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B
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Analysis
of
the
apparent
nuclear
modification
in
peripheral
Pb–Pb
collisions
at
5.02 TeV
.
ALICE
Collaboration
a
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t
i
c
l
e
i
n
f
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Articlehistory:
Received24May2018
Receivedinrevisedform26March2019 Accepted17April2019
Availableonline23April2019 Editor:W.-D.Schlatter
Charged-particlespectraatmidrapidityaremeasuredinPb–Pbcollisionsatthecentre-of-massenergy per nucleon–nucleon pair √sNN=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/c interval,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-parton scatter-ingsintheearlystageofthecollision.Whilepropagatingthrough the expanding medium, these hard partons lose energy due to medium-inducedgluonradiationandcollisionalenergyloss,a pro-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 Ncoll dNAA ch/
dpT dNppch/
dpT=
1 TAA dNAA ch/
dpT dσ
chpp/
dpT,
(1)definedastheratiooftheper-eventyieldsinAA andppcollisions normalizedtoanincoherentsuperpositionof
Ncollbinarypp col-lisions.TheaveragenumberofcollisionsNcollisdeterminedfromE-mailaddress:alice-publications@cern.ch.
aMonteCarloGlaubermodel [3–5] andrelatedtotheaverage nu-clearoverlap
TAA=
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 inalimitedrapidityrangeandbyfittingthecorresponding distri-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 particle pro-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] andwith elec-tromagneticprobesinAA collisions [29–33] (whichshouldnot be affectedby partonicmatter)demonstratedthattheobserved sup-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 impact param-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-particle spec-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 and normaliza-tion,whichareparticularlylargeforperipheralcollisions,wealso providetheratioofRAAinadjacentcentralityintervals,definedas R+1≡
Ri+1=
RiAA RiAA+1=
Ncolli+1 Ncolli dNAAch,i/
dpT dNAAch,i+1/
dpT,
(2)where i
+
1 denotes a 5% more central centrality class than i.Thedefinitionof R+1 corresponds approximatelytothechangeof log RAAwithcentrality,anditsvaluewouldbeconstantforan ex-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 particlemeasurementwithemphasisoncorrectionsand uncertain-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 tracking infor-mationfromtheInnerTrackingSystem(ITS)andtheTime Projec-tionChamber(TPC),bothlocatedinsideasolenoidalmagneticfield of0
.
5 Tparalleltothebeamaxis.TheITS [45] consistsofthreesub-detectors,eachcomposed of two layerstomeasurethe trajectoriesofchargedparticles andto reconstructprimaryvertices.Thetwoinnermostlayersarethe Sil-icon PixelDetectors (SPD),themiddletwolayers areSiliconDrift Detectors (SDD), the outer two layers are Silicon Strip Detectors (SSD).
TheTPC [46] isalarge(90 m3)cylindricaldriftdetector.It cov-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 andincreaseslinearlyapproaching4%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 systematic uncer-tainties related to particle species dependence (see Ref. [22] for details).Eventsare classifiedinpercentilesofthehadronic cross-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%mostperipheral col-lisions.TheV0Mvaluecorrespondingto95%ofthehadroniccross sectionwasdeterminedbyselectingeither95%oftheeventsgiven by the Glauber-NBD parametrization, orthe numberofevents in the 0–90% centrality class multiplied by the factor 95/90, wherethelatterisusedasavariationtoassessthesystematicuncertainty 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 wereestimatedfromsimulationsusingHIJINGandPYTHIA includ-ingsingle- and double-diffractiveprocesses,butignoringpossible differencesfromnucleareffects.TheV0Mdistributioninthe sim-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-biaspp col-lisions.Contaminationoftheperipheralbinsbyelectromagnetic inter-actionswasstudiedinthedataby removingalleventswithsmall energydepositsintheneutron ZDCs.Theresultingchangeofthe spectrumwiththerequirementsofatleastafive-neutron equiva-lentenergyinboth neutronZDCsamountsto5%forthe95–100% centralityclass,3%forthe90-95%classand2%forthe80-85%and 85-90% classes and is assigned assystematic uncertainty. To ac-countforcontaminationofthetriggerfromeventswithout recon-structed vertex, those events are removed fromthe analysis and theresultingchange isassignedassystematicuncertaintyonthe normalization (6.8%inthe95–100%classand0.5%inthe90–95% class).
Systematicuncertaintiesrelatedtovertexselection,track selec-tion,secondary-particle contamination, primary-particle composi-tion, pT resolution, material budget andtracking efficiency were estimatedasdescribedinRef. [22] andareassignedasbin-by-bin uncertainties. The systematicuncertainties relatedto the central-ity selection were estimated by a comparison of the pT spectra whenthelimitsofthecentralityclassesareshiftedduetoan un-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 ofNcoll, the uncertainty ofthe trigger efficiency, the uncertainty of thetriggercontaminationandthenormalizationuncertaintyofthe ppreferencespectrumaddedinquadrature.Notethatmost uncer-taintiesarecorrelatedtoalargeextentbetweenadjacentcentrality binsleadingtoreduceduncertaintiesinR+1.
