Multiplicity dependence of inclusive J/ψ production at midrapidity in pp collisions at at √s=13 TeV

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Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Multiplicity dependence of inclusive J/ ψ production at midrapidity in pp collisions at √

s = ^{13 TeV}

.ALICE Collaboration

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

Articlehistory:

Received9June2020

Receivedinrevisedform26August2020 Accepted31August2020

Availableonline3September2020 Editor: L.Rolandi

MeasurementsoftheinclusiveJ/ψyieldasafunctionofcharged-particlepseudorapiditydensitydNch/dη

inppcollisions at√

s=13 TeV withALICEattheLHCarereported.The J/ψ mesonyieldismeasured atmidrapidity(|^y|<0.9)inthe dielectronchannel,forevents selectedbasedonthe charged-particle multiplicityatmidrapidity(|η_|<1)andatforwardrapidity(−³.7<η<−¹.7 and2.8<η<5.1);both observablesarenormalizedtotheircorrespondingaveragesinminimumbiasevents.Theincreaseofthe normalizedJ/ψyieldwithnormalizeddNch/dηissigniﬁcantlystrongerthanlinearanddependentonthe transversemomentum. Thedataare comparedtotheoreticalpredictions,whichdescribetheobserved trendswell,albeitnotalwaysquantitatively.

©²⁰²⁰^EuropeanOrganizationforNuclearResearch.PublishedbyElsevierB.V.Thisisanopenaccess articleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Hadroniccharmoniumproductionatcolliderenergiesisacom- plex and not yet fully understood process, involving hard-scale processes, i.e.the initial heavy-quarkpair production, which can be describedby meansofperturbativequantum chromodynamics (pQCD), aswell assoft-scaleprocesses, i.e.the subsequent bind- ing intoa color-neutralcharmoniumstate. Thelatterstage isad- dressed via models which assume that it factorizes with respect to the perturbative early stage. The widely used non-relativistic QCD(NRQCD) effectivetheory [1] incorporatescontributionsfrom severalhadronizationmechanisms,likecolor-singletorcolor-octet models(seeRef. [2] forarecentreviewonmodelsandRef. [3] for acomparisonwithdataofRun1attheLHC).TheNRQCDformal- ismcombinedwithaColorGlassCondensate(CGC)descriptionof theincomingprotons [4] isa recentexampleofacomprehensive treatmentofthetransversemomentumpTandrapiditydependent production, in particular extended down to zero transverse momentum.MeasurementsofinclusiveJ/ψ production,asreportedin thispublication,containa non-promptcontributionfrombottom- hadrondecaysandtheproductionofbottomquarkscanbecalcu- latedinQCDpertubatively.

The event-multiplicity dependent production of charmonium and open charm hadrons in pp and p–Pb collisions are observ- ableshavingthepotentialtogivenewinsightsonprocessesatthe partonlevelandontheinterplaybetweenthehardandsoftmech- anisms in particle production andis widely studied at the LHC.

ALICEhasstudied themultiplicity dependenceinpp collisions at

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

√s=^{7 TeV of} ^inclusive ^J/ψ production at mid- and forward rapidity [5],andpromptJ/ψ (includingfeeddownfromψ(2S) and

χ

c),non-prompt J/ψ andD-meson productionatmidrapidity [6].

Thegeneralobservationisan increaseofopen andhiddencharm productionwithcharged-particle multiplicity measuredatmidra- pidity.FortheJ/ψ production,multiplicitiesofabout4timesthe meanvalue were reached. Theresults areconsistent withan approximately linearincrease ofthe normalizedyield asa function of the normalized multiplicity (both observables are normalized totheircorresponding averagesinminimumbiasevents).Forthe D-meson production, normalized event multiplicities of about 6 werereached;astrongerthanlinearincreaseofD-mesonproduc- tionwasobservedatthehighestmultiplicities.Observationsmade by theCMSCollaboration forϒ(nS)production atmidrapidity at

√s=².76 TeV indicate a linear increase with the eventactivity, when measuring it at forwardrapidity, and a stronger than linear increase withtheevent activitymeasured atmidrapidity [7].

