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Physics Letters B
www.elsevier.com/locate/physletb
Analysis of the apparent nuclear modification in peripheral Pb–Pb collisions at 5.02 TeV
.ALICE Collaboration
a r t i c l e i n f o a b s t ra c t
Articlehistory:
Received24May2018
Receivedinrevisedform26March2019 Accepted17April2019
Availableonline23April2019 Editor:W.-D.Schlatter
Charged-particlespectraatmidrapidityaremeasuredinPb–Pbcollisionsatthecentre-of-massenergy per nucleon–nucleon pair √s
NN=5.02 TeV and presented in centrality classes ranging from most central (0–5%)tomostperipheral (95–100%)collisions.Possiblemediumeffectsarequantifiedusingthe nuclear modificationfactor (RAA)bycomparing the measuredspectrawith thosefrom proton–proton collisions, scaled by the number ofindependent nucleon–nucleon collisions obtained from aGlauber model. Atlarge transverse momenta (8<pT<20 GeV/c), the average RAA isfoundto increasefrom about 0.15 in0–5% centraltoamaximumvalue ofabout0.8 in75–85%peripheralcollisions,beyond which it falls off strongly tobelow 0.2 for the most peripheral collisions. Furthermore, RAA initially exhibitsapositiveslopeasafunctionofpTinthe8–20 GeV/cinterval,whileforcollisionsbeyondthe 80% classthe slope is negative. To reduceuncertainties relatedto event selection and normalization, wealsoprovidetheratioofRAAinadjacentcentralityintervals.Ourresultsinperipheralcollisionsare consistentwithaPYTHIA-basedmodelwithoutnuclearmodification,demonstratingthatbiasescausedby theeventselectionandcollisiongeometrycanleadtotheapparentsuppressioninperipheralcollisions.
ThisexplainstheunintuitiveobservationthatRAAisbelowunityinperipheralPb–Pb,butequaltounity inminimum-biasp–Pb collisionsdespitesimilarcharged-particlemultiplicities.
©2019ConseilEuropéenpourlaRechercheNucléaire.PublishedbyElsevierB.V.Thisisanopenaccess articleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
Transport properties of the Quark-Gluon Plasma (QGP) can be extracted from measurements of observables in high-energy nucleus–nucleus (AA) collisions, which involve large momentum transfers,suchasjetsoriginatingfromhardparton-partonscatter- ingsintheearlystageofthecollision.Whilepropagatingthrough the expanding medium, these hard partons lose energy due to medium-inducedgluonradiationandcollisionalenergyloss,apro- cessknown as“jet quenching” [1,2]. Due to theenergy loss,the rateofhigh-pT particlesis expectedto be suppressedrelative to proton–protoncollisions. The effect is typically quantified by the nuclearmodificationfactor
RAA
=
1 NcolldNchAA
/
dpT dNppch/
dpT=
1 TAAdNAAch
/
dpTd
σ
chpp/
dpT,
(1)definedastheratiooftheper-eventyieldsinAA andppcollisions normalizedtoanincoherentsuperpositionofNcollbinaryppcol- lisions.TheaveragenumberofcollisionsNcollisdeterminedfrom
E-mailaddress:alice-publications@cern.ch.
aMonteCarloGlaubermodel [3–5] andrelatedtotheaveragenu- clearoverlapTAA = Ncoll/
σ
inelNN,whereσ
inelNN isthetotalinelastic nucleon-nucleon cross section. The yields measured in AA colli- sions,aswellasNcoll,dependonthecollisioncentrality,andRAA isconstructedtobeunityintheabsenceofnucleareffectswhere particle productionis dominatedby hard processes.The collision centrality is expressed in percentiles of the total hadronic cross section,withthehighest(lowest)centrality0%(100%)referring to the most central (peripheral) collisions with zero (maximal) im- pact parameter. Experimentally, centralityis typically determined by ordering eventsaccordingtomultiplicity orenergy deposition inalimitedrapidityrangeandbyfittingthecorrespondingdistri- butionwithaGlauber-basedmodelofparticleproduction [6].Numerous measurements of RAA reported by experiments at the RelativisticHeavy-IonCollider(RHIC) [7–16] andattheLarge HadronCollider(LHC) [17–22] revealedthat high-pT particlepro- duction is suppressed strongly in central collisions, andthat the suppression reduceswithdecreasingcentrality.Furthermore,con- trol measurements of possible nuclear modification arising from theinitialstateind–Au andp–Pb collisions [23–28] andwithelec- tromagneticprobesinAA collisions [29–33] (whichshouldnot be affectedby partonicmatter)demonstratedthattheobservedsup- pression is dueto final state interactions, such as partonenergy loss. Contrary to expectations, RAA was also found to be below https://doi.org/10.1016/j.physletb.2019.04.047
0370-2693/©2019ConseilEuropéenpourlaRechercheNucléaire.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
unityathighpTinperipheralcollisions,reachinganapproximately constantvalueofabout0.80 above3 GeV/c in80–92%Au–Au col- lisions at √
sNN=0.2 TeV [16] and about 0.75 above 10 GeV/c in 70–90% Pb–Pb collisions at √
sNN=5.02 TeV [21]. In a final- statedominatedscenario, suchdifferencesrelative tounityimply alargejetquenchingparameterforperipheralcollisions,up toan orderofmagnitude largerthan forcold nuclear matter [34], and consequentlyraiseexpectationsoftherelevance ofpartonenergy losseveninsmallcollisionsystems [35–37].However,ithasbeen pointedoutrecently [38] thateventselectionandgeometrybiases
—justlikethosediscussedforp–Pb collisions [39] —cancausean apparent suppression of RAA in peripheral collisions, even inthe absenceof nuclear effects,while self-normalizedcoincidence ob- servables [40,41] arenotaffected.