Orderingeventsaccordingtomultiplicityintroducesabias rel-ativetousingtheimpactparameterinGlauber-basedparticle pro-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, as car-riedout so faratthe LHC.The differenceis below5% upto 80%Fig. 1. Ratioofnumberofcollisionsdeterminedbyslicinginmultiplicity (Nmult
coll)
dividedbythenumberofcollisionsdetermineddirectlyfromtheimpact parame-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%formore periph-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 particularforperipheralcollisionsthewidthsoftherespective dis-tributionsaresignificantlylarger.
The charged particle multiplicity dNch
/
dη
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√sNN=5.02 TeVfor5%-widecentralityclasses.Thefilled,coloured
markersareforthefivemostperipheralclasses,withthecorrespondingglobaluncertaintiesdenotedclosetopT=0.1 GeV/c.Verticalerrorbarsdenotestatistical
uncer-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 atpT
∼
0.
1 GeV/
c.Asusual,ifnototherwisestated,verticalerrorbars denotestatisticaluncertainties,whiletheboxesdenotethe system-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 most pe-ripheral classes, the reduction of the nuclear modification factor withincreasing pT isqualitativelysimilar totheoneobservedfor low multiplicity p–Pb [39] collisions, indicating that the underly-ingbiastowardsmoreperipheralcollisionswithareducedrateof hardscatteringspernucleon–nucleoncollisions isthesame.If in-stead of using Nmultcoll , we had used Ngeocoll in the normalization ofRAA,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,butratherbytheevent selec-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 beforedecreas-Fig. 3. AverageRAAfor8<pT<20 GeV/c versuscentralitypercentileinPb–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,resultingχ
2/
NDF arebelowunity.Whilethe absolutevaluesoftheslopesareverydifferent(notethe normali-sation),theshapeofthecentralitydependenceoftheslopeatlowpT is remarkablysimilar to that extracted athigh pT. This hints ataclosecorrelationbetweenthesetworegimes,possiblyinduced by thegeometryordensitydependenceofpartonenergylosson
Fig. 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.In pe-ripheral collisions, in particular above 90% centrality, the low pT slopeisnegative,indicatingthattheveryperipheraleventsare in-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.AsforRAAthe pe-ripheralcollisionsaredisplayedincolour,withtheircorresponding global uncertainties, whichare significantly smaller than for RAA except for the most peripheral class, denoted around 0.1 on theFig. 5. R+1versuspTforchargedparticlesatmidrapidityinPb–Pb collisionsat√sNN=5.02 TeV.R+1isdefinedastheratioofNcollnormalizedspectraforagivencentrality
classrelativetothe5%morecentralclass,seeEq. (2).Thefilled,colouredmarkersareforthe5mostperipheralclasses,withthecorrespondingglobaluncertaintiesdenoted closetopT=0.1 GeV/c onthepT-axis.Verticalerrorbarsdenotestatisticaluncertainties,whiletheboxesdenotethesystematicuncertainties.Forvisibility,theuncertainties
Fig. 6. AverageR+1for8<pT<20 GeV/c versuscentralitypercentileinPb–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√sNN=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 withcentralityis charac-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.AnapproximateconstantvalueforR+1uptoabout60%centralityimpliesanexponentialdependence oncentrality.
Fig.7showstheslopeofalinearfittothelowmomentum re-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 withχ
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 for pe-ripheralcollisionsabove80%,asexpectedfromorderingevents ac-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%most cen-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 and normaliza-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 and col-lisiongeometrycanleadtoan apparentsuppressioninperipheral collisions.Thisexplainsthecontradictoryandhardtoreconcile ob-servation that RAA is belowunity inperipheral Pb–Pb, butequal tounityinminimum-biasp–Pb collisionsdespitesimilar charged-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 tothe construc-tionoftheexperimentandtheCERNacceleratorteamsforthe
out-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 of Sci-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)and Insti-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 and Reli-gions,Greece;NationalResearchDevelopmentandInnovation Of-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 StoricodellaFisicaeCentroStudieRicercheEnricoFermiand Isti-tutoNazionalediFisicaNucleare(INFN),Italy;Institutefor Innova-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;Nederlandse Organ-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 EducationandScienceoftheRussianFederationandNational Re-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;ScienceandTechnologyFacilities Coun-cil (STFC), United Kingdom; National Science Foundation of the United States ofAmerica (NSF) andUnited StatesDepartment of Energy,OfficeofNuclearPhysics(DOENP),UnitedStatesof Amer-ica.
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