J/ψ production as a function of charged-particle pseudorapidity density in p–Pb collisions at √sNN = 5.02 TeV

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Physics Letters B

www.elsevier.com/locate/physletb

J/ ψ production as a function of charged-particle pseudorapidity density in p–Pb collisions at √

s _NN = ⁵ . 02 TeV

.ALICE Collaboration

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

Articlehistory:

Received6April2017

Receivedinrevisedform20October2017 Accepted4November2017

Availableonline8November2017 Editor: L.Rolandi

WereportmeasurementsoftheinclusiveJ/ψ yieldandaveragetransversemomentumasafunctionof charged-particle pseudorapiditydensitydNch/dηinp–Pbcollisions at√_s

NN=⁵.02 TeV with ALICEat theLHC.Theobservablesarenormalisedtotheircorrespondingaveragesinnon-singlediffractiveevents.

AnincreaseofthenormalisedJ/ψyieldwithnormaliseddNch/dη,measuredatmid-rapidity,isobserved atmid-rapidityandbackwardrapidity.Atforwardrapidity,asaturationoftherelativeyieldisobserved for highcharged-particle multiplicities.The normalisedaveragetransverse momentumatforwardand backward rapidities increases with multiplicity at low multiplicities and saturates beyond moderate multiplicities. In addition, the forward-to-backward nuclear modificationfactor ratio is alsoreported, showing an increasing suppression of J/ψ production at forward rapidity with respect to backward rapidityforincreasingcharged-particlemultiplicity.

©^{2017TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Quarkonium states, such as the J/ψ meson, are prominent probesofthedeconfinedstateofmatter,theQuark–GluonPlasma (QGP),formed inhigh-energyheavy-ioncollisions [1].Asuppres- sion of J/ψ production in nucleus–nucleus (AA) collisions with respect to that in proton–proton (pp) collisions has been ob- served by several experiments [2–10]. A remarkable feature is that, for J/ψ production at low transverse momentum (p_T) at the Large Hadron Collider (LHC), the suppression is significantly smallerthanthatatlowerenergies[5,7,10].Themeasurementsof J/ψ productioninproton(deuteron)–nucleuscollisions,wherethe formationoftheQGPisnotexpected, areessentialtoquantifyef- fects(oftendenoted “cold nuclearmatter, CNM, effects”), present alsoinAAcollisions butnot associatedto theQGP formation.At LHCenergies,gluonshadowing/saturationisthemostrelevantef- fect which was expectedto be quantified withmeasurements in p–Pbcollisions [11,12]. Furthermore,a novel effect,coherent en- ergylossinCNM(medium-inducedgluonradiation),wasproposed [13].

Themeasurements ind–Aucollisions attheRelativistic Heavy Ion Collider (RHIC) have underlined the role of CNM effects in J/ψ productionat√

sNN=^{200 GeV [14–16].At theLHC, thefirst} measurementsofJ/ψ productioninminimum-biasp–Pbcollisions at√

s_NN=⁵.02 TeV [17,18]showed that J/ψ production inp–Pb collisions is suppressed at forward rapidity with respect to the

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expectation from a superposition of nucleon–nucleon collisions.

The datahavebeen furtheranalysed to providemoredifferential measurements anddiscussed incomparisonwithseveraltheoret- ical models[19].A fairagreementis observedbetween dataand models including nuclear shadowing [12] or saturation [20,21];

alsomodelsincludingacontributionfromcoherentenergylossin CNM[13]describethedata.Thesemeasurementsarealsorelevant withrespect toJ/ψ production inPb–Pbcollisions atthe LHC[5, 7],currentlyunderstoodtobestronglyinfluencedbythepresence of a deconfined medium. The measurements of ϒ production in minimum-biasp–Pbcollisions attheLHC[22,23] are alsoconsis- tentwithpredictionsbasedonCNMeffects.Recentmeasurements of theψ(2S) state in p–Pbcollisions have revealeda larger sup- pression than that measured forJ/ψ production[24,25]. Such an observationwasnotexpectedfromtheavailablepredictionsbased onCNMeffects.

Concurrently, measurements of two-particle angular correla- tions in p–Pb collisions at the LHC [26–32] revealed for high- multiplicity events features that, in Pb–Pb collisions, have been interpreted as a result of the collective expansion of a hot and densemedium.Furthermore,theidentifiedparticlep_Tspectra[33]

showfeaturesakintothoseinPb–Pbcollisions,wheremodelsin- cludingcollective flow, assuminglocal thermalequilibrium, agree withthedata.

ThemeasurementofJ/ψ productionasafunctionofcentrality inp–Pbcollisions attheLHC[34]showedthatthenucleareffects depend on centrality. ϒ production has been studied as a func- tion ofcharged-particle multiplicity in pp and p–Pbcollisions by https://doi.org/10.1016/j.physletb.2017.11.008

0370-2693/©^{2017TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

theCMSCollaboration[35].Theyieldsofϒmesonsincreasewith multiplicity,while adecrease ofthe relativeproduction ofϒ(2S) and ϒ(3S) with respect to ϒ(1S) is observed. The measurement ofD-mesonproductionasafunctionofeventmultiplicityinp–Pb collisions[36]exhibitsfeaturessimilartothoseobservedearlierin ppcollisions,bothforJ/ψ [37]andD-meson[38]production.