Theimpact parameterofindividual NN collisionsiscorrelated totheoverallcollisiongeometryleadingto anNN impactparam- eterbiasinthetransverseplane [42],forperipheralcollisionsthe NN impact parameter is biased towards larger values. Centrality classification based on multiplicity can bias the mean multiplic- ityof individual nucleon–nucleon (NN)collisions, andhence the yieldofhardprocessesinAA collisionsduetocorrelatedsoftand hard particle production,amplifying the inherent NN impact pa- rameterbias. The presence of the multiplicity bias in peripheral Pb–Pb collisions was already demonstrated in Ref. [39] showing theaveraged multiplicityoftheGlauber-NBDfitislowerthanthe averagenumberofancestors timesthemeanmultiplicity ofNBD (leftpaneloffigure 8in Ref. [39]).Inthepresentpaper,weaimto studyitsrelevance oncharged-particlespectrainPb–Pb collisions at √
sNN=5.02 TeV, in 20 centrality classes ranging from 0–5%
to 95–100% collisions. The spectra at midrapidity are measured intherange 0.15<pT<30 GeV/c exceptfor the95–100%class, whereitis0.15<pT<20 GeV/c.Usingthecharged-particlespec- tra frompp collisions atthe sameenergy [22], we constructthe nuclear-modificationfactorandstudythecentralitydependenceof its average at high pT, as well asits slope at low andhigh pT. Toreduce uncertaintiesrelated toeventselection andnormaliza- tion,whichareparticularlylargeforperipheralcollisions,wealso providetheratioofRAAinadjacentcentralityintervals,definedas
R+1
≡
Ri+1=
RiAARiAA+1
=
Ncolli+1 NcollidNAAch,i
/
dpTdNAAch,i+1
/
dpT,
(2) where i+1 denotes a 5% more central centrality class than i.Thedefinitionof R+1 corresponds approximatelytothechangeof logRAAwithcentrality,anditsvaluewouldbeconstantforanex- ponentialdependence.
Similar to RAA, we quantify the centrality dependence of the averageR+1athighpT,aswellasitsslopeatlowandathighpT. Wherepossible,theresultsarecomparedtoaPYTHIA-basedmodel of independent pp collisions without nuclear modification [38].
The remainder of the paper is structured as follows: Section 2 describestheexperimental setup.Section3describesthecharged particlemeasurementwithemphasisoncorrectionsanduncertain- tiesrelatedto the mostperipheral collisions. Section 4 describes theresults.Section5providesasummaryofourfindings.
2. Experimentalsetup
The ALICE detector is described in detail in Ref. [43], and a summary ofits performance can be found in Ref. [44]. Charged- particle reconstruction at midrapidity is based on trackinginfor- mationfromtheInnerTrackingSystem(ITS)andtheTimeProjec- tionChamber(TPC),bothlocatedinsideasolenoidalmagneticfield of0.5 Tparalleltothebeamaxis.
TheITS [45] consistsofthreesub-detectors,eachcomposed of two layerstomeasurethe trajectoriesofchargedparticles andto reconstructprimaryvertices.ThetwoinnermostlayersaretheSil- icon PixelDetectors (SPD),themiddletwolayers areSiliconDrift Detectors (SDD), the outer two layers are Silicon Strip Detectors (SSD).
TheTPC [46] isalarge(90 m3)cylindricaldriftdetector.Itcov- ersapseudorapidityrangeof|
η
|<0.9 overfullazimuth,providing up to159reconstructedspacepoints per track.Chargedparticles originating from the primary vertex can be reconstructed down to pT≈100 MeV/c. The relative pT resolution depends on mo- mentum, isapproximately 4%at0.15 GeV/c,1%at 1 GeV/c and increaseslinearlyapproaching4%at50 GeV/c.The pp and Pb–Pb collision data at √
sNN=5.02 TeV were recordedin2015. Intotal,about110·106 pp and25·106 Pb–Pb eventssatisfyingtheminimumbiastriggerandanumberofoffline eventselection criteriawereused intheanalysis. The minimum- bias trigger required a signal in both, the V0-A and V0-C, scin- tillator arrays, covering 2.8<
η
<5.1 and −3.7<η
<−1.7, re- spectively [47].Beambackground eventswere rejectedefficiently byexploitingthetimingsignalsintheV0detectors,andinPb–Pb collisions alsoby usingthetwo ZeroDegreeCalorimeters (ZDCs).The latterare positioned closetobeamrapidity on both sidesof theinteractionpoint.
3. Dataanalysis
Themeasurementsofcharged-particlespectrainppandPb–Pb collisionsat√
sNN=5.02 TeVaredescribedindetailinRef. [22].
The collision point or primary event vertex was determined fromreconstructedtracks.Ifnovertexwasfoundusingtracks,the vertex reconstruction was performed using track segments con- structed from the two innermost layers of the ITS. Events with a reconstructed vertex within ±10 cm from the centre of the detector along the beam directionare used to ensure a uniform acceptanceandreconstructionefficiencyatmidrapidity.