AtRHIC, ameasurement ofJ/ψ productionasa functionofmul- tiplicitywas recentlyperformedbytheSTARCollaboration [8] for

√s=⁰.2 TeV,showingsimilartrendsasobservedintheLHCdata.

The J/ψ production asa function ofcharged-particle multiplicity was studied also in p–Pb collisions, exhibiting signiﬁcant differences for different ranges of rapidity of the J/ψ meson [9,10].

Aclear correlation withtheevent multiplicity (andevent shape) was experimentally established for the inclusive charged-particle production [11] aswellasforidentiﬁedparticles,includingmulti- strangehyperons [12].

Severaltheoreticalmodels, described brieﬂy inSection 4,pre- dictacorrelationofthenormalizedJ/ψ productionwiththenor- malized event multiplicity which is stronger than linear. These includeacoherentparticleproductionmodel [13],thepercolation

https://doi.org/10.1016/j.physletb.2020.135758

0370-2693/©²⁰²⁰^EuropeanOrganizationforNuclearResearch.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

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Table 1

Numberofselectedeventsandcorrespondingintegratedluminositiesforthedifferenttriggersusedinthisanal- ysis.

MB and HM triggers EMCal triggers

MB HM EG1 EG2

Number of events 1.25×¹⁰⁹ ⁰.64×¹⁰⁹ ⁸².4×¹⁰⁶ ¹²⁰×¹⁰⁶ Integrated luminosity 21.6±¹.1 nb⁻¹ 5.4±⁰.1 pb⁻¹ 7.2±⁰.1 pb⁻¹ 0.82±⁰.02 pb⁻¹

model [14],theEPOS3eventgenerator [15],aCGC-complemented NRQCD model [16], the PYTHIA8.2 eventgenerator [17,18], and the3-PomeronCGCmodel [19].Whileforinstancemultipartonin- teractions(as implemented inPYTHIA) playan important role in charm(onium) production,it is importantto notice that the predicted correlationis,inall themodelstoﬁrst order,theresultof a (N_ch-dependent) reduction of the charged-particle multiplicity.

Well known is the color string reconnection mechanism implemented inPYTHIA,butinitial-stateeffectsasinCGCmodelslead, withverydifferentphysics,similarlytoareductioninparticlemul- tiplicity.

InthisLetter,themeasurementsoftheinclusiveJ/ψ yieldasa functionofcharged-particlepseudorapiditydensityinppcollisions at √

s=^{13 TeV are} ^presented. ^The measurements are performed inthedielectronchannelatmidrapiditywiththeALICEdetectorat the LHC. The pT-integrated anddifferential results are presented forminimum biasevents aswell asforevents triggeredon high multiplicity,whichextendthemultiplicityrangeupto7timesthe average multiplicity, and on the electromagnetic calorimetersig- nals,whichallowtoaccesspTvaluesupto15-40 GeV/c.Section2 outlines the experimental setup and the data sample; Section 3 describestheanalysis,whileSection4presentstheresults;abrief summaryandoutlookaregiveninSection5.

2. Experimentanddatasample

ThereconstructionofJ/ψ inthee⁺e⁻ decaychannelatmidra- pidity is performed using the ALICE central barrel detectors, described in detail in Refs. [20,21]. The setup is located in a solenoidal magnet providing a ﬁeld of 0.5 T oriented along the beamdirection.

For this analysis, a minimum bias (MB) trigger, a high multiplicity (HM) trigger, and two triggers based on the deposited energyinthecombinedElectromagnetic Calorimeter(EMCal)and the Di-jetCalorimeter (DCal) [22–24] are employed.Both theMB andHMtriggers areprovidedby theV0detector,thatconsistsof two forward scintillator arrays [25] covering the pseudorapidity ranges −³.7<

η

<−¹.7 and 2.8<

η

<5.1. The MB trigger signal consists of a coincident signal in both arrays, while the HM triggerrequiresasignalamplitudeintheV0arraysaboveathresh- oldwhichcorrespondstothe0.1%highestmultiplicityevents.The EMCal andDCalare located back-to-back in azimuthandform a two-arm electromagnetic calorimeter. While the EMCal detector covers |