InthisLettermeasurementsoftheinclusiveJ/ψ yieldandaver- agetransversemomentumasafunctionofcharged-particlepseu- dorapiditydensityinp–Pbcollisions at√

sNN=⁵.02 TeVarepre- sented.Performedinthreerangesofrapidity forp_T >0 withthe ALICEdetector atthe LHC, these measurements complementthe studies of J/ψ and ψ(2S) production as a function of the event centralityestimatedfromtheenergydepositedintheZeroDegree Calorimeters (ZDC) [34,39]. A measurement asa function of the charged-particle multiplicitydoesnot requireaninterpretation of theeventclasses intermsof thecollision geometry.Importantly, it enables the possibility to study rare events where collective- like effects may arise. The present data allow the investigation ofeventswithveryhighmultiplicities ofchargedparticles,corre- spondingtolessthan 1%ofthehadroniccrosssection andestab- lishaswellaconnectiontotherecentmeasurementsofD-meson productionasafunctionofeventmultiplicity[36].Ameasurement oftheforward-to-backwardJ/ψ nuclearmodificationfactorratiois alsopresented.

2. Experimentanddatasample

The ALICE central barrel detectors are located in a solenoidal magnetic field of 0.5T. The main trackingdevices in thisregion are the Inner Tracking System(ITS), which consistsof six layers of silicondetectors around the beam pipe, andthe Time Projec- tionChamber(TPC),alargecylindricalgaseousdetectorproviding trackingandparticleidentificationviaspecificenergyloss.Tracks arereconstructedintheactivevolumeoftheTPCwithinthepseu- dorapidity range |

η

_|<0.9 in the laboratory frame. The first two layers of the ITS (|

η

|<2.0 and |

η

|<1.4), the Silicon Pixel De- tector (SPD), are used forthe collision vertex determination and thecharged-particlemultiplicitymeasurement.Theminimum-bias (MB)eventsaretriggeredrequiringthecoincidenceofthetwoV0 scintillatorarrayscovering2.8<

η

<5.1 and−³.7<

η

<−¹.7,re- spectively.ThetwoneutronZeroDegreeCalorimeters(ZDC),placed at112.5 monboth sidesoftheinteraction point,areusedtore- ject electromagnetic interactions and beam-induced background.

The muon spectrometer, covering −⁴<

η

<−².5, consists of a front absorber, a 3 T·^{m dipole magnet, ten tracking layers, and} fourtriggerlayerslocatedbehindaniron-wallfilter.Inadditionto theMBtriggercondition,thedimuontriggerrequiresthepresence oftwoopposite-sign particlesinthe muontriggerchambers. The triggercomprisesa minimumtransversemomentum requirement ofpT>0.5 GeV/cattracklevel.Thesingle-muontriggerefficiency curveisnotsharp;theefficiencyreachesaplateauvalueof∼^96%

at p_T∼¹.5GeV/c.TheALICEdetectorisdescribedinmoredetail in[40]anditsperformanceisoutlinedin[41].

The results presented in this Letter are obtained with data recorded in 2013 in p–Pb collisions at √

s_NN =⁵.02 TeV. MB eventsareusedfortheJ/ψ reconstruction inthedielectronchan- nel at mid-rapidity. The dimuon-triggered data have been taken with two beam configurations, allowing the coverage of both forward and backward rapidity ranges. In the period when the dimuon-triggered data sample was collected, the MB interaction ratereachedamaximumof200kHz,correspondingtoamaximum pile-upprobabilityofabout3%.TheMB-triggeredeventsusedfor thedielectronchannelanalysiswerecollectedinoneofthebeam configurationsatalowerinteractionrate(about10kHz)andcon- sequentlyhadasmallerpile-upprobabilityof0.2%.

Duetotheasymmetryofthebeamenergypernucleoninp–Pb collisionsattheLHC,thenucleon–nucleoncenter-of-massrapidity frameisshiftedinrapiditybyy=⁰.465 withrespecttothelab- oratory frame inthe direction ofthe proton beam. This leads to arapiditycoverage inthenucleon–nucleoncenter-of-masssystem

−¹.37<ycms<0.43 for the MB events, while the coverage for the dimuon-triggered data forthe two different beamconfigura- tions is−⁴.46<ycms<−².96 (muonspectrometerlocatedinthe Pb-going direction) and 2.03<y_cms<3.53 (muon spectrometer locatedinthep-goingdirection).Theintegratedluminositiesused inthisanalysisare51.4±¹.9μb⁻¹(mid-rapidity),5.01±⁰.19nb⁻¹ (forward y)and5.81±⁰.20nb⁻¹ (backwardy).

3. Charged-particlepseudorapiditydensitymeasurement

The charged-particle pseudorapidity density dN_ch/d

η

is mea- sured at midrapidity, |

η

_|<1, andis based on the SPD informa- tion. Tracklets,i.e.tracksegments builtfromhitpairs inthe two SPDlayers,areusedtogetherwiththeinteractionvertexposition, which is alsodetermined with theSPD information[42].Several quality criteriaareapplied toselectonlyeventswithan accurate determinationofthezcoordinateofthevertex, zvtx.Toensurefull SPDacceptanceforthetrackletmultiplicity N_trk evaluationwithin

|

η

|<1,thecondition|^zvtx|<10 cmisappliedfortheselectionof theevents.

During the data taking period about 8% of the SPD channels were inactive, the exact fraction being time-dependent. The im- pactoftheinactivechannelsoftheSPDonthetrackletmultiplicity measurement varieswith zvtx.A zvtx-dependentcorrection factor isdeterminedfromdata,asdiscussedin[37].Thisfactoralsotakes into account the time-dependent variations of thefraction ofin- active SPD channels. The correction factor is randomised on an event-by-eventbasisusingaPoissondistributioninordertoemu- late thedispersion betweenthetruecharged-particle multiplicity andthemeasuredtrackletmultiplicities.