Primarychargedparticles [48] weremeasuredinthekinematic range of |
η
|<0.8 and 0.15<pT<30 GeV/c. The detector sim- ulations were performedusing the PYTHIA [49] and HIJING [50]MonteCarloeventgeneratorswithGEANT3 [51] formodelling the detector response. Track-level corrections include acceptance, ef- ficiency, purityand pT resolution, whichwere obtained usingan improvedmethod tuned ondata toreduce the systematicuncer- tainties related to particle species dependence (see Ref. [22] for details).Eventsare classifiedinpercentilesofthehadroniccross- section using the sum of the amplitudes of the V0-A and V0-C signals (V0Mestimator) [6].Theabsolutescaleofthecentralityis definedbytherangeof0–90%centralityinwhichaGlauber-based multiplicity model is fitted to the V0M distribution. The lower centrality limit of 90% ofthis range withits corresponding V0M signal isdenotedthe anchorpoint (AP).The multiplicityforeach particlesource ismodelled witha negativebinomial distribution, where the effective number of independent particle production sources is described by a linear combination of the number of participants (Npart) and collisions (Ncoll). The AP was shifted by
±0.5%, leading to a systematic uncertainty in the normalization of thespectra of up to 6.7% forthe 85–90% centralityclass. Un- like previous measurements inPb–Pb collisions, the analysiswas not limitedto 0–90% most central events, where effects of trig- ger inefficiency and contamination by electromagnetic processes arenegligible,butalsoincludedthe90–100%mostperipheralcol- lisions.TheV0Mvaluecorrespondingto95%ofthehadroniccross sectionwasdeterminedbyselectingeither95%oftheeventsgiven by the Glauber-NBD parametrization, orthe numberofevents in the 0–90% centrality class multiplied by the factor 95/90, where
thelatterisusedasavariationtoassessthesystematicuncertainty ofthe approach. The difference on themeasured yields between the two ways was assigned as additionalsystematic uncertainty.
For the centrality class 90–95% (95–100%) the combined uncer- tainty amounts to afully correlated partof10.8% (11.7%) onthe normalizationof thespectra anda 2.9% (4.6%) residual effecton theshape.
The triggerandevent-vertex reconstruction efficiencyandthe related systematic uncertainties for peripheral Pb–Pb collisions wereestimatedfromsimulationsusingHIJINGandPYTHIAinclud- ingsingle- and double-diffractiveprocesses,butignoringpossible differencesfromnucleareffects.TheV0Mdistributioninthesim- ulationswasreweightedwiththemeasuredV0Mdistribution.The combinedefficiencywasfoundtobe0.985±0.015 forthe90–95%
and0.802±0.057 forthe95–100%centralityclasses,respectively, whilefullyefficientformorecentralcollisions. Inaddition,inthe most peripheral bin a pT-dependent signal loss of up to 14.7%
atlow pT iscorrected for.To accountfor diffractiveprocesses in this correction and its systematic uncertainty, two limiting sce- narioshave beenconsidered: a)the signal loss isassumedto be asinppcollisions intheV0Mrangeofthe95–100%bin; b)only thefractionofeventswitha single nucleon–nucleoncollisionare correctedforassumingthesignallossfromminimum-biasppcol- lisions.
Contaminationoftheperipheralbinsbyelectromagneticinter- actionswasstudiedinthedataby removingalleventswithsmall energydepositsintheneutron ZDCs.Theresultingchangeofthe spectrumwiththerequirementsofatleastafive-neutronequiva- lentenergyinboth neutronZDCsamountsto5%forthe95–100%
centralityclass,3%forthe90-95%classand2%forthe80-85%and 85-90% classes and is assigned assystematic uncertainty. To ac- countforcontaminationofthetriggerfromeventswithoutrecon- structed vertex, those events are removed fromthe analysis and theresultingchange isassignedassystematicuncertaintyonthe normalization (6.8%inthe95–100%classand0.5%inthe90–95%
class).
Systematicuncertaintiesrelatedtovertexselection,trackselec- tion,secondary-particle contamination, primary-particle composi- tion, pT resolution, material budget andtracking efficiency were estimatedasdescribedinRef. [22] andareassignedasbin-by-bin uncertainties. The systematicuncertainties relatedto thecentral- ity selection were estimated by a comparison of the pT spectra whenthelimitsofthecentralityclassesareshiftedduetoanun- certainty of ±0.5% in the fraction of the hadronic cross section usedintheanalysis.Theyaresplitintotwoparts:onepartthatis fullycorrelated betweenthe pT bins assignedasa normalization uncertainty plus an additional part taking into account residual differencesin the spectral shape assignedasa bin-by-bin uncer- tainty.The overall normalizationuncertainty of RAA contains the uncertainty relatedto the centrality selection, the uncertainty of Ncoll, the uncertainty ofthe trigger efficiency, the uncertainty of thetriggercontaminationandthenormalizationuncertaintyofthe ppreferencespectrumaddedinquadrature.Notethatmostuncer- taintiesarecorrelatedtoalargeextentbetweenadjacentcentrality binsleadingtoreduceduncertaintiesinR+1.
Orderingeventsaccordingtomultiplicityintroducesabiasrel- ativetousingtheimpactparameterinGlauber-basedparticlepro- ductionmodels.Itisexpectedthatpartofthebiasintroducedby theorderingcanbe cancelled inRAA,when Ncoll isalsoobtained inthesamewayasinthedata.Thedifferencerelativeto averag- ingoverimpactparameterisquantifiedinFig.1,whichshowsthe ratio of Ncoll by slicing either in multiplicity (estimated using the V0M amplitude)
Nmultcoll
or impact parameter Ngeocoll
, ascar- riedout so faratthe LHC.The differenceis below5% upto 80%
Fig. 1.Ratioofnumberofcollisionsdeterminedbyslicinginmultiplicity (Ncollmult) dividedbythenumberofcollisionsdetermineddirectlyfromtheimpactparame- ter (Ngeocoll).
