergyscale,EMCalenergyresolution, andEMCalnon-linearityisoutlinedin[54]andcombinedleadsto anuncertaintyof4.4%.Theuncertaintyarisingfromthechoice of theEMCalclusteringalgorithm isdetermined byusingadifferent clusterizingmethod,thatformsfixed-sizeclustersfrom3×^{3 tow-} ers. For the background fluctuations, the response matrix RMbkg was constructedwiththesingle-track embeddingmethodforde- termining δpT, asdiscussed above. To estimate the sensitivity of the unfolding to the raw jet pT selection, the pT range ofinput spectraisvariedby extendingtherangeatboththelowandhigh endsby ±^{5 GeV}/c.Theinfluenceofcombinatorialjets, estimated by varying the low edge ofthe unfolded spectrum from0to up to10 GeV/cwasfoundtobenegligible.Sinceallsourcesofuncer- taintyareindependent,eachcontributionisaddedinquadratureto obtainthefinalcorrelateduncertaintyof10.6%to14.5%aslistedin Table 1.TheuncertaintyontheJESis2.4%to3.2%andcanbeob- tainedbydividingtheuncertaintieslistedinTable 1by4.5,where theexponentn=⁴.5 wasobtainedbyfittinga powerlawto the measuredspectrum.

Theshapeuncertaintyisdominatedbytheregularizationused in the unfolding and can be divided into two components: the method by which the solution is regularized, e.g.

χ

² instead of theSVDunfolding,andthevariationoftheregularizationprocess within a given method. The regularization is done by adding a penalty terminthe

χ

² method andbyignoring the components oftheSVDdecompositionthataredominatedbystatisticalfluctua- tions.FortheSVDmethod,theregularizationkfactorisaninteger valueandthuscanonlybevariedinintegersteps.Theuncertainty relatedtothechoiceofthepriorisestimatedbyvaryingtheexpo- nent ofthe powerlawfunction extractedfromthereconstructed spectrum by ±⁰.5,which isused toconstruct theprior.The un- certaintyrelatedtothechoiceofthepriorisestimatedbyvarying the exponentn=⁴.5 by ±⁰.5 toscale the prior.The differences intheunfoldedspectrumwiththesevariationsaresummarizedin Table 1. These variations in the regularization strategy are com- bined assuming that they constitute independent measurements.

Thefinalshape uncertaintyisthusobtainedbysummingthemin quadratureanddividingbythesquarerootofthenumberofvari- ations.

The jet spectrum in pp collisions was measured in the same wayasreportedinRef.[54],butwiththe5 GeV/cleadingcharged particlerequirementnecessaryforthePb–Pbanalysis. Theresult- ing spectrum normalized per inelastic pp collision is shown in Fig. 2. In order to determine the effect of the leading track re- quirement in pp collisions, the ratio of the jet spectra with a 5 GeV/c leading track requirement (the biased jet sample), over thespectrumofjetswithoutaleading trackrequirement(the in- clusivejetsample)withresolutionparameter R=⁰.2 isshownin Fig. 3.Systematicuncertaintiesintheratiowere evaluatedby re- moving theuncertainties that are correlatedbetweenthe spectra obtainedwithandwithoutthecutontheleading particle.Ascan be seeninFig. 3,for p_T,jet above 50 GeV/c morethan 95%ofall reconstructed jetshaveatleastone trackwitha pT greater than 5 GeV/c. PYTHIA tune A (but also other common tunes like the Perugiatunes[57])accuratelydescribes themeasuredratio.

Fig. 3.RatioofthejetspectrumwithaleadingtrackpT>5 GeV/covertheinclusive jetspectrumforR=⁰.2 inppcollisionsat√

s=².76 TeV.

The influence of the leading track requirement in the Pb–Pb measurement,nominally setto 5 GeV/c was tested byvarying it by 40%, i.e. reducing it to 3 and increasing it to 7 GeV/c, and withthemoreextremevaluesof0 and10 GeV/c.Theratiosofjet spectrawiththedifferentleading trackp_T biases,afterallcorrec- tions,areshowninFig. 4for R=⁰.2 jetsin0–10%centralPb–Pb collisions at √

s_NN=².76 TeV. The corrections to these different jetspectrawere done usingthesameunfoldingprocedure asthe nominalspectrum with leading track p_T bias of 5 GeV/c, witha slightly modified response matrix which accounts for the differ- entbiases.Sincetheunfoldingprocedureweakensthecorrelation betweenthe statisticalfluctuationsofthe jet spectrawithdiffer- ent leading track requirements, the statistical uncertainties have beenadded inquadrature inthe ratio.The systematicshape un- certaintyisduetotheunfoldingprocedure,andhasbeentreated ascompletelyuncorrelatedintheratio.Thecorrelateduncertainty isprimarilyduetotheuncertaintyontheJES,whichishighlycor- relatedbetweenthe various spectra.The systematicvariations in the unfolding procedure have been applied consistently for both thedenominator(withaleadingtrack pT>5 GeV/c) andthenu- merators (with a 0, 3, 7 and 10 GeV/c leading track bias), and theresultingdifferenceinthe ratioshasbeentakenasa system- atic uncertainty. The jet spectra withleading trackrequirements of 3 and0 GeV/c are consistent withthe baseline measurement