The overall inefficiency, the production of secondary parti- cles due to interactions in the detector material, particle de- cays and fake-tracklet reconstruction lead to a difference be- tween the number of reconstructed tracklets and the true pri- marycharged-particlemultiplicityNch (seedetailsin[42])¹.Using eventssimulatedwiththeDPMJETeventgenerator[43],thecorre- lationbetweenthetrackletmultiplicity (afterthe zvtx-correction), N^corr_trk , and the generated primary charged particles Nch is deter- mined. The correction factor β to obtain the average dNch/d

η

value corresponding toa givenN_trk^corr biniscomputedfroma lin- ear fit of the N_trk^corr–N_ch correlation. The charged-particle pseu- dorapidity density value in each multiplicity bin is given rela- tive to theevent-averagedvalue andis calculatedas: dN_ch^R/d

η

₌

dN_ch/d

η

/^dNch/d

η

=β· ^N_trk^corr/(

η

· ^dNch/d

η

)^,where

η

=² and ^dNch/d

η

^{is the} charged-particle pseudorapidity densityfor non-singlediffractive(NSD) collisions,whichwas measuredtobe ^dNch/d

η

₌17.64±⁰.01(stat.)±⁰.68(syst.) [42].The resulting valuesforthemultiplicitybinsare summarisedinTables 1 and 2 for forward and mid-rapidity, respectively. For the data at back- wardrapidity,thevaluesarewellwithintheuncertaintiesofthose atforwardrapidity.

The fractionof theMB cross sectioncontained ineach multi- plicity bin (

σ

/

σ

M B, derived from the respective event counts in the multiplicity bins andtotalnumber ofMB events)is reported in Tables 1 and 2.The softest MB events, whichlead to absence

1 Inthiscontext,weregardasprimarycharged-particlesallpromptchargedpar- ticlesincludingalldecayproductsexceptproductsfromweakdecaysoflightflavour hadronsandofmuons.

Table 1

Averagecharged-particle pseudorapiditydensity values(absoluteandrelative) in eachmultiplicitybin,obtainedfromN_trk^corrmeasuredintherange|η|<1.Thevalues correspondtothedatasampleusedfortheforwardrapidityanalysis.Onlysystem- aticuncertaintiesareshownsincethestatisticalonesarenegligible.Thefractionof theMBcrosssectionforeachmultiplicitybinisalsoindicated.

dNch/dη dN_ch^R/dη σ/σM B

4.8±0.2 0.27±0.01 26.4%

10.9±^{0.4 0.62}±^{0.03 14.3%}

14.6±^{0.5 0.83}±^{0.03 7.9%}

17.8±^{0.5 1.01}±^{0.04 9.6%}

21.4±^{0.7 1.22}±^{0.05 8.5%}

25.0±0.8 1.42±0.06 7.2%

28.6±0.8 1.62±0.06 6.0%

32.7±1.0 1.85±0.07 6.7%

37.8±^{1.1 2.14}±^{0.08 4.6%}

44.2±^{1.3 2.51}±^{0.10 4.2%}

54.3±^{1.6 3.08}±^{0.12 2.4%}

71.4±^{2.1 4.05}±^{0.16 0.3%}

Table 2

AsTable 1,butfortheanalysisofJ/ψproductionatmid-rapidity.

dNch/dη dN_ch^R/dη σ/σM B

6.9±^{0.2 0.39}±^{0.02 47.2%}

22.9±^{0.6 1.30}±^{0.05 39.7%}

42.3±^{1.1 2.40}±^{0.10 10.9%}

64.4±^{1.6 3.65}±^{0.15 1.0%}

oftracklets in|

η

|<1 arenot accountedforinthisanalysis.They correspond to1.2% of

σ

M B for the MB-triggeredevents and1.9%

forthemuon-triggereddata;thedifferenceisduetothedifferent fractionofinactivechannelsinSPDandaffects,albeitinanegligi- bleway,onlyourfirstmultiplicitybin.

Themultiplicityselection inthisanalysisallowstosample the datain bins containing a small fractionof the MB cross section.

Therefore, it gives the possibility to study the J/ψ production in rare high-multiplicity events which were not accessible in the centrality-basedanalysis[34] (wherethemost-centraleventclass correspondstotherange2–10%in

σ

/

σ

M B).

4. J/ψmeasurement

FortheJ/ψ analysisatforwardandbackward rapidities,muon candidatesareselectedbyrequiringthereconstructedtrackinthe muonchamberstomatchatracksegmentinthetriggerchambers.

Furthermore,theradial distanceofthe muon trackswithrespect tothe beamaxis atthe endof the front absorber isrequired to be between17.6 and89.5cm. Thiscriterion rejects tracks cross- ingthehigh-densitypartoftheabsorber,wherethescatteringand energy-loss effects are large. Aselection onthe muon pseudora- pidity−⁴<

η

<−².5 isalsoappliedtorejectmuonsattheedges ofthespectrometer’sacceptance.

When building the invariant mass distributions, each dimuon pair(ofagiven pT andy)iscorrectedbythedetectoracceptance timesefficiencyfactor1/(A×

ε

(p_T,y)).The A×

ε

(p_T,y)mapisob- tainedfromaparticle-gunMonteCarlo(MC)simulationbasedon GEANT 3 [44] and simulating the detector response as in [18].