Table 1
SummaryoftheaverageNpart,Ncoll,TAAforallcentralityclassesobtainedbyslicing theV0Mamplitudedistributioninsteadoftheimpactparameter.Alluncertainties listedaresystematicuncertainties.Statisticaluncertaintiesarenegligible.
Centrality class Npart
Ncoll TAA(mb−1)
0–5% 382.3±2.4 1752±28 25.92±0.37 5–10% 329.1±5.0 1367±37 20.22±0.52 10–15% 281.1±5.2 1080±26 15.98±0.36 15–20% 239.4±5.2 850±26 12.57±0.37 20–25% 202.7±4.6 662±25 9.79±0.36 25–30% 170.8±3.1 513±16 7.58±0.22 30–35% 142.5±3.0 390±13 5.77±0.18 35–40% 118.0±2.1 293.4±7.4 4.34±0.11 40–45% 96.3±2.0 215.2±6.4 3.184±0.095 45–50% 77.5±1.5 154.8±4.0 2.290±0.066 50–55% 61.29±0.86 109.0±1.8 1.612±0.033 55–60% 47.43±0.59 74.1±1.4 1.096±0.026 60–65% 35.84±0.67 49.2±1.2 0.728±0.020 65–70% 26.19±0.56 31.6±1.1 0.468±0.018 70–75% 18.60±0.40 19.89±0.77 0.294±0.012 75–80% 12.78±0.32 12.19±0.46 0.1803±0.0075 80–85% 8.50±0.23 7.22±0.30 0.1068±0.0048 85–90% 5.45±0.11 4.12±0.13 0.0609±0.0021 90–95% 3.31±0.19 2.18±0.16 0.0323±0.0024 95–100% 2.24±0.11 1.223±0.096 0.0181±0.0014
centrality,andthenincreasesstronglyupto40%formoreperiph- eral classes.The average quantities fora centralityclass, such as the numberofparticipants Npart,thenumberof binarycollisions Ncoll andthe nuclearoverlapfunction TAA,were obtainedby av- eraging over the V0Mmultiplicity intervals, andare summarized inTable1.Forthecalculationof RAA andR+1 we useonlythose multiplicity averaged quantities.As before [5,6], theuncertainties on the mean were obtained by changing the various ingredients of the Glauber MC model by one standard deviation. The result- ing relative uncertainties on themean are below6%, howeverin particularforperipheralcollisionsthewidthsoftherespectivedis- tributionsaresignificantlylarger.
The charged particle multiplicity dNch/d
η
and the average transversemomentumpTforallcentralityintervalsarelistedin Table 2,valuesgivenfordNch/dη
andpT>0 are extrapolatedto pT=0 using a modified Hagedorn functionfitted tothe data,as describedinRef. [52].Fig. 2.Nuclear-modificationfactorversuspTforchargedparticlesatmidrapidityinPb–Pb collisionsat√s
NN=5.02 TeVfor5%-widecentralityclasses.Thefilled,coloured markersareforthefivemostperipheralclasses,withthecorrespondingglobaluncertaintiesdenotedclosetopT=0.1 GeV/c.Verticalerrorbarsdenotestatisticaluncer- tainties,whiletheboxesdenotethesystematicuncertainties.Forvisibility,theuncertaintiesareonlydrawnfortheperipheralclasses.
Table 2
SummaryoftheaveragedNch/dηandpTin|η|<0.8 forallcentralityclasses.
WhilepT>0.15isaveragedoverthemeasuredrange0.15<pT<10 GeV/c,pT>0 isextrapolatedtopT=0.Alluncertaintieslistedaresystematicuncertainties.Sta- tisticaluncertaintiesarenegligible.
Centrality class dNch/dη pT>0.15(GeV/c) pT>0(GeV/c) 0–5% 1910±49 0.729±0.010 0.681±0.010 5–10% 1547±40 0.731±0.010 0.683±0.010 10–15% 1273±30 0.732±0.009 0.683±0.009 15–20% 1048±25 0.733±0.009 0.683±0.009 20–25% 863±19 0.730±0.009 0.678±0.008 25–30% 703±16 0.727±0.009 0.676±0.008 30–35% 568±13 0.723±0.008 0.671±0.008 35–40% 453±11 0.719±0.008 0.666±0.008 40–45% 356.6±8.4 0.710±0.008 0.657±0.008 45–50% 275.1±6.8 0.704±0.008 0.650±0.007 50–55% 208.5±5.6 0.695±0.008 0.640±0.008 55–60% 154.1±4.5 0.687±0.008 0.631±0.007 60–65% 111.4±3.5 0.676±0.007 0.619±0.007 65–70% 78.0±2.8 0.667±0.007 0.609±0.007 70–75% 53.1±2.1 0.659±0.007 0.599±0.007 75–80% 34.9±1.6 0.650±0.008 0.589±0.007 80–85% 22.0±1.4 0.636±0.014 0.575±0.013 85–90% 12.87±0.98 0.612±0.014 0.551±0.013 90–95% 6.46±0.78 0.574±0.017 0.516±0.015 95–100% 2.71±0.51 0.524±0.031 0.471±0.028
4. Results
Fig.2presentsthenuclear-modificationfactor,giveninEq. (1), versus pT forchargedparticlesatmidrapidity inPb–Pb collisions at√
sNN=5.02 TeVfor5%-widecentralityclasses.Thefocusofthe presentedanalysis ismainly on the peripheralclasses, whichfor convenience are displayed in filled, coloured symbols with their corresponding global uncertainties of about 10–20% denoted at pT∼0.1 GeV/c.Asusual,ifnototherwisestated,verticalerrorbars denotestatisticaluncertainties,whiletheboxesdenotethesystem- aticuncertainties.