η

|<0.7 overan azimuthal angle of80^◦<

ϕ

<187^◦, the DCalcovers0.22<|

η

_|<0.7 for260^◦<

ϕ

<320^◦ and|

η

_|<0.7 for 320^◦<

ϕ

<327^◦.Asaconsequenceofidenticalconstruction,both have identical granularity andintrinsic energyresolution. In this paper,EMCalandDCalwillbe referredto togetherasEMCal.The EMCaltriggerconsistsofthesumofenergyinaslidingwindowof 4×^{4 towers}âboveâ^given^threshold^(a^towerîs^the^smallest^seg- mentation ofthe EMCal).Inthisdataset,the triggerrequiresthe presenceofaclusterwithaminimumenergyof9GeV(EG1)or4 GeV(EG2)incoincidencewiththeMBtriggercondition.

Tracksare reconstructed inthepseudorapidity range|

η

_|<0.9 using the Inner TrackingSystem (ITS) [26], which consists ofsix layers of silicon detectors around the beam pipe, and the Time Projection Chamber (TPC) [27], a large cylindrical gas detector

providing tracking and particle identification via specific ioniza- tion energyloss dE/dx. The first two layers of the ITS (covering

|

η

_|<2.0 and|

η

_|<1.4), theSiliconPixelDetector (SPD),areused forthe charged-particle multiplicity measurement at midrapidity bycountingtracklets, reconstructedfrompairsofhitsin thetwo SPDlayerspointingtothecollisionvertex.

The results presented in this Letter are obtained using data recordedbyALICEduringtheLHCRun 2datatakingperiodforpp collisionsat√

s=^{13 TeV.}^The ^numberôf^selected êventsând^the correspondingintegratedluminosities [28] arelistedinTable1for thedifferent triggersused in thisanalysis. Forthe analyzeddata set, the maximum interaction rate was 260 kHz, and the maxi- mumpileupprobabilitywasabout5×¹⁰⁻³^.

3. Analysis

InthisworktheinclusiveproductionofJ/ψ mesonsisstudied asafunctionofthepseudorapiditydensityofchargedparticlesat midrapidity, dN_ch/d

η

.The J/ψ yield ina givenmultiplicity interval andin a given rapidity (y) range dN_J/_ψ/dy is normalized to theJ/ψ yieldinthe INEL>0eventclass,^dNJ/ψ/dy^.^The ^INEL>0 eventclasscontains all eventswithatleast1chargedparticlein

|

η

|<1.In thisratio,mostofthe systematicuncertainties related totrackingandparticleidentiﬁcationcancel.

3.1. Eventselection

Alleventsselectedinthisanalysisarerequiredtohavearecon- structed collision vertex within the longitudinal interval |^zvtx|<

10 cm inorderto ensureuniform detectorperformance andone SPDtracklet in |

η

_|<1. Beam-gas events are rejectedusing tim- ing cuts with the V0 detector. Pileup events are rejected using a vertex ﬁnding algorithm based on SPD tracklets [21], allowing the removal of events with 2 vertices. Because of the relatively smallin-bunchpileup probability andthefurther eventselection performedintheanalysis,thefractionofremainingpileupisneg- ligibleintheminimumbiaseventssampleandatmost2%inthe highmultiplicitytriggeredsample.

Events are binned in multiplicity classes based on either the SPD or the V0 detector signals, as shown in Fig. 1. Events cor- respondingto the onsetofthe V0 HMtrigger are excluded;that onsetisrathersharp.Thesmearingseeninthedistributioninthe rightpanel of Fig.1 isdue tothe different thresholdsused dur- ingoperation. Toillustratethis, theV0-amplitude distributionfor asingledatatakingperiodisincludedinFig.1(rightpanel,open squares).

For the measurement of the charged-particle pseudorapidity density dN_ch/d

η

at midrapidity, |

η

|<1, the SPD tracklets are used [29]. Giventhe close proximity of the SPD detector to the interactionpoint(thetwolayersareatradialdistancesof3.9and 7.6cm), its geometrical acceptance changes by up to 50% in the z_vtx interval selected for analysis. In addition, the meannumber ofSPD trackletsalso varied during the3-year Run2 datataking period dueto changes in the number of active SPD detector el- ements. In order to compensate forthese detectoreffects, a zvtx andtime-dependentcorrectionfactorisappliedsuchthatthemea- suredaverage multiplicity is equalized to a referencevalue. This

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Fig. 1.DistributionofthecorrectedSPDtrackletsN^corr_trk (left)andV0amplitude(right)fortheMBeventsaswellastheHM- andEMCal-triggeredeventsusedintheanalysis.