Since the A×

ε

-factor does not depend on the multiplicity for theeventmultiplicities relevantforthe p–Pbanalyses,the simu- latedeventsonlycontainadimuonpairatthegeneratorlevel.The simulations assume an unpolarised J/ψ production. The samere- constructionprocedureandselectioncutsareappliedtoMCevents andto real data.The extractionof the J/ψ signal in the dimuon channel is performed via a fit to the A×

ε

-corrected opposite- sign(OS)dimuon invariant massdistributions obtained for p_T <

15GeV/c.Thefittingprocedureissimilarto thatusedinaprevi- ousJ/ψ analysisinp–Pbcollisions[18].Thedistributionsarefitted

usinga superpositionofJ/ψ andψ(2S) signalsanda background shape.TheresonancesareparameterizedusingaCrystalBallfunc- tion with asymmetric tails while for the background a Gaussian withits widthlinearlyvarying withmassis used.In thepresent analysis,theparametersofthenon-Gaussian tailsoftheresonance shapearedetermined fromfitsoftheMCJ/ψ signal,andfixed in thedatafittingprocedure.Examplesoffitsofthe A×

ε

-corrected dimuoninvariantmassdistributionsfortwoselectedbins,lowand highmultiplicities,aregivenintheleftpanelofFig. 1.

Inthedielectrondecaychannel,electronsandpositronsarere- constructedinthecentralbarreldetectorsbyrequiringaminimum of 70out ofmaximally 159track points in the TPCand a max- imum value of 4 for the track fit

χ

² over the number of track points. Furthermore,onlytracks withatleasttwo associatedhits intheITS, oneoftheminthe innermostlayer, areaccepted.This selectionreducestheamountofelectronsandpositronsfrompho- ton conversions in the material of the detector beyond the first ITSlayer. Inaddition a vetocut ontopologically identifiedtracks fromphoton conversions isapplied. The electronidentification is achieved by the measurement of the energy deposition of the track in the TPC, which is required to be compatible with that expected for electrons within 3 standard deviations. Tracks with specificenergylossbeingconsistentwiththatofthepionorpro- ton hypothesis within 3.5standard deviationsare rejected. These selectioncriteriaareidenticaltothoseusedin[34].Electronsand positronsareselectedinthepseudorapidityrange|

η

_|<0.9 andin thetransversemomentumrangep_T>1GeV/c.

The background in the OS invariant mass distribution is es- timated with dielectron pairs formed with tracks from differ- ent events (mixed-event background). The background shape is normalised such that its integral over ranges of the invariant mass in the sidebands of the J/ψ mass peak equals the num- ber of measured OS dielectron pairs in the same ranges (typical ranges usedare [³.2,3.7] ^{GeV/c2 and}[².0,2.5] ^{GeV/c2).The sig-} nal itselfis extractedby countingtheentries inthe background- subtractedinvariant massdistribution(the standardrangeusedis [².92,3.16] ^{GeV/c2). Due to} bremsstrahlung of the electron and positron inthe detectormaterial andradiative correctionsof the decayvertex, theJ/ψ signalshapehasatailtowardslowerinvari- antmasses.The standardrangeforthesignalextractioncontains, according to MC simulations, about 69% of the J/ψ signal. The numberofreconstructedJ/ψ mesonsanditsstatisticaluncertainty are derived from the mean obtainedwhen varying the counting window for the signal extraction and the invariant mass ranges usedforthenormalisationofthebackground.The variationsthat are taken intoaccount are thesame asin [34].Examples of the dielectron invariant mass distributions in data, for two selected analysisbinsatlow andhighmultiplicities,aregivenintheright panelofFig. 1.

The correction for the acceptance and efficiency of the raw yieldsisbasedonsimulatedp–PbcollisionswiththeHIJINGevent generator[45]withaninjectedJ/ψ signal.Thedielectrondecayis simulatedwiththeEVTGENpackage[46]usingPHOTOS[47,48]to describethefinal stateradiation.Theproductionisassumedtobe unpolarisedasinthe muondecaychannel analysis. Thepropaga- tionofthesimulatedparticlesisdonebyGEANT 3[44]andafull simulationofthedetectorresponseisperformed.Thesamerecon- struction procedure and selection cuts are applied to MC events andtorealdata.

The inclusive J/ψ yield per event is obtained in each multi- plicity bin as NJ/ψ =^Ncorr_J/ψ/NMB, where N^corr_J/ψ is the number of reconstructed J/ψ mesons corrected for the acceptance timesef- ficiencyfactor.Inthedimuondecaychannelanalysis, thenumber ofMBeventsequivalentto theanalysed dimuonsample(NMB) in eachmultiplicitybinisobtainedfromthenumberofdimuontrig-

Fig. 1.Opposite-signinvariantmassdistributionsofselectedmuon(leftpanel,fortheforwardrapidity)andelectron(rightpanel)pairs,forselectedmultiplicitybins.Inthe leftpanel,thedistributionsarecorrectedforA×ε.Thecurvesshowthefitfunctionsforsignal,backgroundandcombinedsignalwithbackground(seetextfordetails).In therightpanel,thebackgroundisevaluatedwiththeevent-mixingtechnique,andtheoverlaidsignalisobtainedfromMonteCarlo(seetextfordetails).

gers(N_DIMU),throughthenormalisationfactorofdimuon-triggered toMB-triggeredevents F2μ/MB,asNMB=^F2μ/MB·^NDIMU.Thisfac- toriscomputedusingtwodifferentmethods,asdiscussedin[34].

TheJ/ψ crosssectionvaluesforminimum-biaseventsobtainedin thedimuonchannelatforwardandbackwardrapidities,andinthe dielectronchannelatmid-rapidityarecompatiblewiththosepre- sented in [18] and[19], respectively. The results presented here areprovidedrelativetotheyieldinNSDevents,^dNJ/ψ/dy^.The event-averagedyieldisnormalisedtotheNSDeventclass;thenor- malisationuncertaintyis3.1%[42].