From central to peripheral collisions RAA increases, which in particular above about 10 GeV/c can be understood asthe pro- gressivereductionofmedium-inducedpartonenergyloss.Further- more,theshapeissimilarfromthemostcentraluptothe80–85%
centralityclass,namelyanincreaseatlow pT,amaximumaround 2–3 GeV/c, related to radial flow, then a decrease with a local minimum atabout 7 GeV/c, followed by a mild increase. Above 80–85% centrality, theevolution isdifferentasalreadyat low pT the slope is negative and RAA decreases monotonously with in- creasingpT.Thechangeinbehaviourseemstooccurinthe75–85%
interval, since the 80–85% RAA values appear to be the same or even lower than those ofthe 75–80% interval. For the mostpe- ripheral classes, the reduction of the nuclear modification factor withincreasing pT isqualitativelysimilar totheoneobservedfor low multiplicity p–Pb [39] collisions, indicating that theunderly- ingbiastowardsmoreperipheralcollisionswithareducedrateof hardscatteringspernucleon–nucleoncollisions isthesame.Ifin- stead of using Nmultcoll , we had used Ngeocoll in the normalization of RAA,theresultsforperipheralcollisionsabove80%wouldbeeven lower,namelybytheratioquantifiedinFig.1.
To quantify these observations we provide in Fig. 3 the av- erage RAA at high pT (within 8<pT<20 GeV/c), which in- creases smoothly frommostcentral up to 70–75% centrality and drops strongly beyondthe 80–85% centrality class. The data are compared to the high pT limit of a PYTHIA-based model (HG- PYTHIA) [38], which for every binary nucleon–nucleon collision superimposes a number of PYTHIA events incoherently without nuclear modification. The essential feature of the model is that particleproduction per nucleon–nucleoncollision originatesfrom a fluctuatingnumber ofmultiplepartonic interactions depending on the nucleon–nucleon impact parameter. Despitethe fact that HG-PYTHIA is a rather simple approach, for 75–80% and more peripheral collisions, it describes the average RAA relatively well suggestingthat theapparent suppression forperipheralcollisions isnotcausedbypartonenergyloss,butratherbytheeventselec- tioncriteriaimposedtodeterminethecentralityofthecollisions.
The data are significantly lower than the model calculation for themostperipheralcentralityclasses,possiblyduetoasignificant contribution ofdiffraction, which isnot modelled in HG-PYTHIA.
Theslopeofalinearfitto RAAperformedfor8<pT<20 GeV/c, theregion wherethe RAA incentralcollisions risesafterits min- imum,isshowninFig.4asafunction ofcentrality.Thishigh-pT slope is positive and initially increasing mildly before decreas-
Fig. 3.AverageRAAfor8<pT<20 GeV/cversuscentralitypercentileinPb–Pb col- lisionsat√
sNN=5.02 TeVcomparedtopredictionsfromHG-PYTHIA [38].Vertical errorbarsdenotestatisticaluncertainties,whiletheboxesdenotethesystematic uncertainties.
ingwithdecreasing centralityupto about80%centrality, beyond whichitisclosetozero,andthenevenisnegativeinthehighest centralityclass.AtlowtointermediatepT(within0.4–1.2 GeV/c), theregimewhichisstronglyinfluenced bythehydrodynamic ex- pansion,the RAA exhibitsanotherrise.The slopeextractedinthe pT range0.4–1.2 GeV/c is alsoshown inFig. 4.The RAA atlow andhigh pT isconsistent withbeinglinearlydependenton pT in thechosenfitranges,resulting
χ
2/NDF arebelowunity.Whilethe absolutevaluesoftheslopesareverydifferent(notethenormali- sation),theshapeofthecentralitydependenceoftheslopeatlow pT is remarkablysimilar to that extracted athigh pT. This hints ataclosecorrelationbetweenthesetworegimes,possiblyinduced by thegeometryordensitydependenceofpartonenergylossonFig. 4.SlopeofRAAatlowpT(in0.4<pT<1.2 GeV/c)andathighpT(in8<pT<
20 GeV/c)scaledbyfactor15forvisibilityversuscentralitypercentileinPb–Pb collisionsat √
sNN=5.02 TeV.Verticalerrorbarsdenotestatisticaluncertainties, whiletheboxesdenotethesystematicuncertainties.
the one handandcollectiveexpansion on theother hand.Inpe- ripheral collisions, in particular above 90% centrality, the low pT slopeisnegative,indicatingthattheveryperipheraleventsarein- creasinglysofter.
In order to studythe shape evolution of RAA in more detail, we compute theratioofadjacentcentralityintervals, asgivenby Eq. (2).Inthiswayalargepartoftheglobaluncertaintiesaswell asofthesystematicuncertainties cancel.Fig.5presents R+1 ver- sus pT forcharged particlesat midrapidityinPb–Pb collisions at
√sNN=5.02 TeVfor5%-widecentralityclasses.AsforRAAthepe- ripheralcollisionsaredisplayedincolour,withtheircorresponding global uncertainties, whichare significantly smaller than for RAA except for the most peripheral class, denoted around 0.1 on the
Fig. 5.R+1versuspTforchargedparticlesatmidrapidityinPb–Pb collisionsat√
sNN=5.02 TeV.R+1isdefinedastheratioofNcollnormalizedspectraforagivencentrality classrelativetothe5%morecentralclass,seeEq. (2).Thefilled,colouredmarkersareforthe5mostperipheralclasses,withthecorrespondingglobaluncertaintiesdenoted closetopT=0.1 GeV/conthepT-axis.Verticalerrorbarsdenotestatisticaluncertainties,whiletheboxesdenotethesystematicuncertainties.Forvisibility,theuncertainties areonlydrawnfortheperipheralclasses.