Theverticallinesindicatetheusedmultiplicity intervals(seeTable2;theﬁrstbinspansfrom0tothepositionoftheﬁrstline).FortheHM-triggeredevents,theV0 amplitudedistributionforasingledatatakingperiodisincludedforillustration(opensquares).

reference was chosen to be the largest mean SPD tracklet mul- tiplicityobserved overtime andzvtx.Thisprocedure issimilar to whatwasdonepreviouslyinRef. [5].Thecorrectionfactorforeach eventisrandomlysmearedusingaPoissondistributiontotakeinto accountevent-by-eventﬂuctuations.Inthecaseoftheeventselec- tion basedontheforwardmultiplicity measurement withthe V0 detector,thesignalamplitudesareequalizedtocompensateforde- tectoraging andforthesmallacceptancevariationwiththeevent vertexposition.

The overall ineﬃciency,the productionof secondary particles duetointeractionswiththedetectormaterial andparticledecays lead to a difference betweenthe number ofreconstructed tracklets and the true primary charged-particle multiplicity N_ch (see details in Ref. [29]).Usingevents simulatedwiththe PYTHIA8.2 event generator [30] (Monash 2013 tune, Ref. [31]), the correlation between the tracklet multiplicity (after the zvtx-correction), N^corr_trk , and the generated primary charged particles Nch is determined. The propagationof the simulated particles is done by GEANT 3 [32] with a full simulation of the detector response, followed by the same reconstruction procedure as for real data.

The correction factor β(N_trk^corr)=^Nch/N^corr_trk to obtain the average dN_ch/d

η

value corresponding to a given N^corr_trk bin is computed from the N_trk^corr–Nch correlation, shown in Fig. 2 for events simulated withPYTHIA8.2 andparticle transport through GEANT 3.

As thegeneratedcharged-particlemultiplicity inMonteCarlodif- fers from data, a corrected N_ch distribution is constructed from themeasured N^corr_trk distributionusingBayesianunfolding.Fromit, thecorrectedβ factorsareobtained.AMonteCarloclosuretestin PYTHIA 8.2withunfolding basedon EPOS-LHC eventsis used to validatetheprocedure.

Thenormalizedcharged-particlepseudorapiditydensityineach eventclassiscalculatedas:

dN_ch

/

d

η

^dNch

/

d

η

INEL>0

= β ×

^N^corr_trk

η ×

^dNch

/

d

η

INEL>0

,

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where ^N_trk^corr îs ^the âveraged ^value ôf ^N^corr_trk ⁱⁿ êach ^multiplicity class,corrected for thetrigger andvertex finding efficiencies.

The former is estimated from Monte Carlo simulations and the latter with a data driven approach. They are below unity only for the low-multiplicity events. The value corresponding to INEL

> 0 events, ^dNch/d

η

INEL>0, was cross-checked with the pub- lished ALICEmeasurement [29], andis found tobe in very good agreement. A similar procedure is also used for the event selection based on the V0 amplitude, measured as a sum of signals fromchargedparticlesinthe intervals−³.7<

η

<−¹.7 and

Fig. 2.Correlationbetweenthenumberofgeneratedprimarychargedparticles,Nch, andthenumberofreconstructedSPDtracklets,N^corr_trk,in|η|<1,fromPYTHIA8.2 simulatedcollisionswithdetectortransportthroughGEANT 3.Theblackpointsrep- resentthemeanvaluesofNch.

Table 2

Averagenormalized charged-particle pseudorapidity density in |η|<1 for each eventclassselectedinN^corr_trk measuredinSPD(|η|<1;leftpart)andinV0am- plitude(−3.7<η<−1.7 and2.8<η<5.1;rightpart).Thevaluescorrespondto thedatasampleusedforthepT-integratedanalysis.Onlysystematicuncertainties areshownsincethestatisticalonesarenegligible.Thecorrespondingfractionofthe INEL>0crosssectionforeacheventclassisalsoindicated.