witha5 GeV/crequirement.Theunfoldingisnotasstableaswith a 5 GeV/c requirement, whichleads toalarger systematicuncer- taintyduetotheunfoldingcorrectionprocedure,especiallyforthe inclusive spectrum. All measurements of the ratio of jet spectra withdifferentleadingtrackbiases,particularlythosewithahigher leadingtrackpT requirementthanthenominal,arewelldescribed by PYTHIA 6 (tune A), within one sigmaof the uncertainties or less.

The nuclearmodificationfactor, RAA,isdefinedastheratioof the jet spectrum in Pb–Pb divided by the spectrum in pp colli- sions scaledby N_coll.Itisconstructed suchthat R_AA equals unity if thereis nonet nuclear modificationof thespectrum inPb–Pb collisions ascomparedtoan incoherentsuperpositionofindepen- dentpp collisions.TheresultingR_AAofjetswitha5 GeV/cleading track requirement for R=⁰.2 in the 0–10% and10–30% central Pb–PbcollisionsisreportedinFig. 5.Thesystematicandstatistical uncertainties from the Pb–Pb and pp measurements (see Fig. 2) are added in quadrature. The resulting uncertainty on the nor- malization is fromscaling the pp cross section with the nuclear overlap TAA=²³.5±⁰.87 mb⁻¹ for0–10%and11.6±⁰.60 mb⁻¹ for10–30%collisions. As canbe seen,jetsinthemeasured p_T,jet range are strongly suppressed. The average RAA in both 0–10%

and 10–30% central eventswas found to have a negligible pT,jet dependence. In the 10% mostcentral events, combining the sta- tisticalandsystematicuncertaintyinquadrature,theaverage R_AA is found to be 0.28±⁰.04. The suppression is smaller in mag- nitude in the 10–30% central events, leading to an average RAA of0.35±⁰.04.Theseresultsqualitativelyagreewiththesuppres- sionobtainedfrommeasurementsusingcharged-particlejets[46], thoughthejetenergyscaleisnotthesameinbothcases,andsoa directcomparisonisnotpossible.Furthermore,theresultsarecon- sistent withthe RAA reportedbyATLAS forR=⁰.4 jetsscaled by theratiooftheyields withthedifferentresolution parametersin different pT,jetbins[36,41].

Inordertointerprettheresultsandmovetoamorequantita- tive understandingofjetquenchingmechanisms,acomparisonof themeasured RAA in0–10%centralcollisionstocalculationsfrom two differentmodelsisalsoshownin Fig. 5.Thefirstmodel,Ya- JEM[61],usesa2+^1DhydrodynamicalcalculationandaGlauber MC for theinitial geometry,as well asa LOpQCD calculation to determine the outgoingpartons. Parton showersare modified by a medium-induced increase of the virtuality during their evolu- tion throughthemedium. TheLund modelinPYTHIAisusedfor hadronization intofinal state particles.The kinematicsofthe vir- tual partons intheevolving partonic shower weremodified with aparameterrelatedtothetwotransportcoefficients,^qˆ ^ande,ˆ ^that describeshowstronglyapartonofagivenmomentumcouplesto

Fig. 4.RatiosofjetspectrawithdifferentleadingtrackpTrequirements(“0over5”,“3over5”,“7over5”and“10over5”)forR=0.2 jetsin0–10%Pb–Pbcollisionsat

√_s

NN=².76 TeV.ThesolidblacklinesrepresentpredictionsfromPYTHIA.

Fig. 5.RAAforR=⁰.2 jetswiththeleadingtrackrequirementof5 GeV/cin0–10%(left)and10–30%(right)mostcentralPb–Pbcollisionscomparedtocalculationsfrom YaJEM[61]andJEWEL[62].TheboxesatRAA=1 representthesystematicuncertaintyonTAA.

themedium.Theparameterwasfixedsothatthemodelaccurately describesthe RAA for chargedhadrons at10 GeV/c [17], butno additionalchanges were made forthe prediction of the jet RAA. Thesecond model,JEWEL[62],takes a differentapproach inthe descriptionof theparton–medium interaction by givinga micro- scopicaldescriptionofthetransportcoefficient,^q.ˆ Essentiallyeach scatteringoftheinitialpartonwithmediumpartonsiscomputed andtheaverageoverallscattersdetermines^q.ˆ ^{JEWELusesacom-} binationofGlauberandPYTHIAtodeterminetheinitialgeometry, a 1D Bjorken expansion for the medium evolution, and PYTHIA forhadronizationintofinalstateparticles.Thetransversemedium densityprofileinJEWELisproportionaltothedensityofwounded nucleonscombinedwitha1DBjorkenexpansionforthetimeevo- lution.Hardscatters aregenerated accordingto Glauber collision geometry,andsufferfromelasticandradiativeenergylossinthe medium,includingaMonte CarloimplementationofLPMinterfer- enceeffects. PYTHIA is used for the hadronization of final state particles.Despitetheir differentapproaches, bothcalculationsare foundtoreproducethejetsuppression.YaJEM,however,exhibitsa slightlysteeper increasewithjet pT thanthedata.Thecalculated