Inpreviousanalyses,e.g.[19],theJ/ψ yieldwasextractedinpT bins,andthe resultingdistribution was fittedto extract the ^pT value.Thepresentanalysisaimsatstudyingeffectsthatmayarise athighcharged-particle multiplicities,wheretheusualmethodis no longersuitable due tostatistical limitations.The methodpre- sentedheredoesnotrequiretosample thedatainpT bins,hence allowing the analysis infiner multiplicity bins. The extractionof theaveragetransversemomentumofJ/ψ mesonsisdoneviaafit to the dimuon meantransverse momentum as a function ofthe invariant mass,^pμ_T^+μ−(^mμ⁺μ⁻).Acorrectionforthe acceptance times efficiencyhas to be applied when building thesedistribu- tions.Hence, thecontributionofeachdimuonpairwithacertain pT and y in a given invariant mass bin is weighted with the two-dimensional A×

ε

(p_T,y).InordertoextracttheJ/ψ ^pT^,the A×

ε

-corrected ^pμT^+μ−(mμ⁺μ⁻) distributions, whichare shown inFig. 2,arefittedusingthefollowingfunctionalshape:

^pμ_T^+μ−

(

m_μ+μ⁻

) = α

^J/ψ

(

m_μ+μ⁻

) ×

^p_T^J/ψ

+ α

^{ψ (2S)}

(

m_μ+μ⁻

) ×

^{pψ (}_T ^2S)

+

1

− α

^J/ψ

(

m_μ+μ⁻

) − α

^{ψ (2S)}

(

m_μ+μ⁻

)

×

^pbkg_T

⁽¹⁾

Fig. 2.Averagetransversemomentumofopposite-signmuonpairsasafunctionof theinvariantmassatforwardrapidity,fortwomultiplicitybins.Thecurvesarefits ofthebackgroundandcombinedsignalandbackground(seetext).

where

α

(mμ⁺μ⁻)=^S(mμ⁺μ⁻)/(S(mμ⁺μ⁻)+^B(mμ⁺μ⁻)); the sig- nal (S) andbackground(B) dependenceon thedimuoninvariant massisextractedfromthecorrectedinvariant massspectrumfits mentionedabove.TheJ/ψ andψ(2S)averagetransversemomenta,

Table 3

TherelativesystematicuncertaintiesoftherelativeJ/ψyieldmeasurementinthethreerapidityranges.Thevaluesin parenthesescorrespondtotheabsoluteyieldmeasurementwhendifferentfromtherelativeones.Therangesrepresent theminimumandmaximumvaluesoftheuncertaintiesoverthemultiplicitybins.Forthevertexqualityselection,the uncertaintiesmarkedwith ^∗referonlytothelowest-multiplicitybin;forallotherbinsthevalue is0.3%.Thetrigger, trackingandmatchingefficiencyuncertaintiesarenotlistedinthetable.

Source 2.03<ycms<3.53 −⁴.46<ycms<−².96 −¹.37<ycms<0.43

Sig. Extr. 0.6–1.9% 0.5–1.8% 3.2–8.4%

F2μ/M Bmethod 0.3–3.9% 0.3–3.9% Not applicable

A×ε/bin-flow 1–5.9% 1.4–3.9% 3.1–9.9%

Pile-up 1–4% 1–1.5% Negligible

Signal tails 0.5% (2%) 0.5% (2%) Not applicable

Vertex quality sel. 0.3%–0.6%^∗(0.9%^∗) 0.3%–0.6%^∗(0.9%^∗) Negligible

Total 2.1–8.3% (3.0–8.6%) 2.1–6.0% (2.9–6.4%) 4.5–13%

^pT^{J/ψ and pψ (}T ^2S), respectively, are fit parameters assumed to beindependentof theinvariantmass,while thebackgroundone, ^pbkg_T ^,isparameterizedwithasecondorderpolynomialfunction.

Notethat,asfortheyieldextraction,thequantity ^{pψ (}_T ^{2S) isnot} a measurement ofthe ψ(2S) mean transverse momentum, since the A×

ε

isobtainedonlyfromJ/ψ signalsinthesimulation.The ^pT ^{resultspresentedhereforbinsin}multiplicity are relativeto thevalueobtainedforinclusiveevents,^pTMB[19].

5. Systematicuncertainties

The systematic uncertainty of the overall average charged- particle pseudorapidity density was estimated to be 3.8% [42].

This includes effects related to the uncertainties in the simula- tions,detectoracceptanceandeventselection efficiency,anditis dominatedby the normalisation tothe NSD eventclass.Possible correlationbetweentheaveragemultiplicityandthatevaluatedin agivenbinwouldleadtoapartialcancellationofcertain sources ofuncertaintywhencomputingtherelativemultiplicity.Asacon- servative estimate, the uncertainty on the relative multiplicity is consideredtobe equaltotheuncertaintyontheoverallcharged- particlepseudorapiditydensity.

Theinfluenceofvariationsofthe

η

distributioninthecalcula- tionof the β correction factors, isestimated fromthe difference between the average number of tracklets obtained in the data takenwiththetwodifferentbeamconfigurations.Thecorrespond- inguncertainty onthemultiplicity determination amountsto 1%.