Fig. 6.AverageR+1for8<pT<20 GeV/cversuscentralitypercentileinPb–Pb col- lisionsat√
sNN=5.02 TeVcomparedtopredictionsfromHG-PYTHIA [38].Vertical errorbarsdenotestatisticaluncertainties,whilethe boxesdenotethe systematic uncertainties.
Fig. 7.Slope of R+1 at low pT (in 0.4<pT<1.2 GeV/c)and at high pT (in 8<pT<20 GeV/c)versuscentralitypercentileinPb–Pb collisionsat√s
NN=5.02 TeV.Verticalerrorbarsdenotestatisticaluncertainties,whiletheboxesdenotethe systematicuncertainties.
abscissa.Theratioisfoundtobenearly identicalfor0–5%central to70–75%peripheralcollisions(14curves)within10%.Inaddition, inthiscentralityrange,theratioisonlyslightly pT-dependent,al- though explained typically by distinct mechanism (radial flow at lowpTandenergylossathighpT).Formoreperipheralcollisions, however,the R+1 changes significantly andreduces toabout 0.4 formostperipheralcollisions. While thequenchingpower ofthe medium apparently only gradually changes forabout 75% of the Pb–Pb cross-section,thesuddendropformorethan75%peripheral collisionscanhardlybeexplainedbyanincreaseinquenching.
Theevolutionofthe R+1 athigh pT withcentralityischarac- terizedbytakingthe average R+1 for8<pT<20 GeV/c, shown inFig. 6.The average is about1.14,slightly decreasingwith de- creasingcentralityandbeyond75%centralityfallsstrongly,similar topredictionsfromHG-PYTHIA.Anapproximateconstantvaluefor
R+1uptoabout60%centralityimpliesanexponentialdependence oncentrality.
Fig.7showstheslopeofalinearfittothelowmomentumre- gion (0.4–1.2 GeV/c) and the high-momentum region (8<pT<
20 GeV/c) of R+1. In the chosen fit ranges, the R+1 can be fit- ted by a linear function with
χ
2/NDF<1. At low momentum, the slope of R+1 exhibits a mild centrality dependence, related to the reduced strength ofradial flow, dropping strongly forpe- ripheralcollisionsabove80%,asexpectedfromorderingeventsac- cordingtomultiplicity.Athighmomentum,theslopeisnon-zero,−0.0031±0.0006,andwithintheuncertaintiesnotdependenton centrality.
5. Summary
Charged-particlespectra atmidrapiditywere measured inPb–
Pb collisions at a centre-of-mass energy per nucleon pair of
√sNN=5.02 TeVandpresentedincentralityclassesrangingfrom the most central (0–5%) to the most peripheral (95–100%) colli- sions. Measurementsbeyond the 90% peripheral collisions at the LHC are presented for the first time. For a consistent treatment of themost peripheral collisions the numberof binary collisions was calculated froma Glauber model inintervals of multiplicity ratherthan inimpactparameter (Fig.1).Possible medium effects were quantified by comparing the measured spectra with those from proton–proton collisions normalized by the number of in- dependent nucleon–nucleon collisions obtained from a Glauber model (Fig.2).At largetransversemomenta (8<pT<20 GeV/c), theaverage RAAincreasesfromabout0.15 inthe0–5%mostcen- tral collisions to a maximum value of about 0.8 in the 75–85%
peripheral collisions, beyond which it strongly falls off to be- low 0.2 for the most peripheral collisions (Fig. 3). Furthermore, RAA initially exhibits a positive slope asa function of pT in the 8–20 GeV/c interval, while for collisions beyond the 80% class the slope is negative (Fig. 4). The shape of the slope extracted atlow pT,within0.4–1.2 GeV/c,isremarkablysimilar,indicating thattheremaybeaclosecorrelationbetweenthesetworegimes.
Toreduce uncertainties relatedtoeventselection andnormaliza- tion, the ratio of RAA in adjacent centrality intervals was mea- sured (Fig.5). Up to about60% peripheral collisions, thisratio is fairlyconstant,evenasafunctionof pT.Itthenstartstodecrease andfinally,forcentralitiesbeyond75%,itfallsoffstrongly (Fig.6) withitsslopesatlowandhighmomentumvaryingonlymildlyor notatallexceptforthemostperipheralcentralityintervals (Fig.7).
The trends observed in peripheral collisions are consistent withasimplePYTHIA-based modelwithoutnuclear modification, demonstratingthat biasescaused bythe eventselection andcol- lisiongeometrycanleadtoan apparentsuppressioninperipheral collisions.Thisexplainsthecontradictoryandhardtoreconcileob- servation that RAA is belowunity inperipheral Pb–Pb, butequal tounityinminimum-biasp–Pb collisionsdespitesimilarcharged- particle multiplicities. With a correct treatment of the biases a smooth transition betweenPb–Pb and minimum-bias p–Pb colli- sions isexpectedwithout theneed toinvolvepartonenergyloss inperipheralcollisions.Withoutsuchtreatment,themeasurement and interpretation of RAA in peripheral collisions, in particular above80%centrality,havecomplicationssimilartop–Pb collisions, wheretheobservable wasnamed QpPb[39] todistinguishitfrom theunbiasednuclearmodificationfactor.