χ

² are 1.690 for YaJEM and 0.368 for JEWEL, obtainedby com- paringthemodelswiththedata.Additionalmeasurementswillbe neededinordertofurtherconstrainthemodels,suchasmeasuring thejetsuppressionrelativetotheeventplaneangle,whichwould requireamoreaccurate modelingofthe path-lengthdependence ofjetquenching.

6. Summary

The transverse momentum (pT) spectrum and nuclear modi- fication factor (RAA) of jetsreconstructed from charged particles measuredby the ALICEtrackingsystemandneutralenergy mea- suredbytheALICEElectromagneticCalorimeteraremeasuredwith R=⁰.2 in the range of 40<p_T,jet<120 GeV/c for 0–10% and in30<pT,jet<100 GeV/c for10–30% most central Pb–Pb colli- sionsat√

s_NN=².76 TeV were measured.The jetswererequired to contain at least one charged particle with pT>5 GeV/c. The effectofthis requirementonthe reported R_AA was evaluated by theratios ofthe jet spectrawiththe 5 GeV/c to no requirement compared to expectations on PYTHIA, andfound not to have an observableeffectwithintheuncertaintiesofthemeasurement.Jets with40<pT,jet<120 GeV/c are stronglysuppressed inthe 10%

mostcentralevents,with R_AA about0.28±⁰.04,independentof pT,jet within theuncertainties ofthe measurement.The suppres- sionin10–30%eventsis0.35±⁰.04,slightlylessthaninthemost

centralevents.Theobservedsuppressionisinfairagreementwith expectationsfromtwojetquenchingmodelcalculations.

Acknowledgements

The ALICE Collaboration would like to thank all its engineers andtechniciansfortheir invaluablecontributions totheconstruc- tionoftheexperimentandtheCERNacceleratorteamsfortheout- standingperformanceoftheLHCcomplex.TheALICECollaboration gratefully acknowledges the resources and support provided by all Gridcenters and theWorldwide LHC ComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the follow- ing funding agencies for their support in building and running theALICEdetector:StateCommittee ofScience,WorldFederation of Scientists (WFS)and SwissFonds Kidagan, Armenia; Conselho Nacional de DesenvolvimentoCientífico e Tecnológico (CNPq), Fi- nanciadorade Estudos eProjetos(FINEP),Fundação de Amparoà Pesquisa do Estado de São Paulo (FAPESP); National Natural Sci- enceFoundation ofChina (NSFC), theChinese Ministryof Educa- tion(CMOE)andtheMinistryofScienceandTechnologyofChina (MSTC); Ministry of Education andYouth ofthe Czech Republic;

Danish Natural Science Research Council, the Carlsberg Founda- tion andthe DanishNationalResearch Foundation;TheEuropean ResearchCouncilundertheEuropeanCommunity’sSeventhFrame- work Programme; Helsinki Institute of Physics andthe Academy ofFinland;FrenchCNRS–IN2P3,the‘RegionPaysdeLoire’,‘Region Alsace’, ‘Region Auvergne’ andCEA, France; German Bundesmin- isterium fur Bildung, Wissenschaft, Forschung und Technologie (BMBF)andtheHelmholtzAssociation;GeneralSecretariatforRe- searchandTechnology,MinistryofDevelopment,Greece;Hungar- ianOrszagosTudomanyosKutatasiAlappgrammok(OTKA)andNa- tionalOfficeforResearch andTechnology (NKTH); Departmentof Atomic EnergyandDepartmentofScience andTechnologyofthe Governmentof India;Istituto Nazionale diFisica Nucleare(INFN) and Centro Fermi – Museo Storico della Fisica e Centro Studi e Ricerche“EnricoFermi”,Italy;MEXTGrant-in-AidforSpeciallyPro- motedResearch,Japan;JointInstituteforNuclearResearch,Dubna;

National Research Foundation of Korea (NRF); Consejo Nacional de Cienca y Tecnologia (CONACYT), Direccion General de Asun- tos del Personal Academico (DGAPA), México, Amerique Latine Formation academique–European Commission (ALFA–EC) and the EPLANETProgram(EuropeanParticle PhysicsLatin AmericanNet- work); StichtingvoorFundamenteelOnderzoekderMaterie(FOM) andtheNederlandseOrganisatievoorWetenschappelijkOnderzoek