Theuncertainties arising fromthe fit procedureof the N^corr_trk –N_ch correlationinsimulatedevents,usedtoobtainthecorrectionfac- tors, are also included.This uncertainty ranges between0.2% (at high multiplicity) and 2% (at low multiplicity). The event selec- tionrelated to the vertexquality has a 1% effecton the average multiplicity in the lowest multiplicity bin anda negligible effect fortheother bins.Duetotheuncertaintyonthedeterminationof themultiplicity ofthe individual events,there couldbe a migra- tionofeventsamongthemultiplicitybins(bin-flow).Thisbin-flow effectisdeterminedbyrunningtheanalysisseveraltimeswithdif- ferent seeds for the random factor of the multiplicity correction (bin-flow test). The bin-flow uncertainties are obtainedfrom the dispersionofthe averagemultiplicity valuesinthebin-flowtests foreach multiplicity bin. Finally,the effect of pile-up is studied usingatoymodelthatreproducesthemainfeaturesofthemulti- plicitydetermination,andtakesintoaccountthemis-identification ofmultiplecollisionsinthesameevent. Thecontributionsofbin- flow and pile-up to the measured multiplicities are found to be negligibleforallthedatasets(takenatdifferentinteractionrates).

Thebin-dependentuncertaintyisaddedinquadraturetothe3.8%

uncertaintyof^dNch/d

η

,resultingina systematicuncertaintyof therelative charged-particle multiplicity of 4–4.5% depending on themultiplicitybin.

The yields reported here are provided relative to the event- averageyieldandtheuncertaintiesareestimatedforthisratio.The systematicuncertainties related totrigger, tracking andmatching efficiencyare correlated betweenthe multiplicity-differential and theintegrateddeterminations.Theycancelouttoalargeextent.

In the dimuon analysis, a combined systematic uncertainty whichincludesthe A×

ε

variations duetotheuncertaintyofthe J/ψ pTandrapidityinputdistributionsusedinthesimulationand multiplicitybin-floweffectsisderived.Duetothemultiplicitybin- flow, andthe fact that the invariant mass and ^pμ_T^+μ−(mμ⁺μ⁻) spectra are weighted by A×

ε

, these uncertainties can not be computedseparately. Thecombined uncertaintyis obtainedfrom ther.m.s. oftherelative yieldvaluesobtainedrunningtheanaly- sisseveraltimeswithdifferentseeds fortherandomfactorofthe multiplicity correction. In additionthe systematicuncertainty for the signal extraction isestimated asthe r.m.s. ofthe results ob- tainedusingdifferentfittingassumptionsforagivenbin-flowtest.

The fit procedure is varied by adoptinga pseudo-Gaussian func- tionforthesignal,apolynomialtimesanexponentialfunctionfor thebackgroundandbyusingtwoadditionalfittingranges.Theun- certaintyduetothedeterminationoftheparametersofthesignal tailsis estimatedbyusingseveralsets ofparameters fromdiffer- ent MC simulations. The uncertainty related to the computation method of the relative F2μ/M B is estimated considering the dif- ference betweenthetwoavailable methodstomeasurethefactor inmultiplicity bins[34].Theeffectofthevertexqualityselection is estimatedfromthe difference ofthe obtained yields withand without this selection. Finally, in order to determine the pile-up effectonthe measuredyield ineach multiplicitybin,the pile-up toy model is extended by including the production of J/ψ using as input the measured yields as a function of multiplicity. The difference between the measured andtoy MC yields is taken as systematicuncertainty.Alltheseeffectsareuncorrelatedwithina givenmultiplicitybin,hencetheyareaddedquadraticallytoobtain the systematic uncertainty of the relative yield in a multiplicity bin.Also, thesesystematicuncertainties are consideredasuncor- relatedbetweenthedifferentrapidityintervals. Asummaryofthe maximumandminimumrelativeyieldsystematicuncertainties is shownin Table 3. Inaddition, the3.1% uncertaintyof theevent- averageyieldnormalisationtoNSD,isreportedseparately.

Thesystematicuncertaintiesarecomputedalsofortheabsolute yieldsinmultiplicitybinsatforwardandbackwardrapidities.The absoluteyieldsareusedtocomputetheratioofthenuclearmod- ificationfactorsatforwardandbackward rapidities.Thevaluesof theuncertaintiesontheabsoluteyields areshowninparentheses inTable 3,whentheyaredifferentfromtheonesobtainedforthe relativeyield.Inaddition,fortheabsoluteyieldmeasurement,the muontracking,triggerandmatchingefficiencyuncertainties need tobe takenintoaccount[18].Theyamountto4% (6%),3% (3.4%) and1%(1%)atforward(backward)rapidities.

Table 4

The systematicuncertainties for the relative^pT measurementat forwardand backwardrapidities.Thevaluesrepresenttheminimumandmaximumvaluesof theuncertaintiesoverthemultiplicitybins.Theuncertaintiesmarkedwith^∗only refertothetwohighest-multiplicitybins.

Source 2.03<ycms<3.53 −4.46<ycms<−2.96

Sig. extr. 0.2–1.2% 0.2–0.5%

A×ε/bin-flow 0.5–2.0% 0.7–2.7%

Pile-up 0.2–0.7%^∗ 0.2–0.8%^∗

Total 0.6–2.4% 0.7–2.9%

Forthe dielectron decay channel, the signal extraction uncer- tainty is derived basedon the r.m.s.value of thedifferent signal yieldratiosobtainedforthevariationsofthebackgroundandthe signalintegrationwindowasin[34].Theuncertaintyislargestfor thehighestmultiplicitybins.Sincethe p_T distributionofJ/ψ may depend on multiplicity, the unmeasured pT spectrum leads to a multiplicity-dependent uncertainty, determinedas in[34]. As ex- plained in section 2, the pile-up contamination is very low and the induced uncertainty is negligible for all the multiplicity in- tervals.The uncertaintyrelatedto bin-flowisestimatedwiththe samemethodasinthedimuonanalysis. Thetotalsystematicun- certaintyvariesasafunctionofmultiplicitybetween4.5%and13%, seeTable 3.