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 Gridcentres andtheWorldwide LHCComputing Grid(WLCG) collaboration. The ALICE Collaboration acknowledges the follow- ingfundingagenciesfortheirsupportinbuildingandrunningthe ALICEdetector:A.I.AlikhanyanNationalScienceLaboratory(Yere- vanPhysicsInstitute) Foundation(ANSL),State Committee ofSci- enceandWorldFederationofScientists(WFS),Armenia; Austrian AcademyofSciencesandNationalstiftungfürForschung,Technolo- gie und Entwicklung, Austria; Ministry of Communications and High Technologies, NationalNuclear Research Center, Azerbaijan;
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do Rio Grande do Sul (UFRGS), Fi- nanciadoradeEstudoseProjetos(Finep)andFundaçãodeAmparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil; Ministry of Science & Technology of China (MSTC), National Natural Science Foundation of China (NSFC) and Ministry of Education of China (MOEC), China; Ministry of Science andEducation, Croatia; Min- istryofEducation,YouthandSportsoftheCzech Republic,Czech Republic; The Danish Council for Independent Research — Natu- ral Sciences, the Carlsberg Foundation and Danish National Re- search Foundation (DNRF), Denmark;Helsinki Institute ofPhysics (HIP),Finland;Commissariatàl’EnergieAtomique(CEA)andInsti- tut Nationalde Physique Nucléaire etde Physique desParticules (IN2P3)and Centre Nationalde laRecherche Scientifique(CNRS), France; Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI Helmholtzzentrum für Schw- erionenforschung GmbH, Germany; General Secretariat for Re- search andTechnology, Ministryof Education,Research andReli- gions,Greece;NationalResearchDevelopmentandInnovationOf- fice,Hungary;DepartmentofAtomicEnergy,GovernmentofIndia (DAE),DepartmentofScienceandTechnology,GovernmentofIndia (DST), University GrantsCommission, Governmentof India(UGC) andCouncilofScientific andIndustrial Research(CSIR),India;In- donesian Institute of Sciences, Indonesia; Centro Fermi - Museo StoricodellaFisicaeCentroStudieRicercheEnricoFermiandIsti- tutoNazionalediFisicaNucleare(INFN),Italy;InstituteforInnova- tiveScienceandTechnology,NagasakiInstitute ofAppliedScience (IIST),Japan SocietyforthePromotionofScience (JSPS)KAKENHI and Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia (CONA- CYT)yTecnología,throughFondodeCooperaciónInternacionalen Cienciay Tecnología(FONCICYT)andDirección General de Asun- tosdelPersonalAcademico(DGAPA),Mexico;NederlandseOrgan- isatie voorWetenschappelijkOnderzoek(NWO), Netherlands;The ResearchCouncilofNorway,Norway;CommissiononScienceand TechnologyforSustainableDevelopmentintheSouth(COMSATS), Pakistan;PontificiaUniversidadCatólicadelPerú,Peru;Ministryof ScienceandHigherEducationandNationalScienceCentre,Poland;
KoreaInstituteofScienceandTechnologyInformationandNational ResearchFoundationofKorea(NRF),RepublicofKorea;Ministryof EducationandScientific Research,Institute ofAtomic Physicsand RomanianNationalAgencyforScience,TechnologyandInnovation, Romania; Joint Institute for Nuclear Research (JINR), Ministry of EducationandScienceoftheRussianFederationandNationalRe- search Centre Kurchatov Institute, Russia; Ministry of Education, Science,Research andSportofthe Slovak Republic, Slovakia; Na- tionalResearchFoundationofSouthAfrica,SouthAfrica;Centrode AplicacionesTecnológicasyDesarrolloNuclear(CEADEN),Cubaen- ergía,CubaandCentrodeInvestigacionesEnergéticas,Medioambi- entalesyTecnológicas(CIEMAT),Spain;SwedishResearchCouncil (VR)andKnut&AliceWallenbergFoundation(KAW),Sweden;Eu- ropean Organization for Nuclear Research, Switzerland; National Science andTechnology DevelopmentAgency (NSDTA), Suranaree University of Technology (SUT) and Office of the Higher Educa-
tionCommissionunderNRUprojectofThailand,Thailand;Turkish Atomic Energy Agency (TAEK), Turkey;National Academy of Sci- encesofUkraine,Ukraine;ScienceandTechnologyFacilitiesCoun- cil (STFC), United Kingdom; National Science Foundation of the United States ofAmerica (NSF) andUnited StatesDepartment of Energy,OfficeofNuclearPhysics(DOENP),UnitedStatesofAmer- ica.
References
[1]M.Gyulassy,M.Plumer,Jetquenchingindensematter,Phys.Lett.B243(1990) 432–438.
[2]R.Baier,Y.L.Dokshitzer,S.Peigne,D.Schiff,InducedgluonradiationinaQCD medium,Phys.Lett.B345(1995)277–286,arXiv:hep-ph/9411409 [hep-ph].
[3]B.Alver,M.Baker,C.Loizides,P.Steinberg,ThePHOBOSGlauberMonteCarlo, arXiv:0805.4411 [nucl-ex].
[4]C.Loizides,J.Nagle,P.Steinberg,Improved versionofthePHOBOSGlauber MonteCarlo,SoftwareX1–2(2015)13–18,arXiv:1408.2549 [nucl-ex].
[5]C.Loizides,J.Kamin,D.d’Enterria,PrecisionMonteCarloGlauberpredictions atpresentandfuturenuclearcolliders,arXiv:1710.07098 [nucl-ex].
[6]ALICECollaboration,B.Abelev,et al.,CentralitydeterminationofPb–Pb col- lisionsat √s
NN=2.76 TeV withALICE, Phys.Rev.C88 (4)(2013) 044909, arXiv:1301.4361 [nucl-ex].
[7]PHENIXCollaboration,K.Adcox,etal.,Suppressionofhadronswithlargetrans- versemomentumincentralAu–Au collisionsat√
sNN=130 GeV,Phys.Rev.
Lett.88(2002)022301,arXiv:nucl-ex/0109003 [nucl-ex].
[8]STARCollaboration,C.Adler,etal.,CentralitydependenceofhighpT hadron suppressioninAu–Au collisionsat√
sNN=130 GeV,Phys.Rev.Lett.89(2002) 202301,arXiv:nucl-ex/0206011 [nucl-ex].
[9]PHENIXCollaboration,K.Adcox,etal.,CentralitydependenceofthehighpT chargedhadronsuppressioninAu–Au collisionsat√
sNN=130 GeV,Phys.Lett.
B561(2003)82–92,arXiv:nucl-ex/0207009 [nucl-ex].
[10]PHENIX Collaboration,S.S. Adler,et al.,Suppressed π0 production at large transversemomentumincentralAu–Au collisionsat√
sNN=200 GeV,Phys.
Rev.Lett.91(2003)072301,arXiv:nucl-ex/0304022 [nucl-ex].
[11]STARCollaboration,J.Adams,etal.,Transversemomentumandcollisionen- ergydependenceofhighpThadronsuppressioninAu–Au collisionsatultra- relativisticenergies,Phys.Rev.Lett.91(2003)172302,arXiv:nucl-ex/0305015 [nucl-ex].
[12]PHOBOSCollaboration,B.B.Back,etal.,Chargedhadrontransversemomentum distributionsinAu–Au collisionsat√s
NN=200 GeV,Phys.Lett.B578(2004) 297–303,arXiv:nucl-ex/0302015 [nucl-ex].
[13]PHOBOSCollaboration,B.Alver,etal.,Systemsizeandcentralitydependenceof chargedhadrontransversemomentumspectrainAu–Au andCu–Cu collisions at√s
NN=62.4 GeVand200GeV,Phys.Rev.Lett.96(2006)212301,arXiv:
nucl-ex/0512016 [nucl-ex].
[14]PHENIXCollaboration,S.S.Adler,etal.,Adetailedstudyofhigh-pTneutralpion suppressionandazimuthalanisotropyinAu–Au collisionsat√s
NN=200 GeV, Phys.Rev.C76(2007)034904,arXiv:nucl-ex/0611007 [nucl-ex].
[15]PHENIXCollaboration,A.Adare,etal.,Quantitativeconstraintsontheopacity ofhotpartonicmatterfromsemi-inclusivesinglehightransversemomentum pionsuppressioninAu–Au collisions at √s
NN=200 GeV, Phys. Rev.C77 (2008)064907,arXiv:0801.1665 [nucl-ex].
[16]PHENIXCollaboration,A.Adare,etal., Neutralpionproductionwithrespect tocentralityandreactionplaneinAu–Au collisionsat√
sNN=200 GeV,Phys.
Rev.C87 (3)(2013)034911,arXiv:1208.2254 [nucl-ex].
[17]ALICECollaboration,K.Aamodt,etal.,Suppressionofchargedparticleproduc- tionatlargetransversemomentumincentralPb–Pb collisionsat√
sNN=2.76 TeV,Phys.Lett.B696(2011)30–39,arXiv:1012.1004 [nucl-ex].
[18]ALICECollaboration,B.Abelev,etal.,Centralitydependenceofchargedparticle productionatlargetransversemomentuminPb–Pb collisionsat√
sNN=2.76 TeV,Phys.Lett.B720(2013)52–62,arXiv:1208.2711 [hep-ex].
[19]CMSCollaboration,S.Chatrchyan,etal.,Studyofhigh-pTchargedparticlesup- pressioninPb–Pb comparedtoppcollisionsat√
sNN=2.76 TeV,Eur.Phys.J.
C72(2012)1945,arXiv:1202.2554 [nucl-ex].
[20]ATLASCollaboration,G.Aad,etal.,Measurementofcharged-particlespectrain Pb–Pb collisionsat√s
NN=2.76 TeVwiththeATLASdetectorattheLHC,J.
HighEnergyPhys.09(2015)050,arXiv:1504.04337 [hep-ex].
[21]CMSCollaboration,V.Khachatryan,etal.,Charged-particlenuclearmodification factorsinPb–Pb andp–Pb collisionsat√s
NN=5.02 TeV,J.HighEnergyPhys.
04(2017)039,arXiv:1611.01664 [nucl-ex].
[22]ALICECollaboration,S.Acharya,etal.,Transversemomentumspectraandnu- clearmodificationfactorsofchargedparticlesinpp,p-PbandPb-Pbcollisions attheLHC,J.HighEnergyPhys.11(2018)013,arXiv:1802.09145 [nucl-ex].
[23]BRAHMS Collaboration, I. Arsene, et al., Transverse momentum spectra in Au–Au andd–Au collisions at√
sNN=200 GeVand thepseudorapidityde- pendenceofhigh pT suppression, Phys.Rev.Lett.91(2003)072305, arXiv:
nucl-ex/0307003 [nucl-ex].