Fortherelative J/ψ ^pT^{,theeffectsof the}uncertaintyonthe determinationofA×

ε

,the^pT^{extractionprocedureandbin-flow} are computed together following the same procedure asfor the relativeyield.The^pT^extractionuncertaintyisobtainedfromthe dispersionoftheresultsusingdifferentfitcombinations,including variations of the invariant mass signal and background parame- terisations,fittingrangeandtheuseofasecond orderpolynomial timesanexponentialfunctionforthe^pT^{ofbackgrounddimuons.}

TheeffectofconsideringtheJ/ψ ^pT^asindependentoftheinvari- antmassinthe^pμ_T^{+μ−fitsisfoundtobe}negligible.Theimpact offixing thesignal andbackgroundparametersduring the fitting procedureisobservedtobenegligibleaswell.Theeventsremoved bythevertexqualityselectiondonot havereconstructed J/ψ and thereforethe^pT^{remainsunmodified.Finally,usingapile-uptoy} model,itisshownthatthepile-uphasnoeffectonthe^pT^mea- surement, except for the two bins corresponding to the largest multiplicities.Alltheseeffectsareconsideredasuncorrelatedina givenmultiplicity binandhencetheirrespectiveuncertaintiesare added quadraticallyto obtain the relative ^pT ^{systematic uncer-} tainty ineachmultiplicity bin.Thesesystematicuncertainties are consideredasuncorrelatedbetweenthedifferentrapidityintervals.

Theresultsoftheuncertainties enteringintherelative^pT^mea- surementarereportedinTable 4.

6. Resultsanddiscussion

The dependence of the relative J/ψ yield on the relative charged-particle pseudorapidity density for three J/ψ rapidity rangesispresentedinFig. 3.Anincreaseoftherelativeyieldwith charged-particle multiplicity is observed forall rapidity domains, with a similar behaviour at low multiplicities. At multiplicities beyond 1.5–2 times the event-average multiplicity, two different trendsare observed.Therelativeyields atmid-rapidityandback- wardrapiditykeep growingwiththerelativemultiplicity inp–Pb collisions similarly to the observation in pp collisions at 7 TeV [37]. At forward rapidity the trend is different. In this rapidity window a saturation of the relative yield sets in for high mul- tiplicities. In lack of theoretical model calculations, it is unclear at the moment what is the causeof this observation. We recall thatthe exploredBjorken xranges intheforwardrapidityregion

Fig. 3.RelativeyieldofinclusiveJ/ψmesons,measuredinthreerapidityregions, asafunctionofrelativecharged-particlepseudorapidity,measuredatmid-rapidity.

Theerrorbarsshowthestatisticaluncertainties,andtheboxesthesystematicones.

Thedashedlineisthefirstdiagonal,plottedtoguidetheeye.

Fig. 4. Relative yieldofinclusiveJ/ψmesonsas afunction ofrelativecharged- particle pseudorapidity density, measured at mid-rapidity, in comparison to D mesons(averageofD⁰,D⁺,andD^∗+ species),forthepTinterval2–4GeV/c[36].

Theerrorbarsshowthestatisticaluncertainties,andtheboxesthesystematicones (additionalsystematicuncertaintiesduetothebfeed-downcontributionsandthe eventnormalisationarenotshownfortheDmesons).

are in thedomain ofshadowing/saturation, andthat a variety of models [12,13,49,20,21] arefairly successfulin describingthe re- cent centrality-integratedanddifferential measurements ofALICE [19,34],whichcorrespondintermsofourrelativemultiplicitiesto dN_ch/d

η

/^dNch/d

η

².5 atmost.

In Fig. 4the J/ψ measurementatmid-rapidity iscompared to that forprompt Dmesons (average ofD⁰, D⁺, andD^∗+ species) for the pT range 2–4GeV/c [36]. Similar trends are seen forthe J/ψ andDmesons,asobservedearlierinppcollisions[38].

ThenuclearmodificationfactorforJ/ψ productioninp–Pbcol- lisions (RpPb) as a function of centrality was presented in [34].

The relationship betweengeometry-related quantities, that quan- tifythecentralityofthecollision,andexperimentalobservablesin p–Pbcollisionsmaybesubjecttoaselectionbias[50]whichneeds careininterpretation.Byperformingtheratioofthenuclearmod- ification factors atforwardandbackward rapidities asa function of multiplicity,the dependenceon geometry-related quantities is eluded. Theforward-to-backwardnuclearmodificationfactorratio isdefinedas:

R_FB

=

^RpPb

(

2

.

03

<

ycms

<

3

.

53

)

R_pPb

(−

⁴

.

46

<

y_cms

< −

²

.

96

)

Fig. 5.RFB ofinclusiveJ/ψinp–Pb collisionsat√

sNN=5.02TeV asafunction ofrelativecharged-particlepseudorapiditydensity,measuredatmid-rapidity.The filledboxatunityrepresentstheglobaluncertainty.Theerrorbarsshowthestatis- ticaluncertainties,andtheboxesthesystematicones.

=

^Y

J/ψ

pPb

(

2

.

03

<

ycms

<

3

.

53

)

Y_pPb^J/ψ

( −

⁴

.

46

<

ycms

< −

²

.

96

)

×

^d

σ

_pp^J/ψ

/

dy

(−

⁴

.

46

<

y_cms

< −

²

.

96

)

d

σ

pp^J/ψ

/

dy

(

2

.

03

<

y_cms

<

3

.

53

)

(2)

Since theaverage charged-particle multiplicities andtheir uncer- taintiesareconsistentwitheachotherforthetwosetsofdata,the valuesof RFB are shown versus the average value of the two in eachmultiplicitybin.Notethat,differentlythanforthecaseofthe nuclearmodification factor measurement in[18],for the present measurementtherapidity ranges arenot symmetricwithrespect to y_cms=^{0 totake advantageofallthesignal yield,allowingthe} studyuptohighmultiplicities.Thevaluesofthereferencepp cross sectionwereobtainedbymeansofaninterpolationprocedureus- ing measurements at center-of-massenergies of 2.76 and 7 TeV [51]. The resulting backward-to-forward ratio of J/ψ production crosssectionsinpp collisionsis0.691±⁰.048,leadingtoaglobal uncertaintyonthe R_FBmeasurementof6.9%.

Forthe RFB ratio,thesystematic uncertainties ofthe absolute yields inp–Pbcollisions (Table 3) are considered asuncorrelated betweenforwardandbackwardrapidities,andthereforeaddedin quadrature.Theuncorrelated systematicuncertainties ofthe pro- ductioncrosssectionsinpp collisionsare thesameasafunction ofmultiplicity,sothey areaddedinquadratureto theglobalun- certainty (quadratic sumof muon tracking, trigger andmatching efficiencyuncertainties)ofthep–Pbdata,resultinginatotalrela- tiveuncertaintyof11%.

The R_FB ratio is shownas a function ofthe relative charged- particle pseudorapidity density inFig. 5. In multiplicity-inclusive collisions for symmetric y ranges at forward and backward ra- pidities[18], R_FB issmallerthanunityanddescribed bytheoreti- calmodels.Thepresentmeasurementshowsthatthesuppression of J/ψ production at forward rapidity with respect to backward rapidity increases significantly with charged-particle multiplicity, since RFB reaches values as low as 0.34 ± ^{0.06 (stat.)} ± ^0.05 (syst.). A forward–backward asymmetry can be noticed for in- clusive charged-particle production studied in [50]. Even though therangeofrelativecharged-particle multiplicitiesprobedinthat measurement is not as large as in the present measurement of J/ψ production,theapparent similarityofthetrendseeninFig. 5 tosoftparticleproductionisintriguing.

In Fig. 6 the relative ^pT ^{of J/}ψ mesons at backward and forwardrapidity is shown asa function of the relative charged- particlepseudorapiditydensity.The resultsaresimilaratforward

Fig. 6.Relative^pT^ofJ/ψmesonsforbackwardandforwardrapidityasafunction ofthe relativecharged-particlepseudorapidity density,measuredatmid-rapidity.

Thebarsshowthestatisticaluncertainties,andtheboxesthesystematicones.The dataforchargedparticles(h^±)[52]areincludedforcomparison.Thelatterarefor

|ηcms|<0.3 andwith pT intherange0.15to10GeV/c andhaveanadditional normalisationuncertaintyof3.4%.

andbackwardrapidities.Anincreaseoftherelative^pT^withmul- tiplicity at low charged-particle multiplicity is observed, but for multiplicities beyond 1.5 times the average multiplicity it satu- rates.Forbackwardrapidity,thesimultaneousincreaseoftheyield andthe saturation of the relative ^pT ^{could be an indication of} J/ψ productionfromanincoherentsuperpositionofparton–parton interactions,assuggestedbydataoncorrelationsofjet-likeyields pertriggerparticle[32].

The pT broadening observedin theanalysisof J/ψ production inp–Pbcollisionsasafunctionofcentrality[34] iswelldescribed by initialandfinal-statemultiplescatteringofpartonswithinthe nuclear medium [53]. The comparisonof data to model calcula- tions, performed in [34], corresponds in terms of relative mul- tiplicities to a range up to roughly dN_ch/d

η

/^dNch/d

η

=².5. It remains to be seen whether such models can explain the satu- rationobserved inthe relative^pT ^oftheJ/ψ mesons forevents withhighermultiplicities.

It is interesting to contrast the observed saturation of ^pT for J/ψ mesons withthe monotonic increase of ^pT ^{for charged} hadrons(dominatedbypionproduction)[54]withthemultiplicity measuredatmid-rapidityalsoshowninFig. 6.Notethatthismea- surementisforparticlesin|

η

cms|<0.3 andwithpT intherange 0.15 to 10 GeV/c, and it is relative to events with at least one particleinthiskinematicrange(forwhich^Nch=¹¹.9±⁰.5 and ^pT=⁰.696±⁰.024 GeV/c[54]).Althoughthedifferentkinematic regionsmayplayaroleandcareisneededintheinterpretation,it isapparent that thetwo observables, characterisedby ratherdif- ferent production mechanisms (and momentum-transfer) exhibit different patterns in the multiplicity dependence of the average transversemomentum.

7. Conclusions

Measurementsoftherelative J/ψ yieldandaverage transverse momentum asa functionofthe relativecharged-particle pseudo- rapiditydensityinp–Pbcollisions attheLHCat√

s_NN=⁵.02TeV have been presented inthis letter. The measurements were per- formedwithALICEinthreerangesofrapidity.Thecharged-particle multiplicity was measured atmid-rapidity; multiplicities up to 4 times the value of NSD events were reached, corresponding to rareeventsoflessthan1% ofthetotalhadronicinteraction cross section.AnincreaseoftherelativeJ/ψ yieldwiththerelativemul- tiplicityisobserved,withatrendtowardssaturationathighmul-