SPD selection V0 selection

dN_ch/dη

dN_ch/dηINEL>0 σ/σINEL>0 dN_ch/dη

dN_ch/dηINEL>0 σ/σINEL>0

0.23±⁰.01 32% 0.40±⁰.01 37%

0.60±⁰.01 25% 0.76±⁰.01 26%

1.23±⁰.02 25% 1.41±⁰.02 25%

2.11±0.03 11% 2.26±0.03 9.0%

2.98±0.05 4.7% 3.03±0.04 2.5%

3.78±0.06 1.8% 3.92±0.06 0.5%

4.58±⁰.08 0.6% 4.33±⁰.07 0.08%

5.37±⁰.09 0.2% 4.96±⁰.08 0.01%

6.17±⁰.11 0.05%

7.13±⁰.12 0.02%

2.8<

η

<5.1.The resultingvaluesofthe normalizedmultiplicity fortheeventclassesconsideredintheanalysisaresummarized in Table 2 alongsidethe respective fractions of the INEL > 0 cross section.

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Fig. 3.Top:Invariantmassdistributionofelectron-positronpairsforMB(left),HM(middle)andEMCal(right)triggers,togetherwithcombinatorialbackgroundestimation fromthetrack-rotationmethod(bluelinesintheleftandmiddlepanels)andthefullbackgroundestimation(blacksquares).Inthelowerpanels,theJ/ψ signalobtained afterbackgroundsubtractionisshowntogetherwiththeJ/ψsignalshapefromMonteCarlosimulations.Theentriescontainacorrectionfortherelativeeﬃciency(seetext).

Theverticallinesindicatethemassrangeforthesignalcounting.

3.2. J/ψsignalextraction

The J/ψ meson is measured in the dielectron decay channel at midrapidity. Electrons and positrons are reconstructed in the centralbarreldetectorsbyrequiringaminimumof70outofmax- imally 159trackpointsintheTPCandavalueofthetrackﬁt

χ

²

over thenumber oftrackpoints smallerthan 4[27].Only tracks with atleast two associated hitsin the ITS, andone of them in the twoinnermostlayers, areaccepted.Thisrequirementensures bothagoodtrackingresolutionandtherejectionofelectronsand positronsproducedfromphotonsconvertinginthedetectormate- rial.IntheMBandHMtriggeranalysis,afurthervetoonthetracks belonging to identiﬁed photon conversion topologies is applied.

Theelectronidentificationisachievedbythemeasurementofthe specific energyloss ofthe trackin theTPC, which isrequired to be compatiblewiththat expectedforelectrons within3standard deviations.Trackswithaspecificenergylossbeingconsistentwith that of thepion orproton hypothesis within 3.5standard deviations arerejected. Fortheanalysisofthe EMCal-triggeredevents, the energy deposition of the track in the TPC is required to be in arange between−^2.25^to+³^standard ^deviations âround ^the mean expected value for the electrons. In addition, at least one of the J/ψ decay electrons is required to be matched to a clus- terintheEMCal,withaclusterenergyabovethetriggerthreshold andan energy-to-momentum ratiointhe range0.8<E/p<1.3.

Electrons and positrons are selected in the pseudorapidity range

|

η

|<0.9 andinthetransversemomentumrangep_T>1 GeV/c.

The numberof reconstructedJ/ψ isobtained fromtheinvari- ant mass distribution of all the opposite-sign (OS) pairs, which contains e⁺e⁻pairsfromJ/ψ decaysaswellascombinatoricsand other sources. In the MB andHM trigger analysis, the combina- torialbackgroundisestimatedusingatrackrotationprocedurein which one of thetracks is rotatedby a randomazimuthal angle multiple times to obtain a high statistics invariant mass distribution. Thisdistributionis then normalizedsuch thatits integral over arangeoftheinvariant masswell abovetheJ/ψ masspeak matchestheoneofrealOSpairs,andissubtractedfromthelatter distribution.Theremainingresidualbackground,whichcanbeat- tributedtophysicalsources,e.g.correlatedsemileptonicdecaysof heavy-quark pairs, is estimated using a second-order polynomial

function. For the analysis of the EMCal-triggered events, a ﬁt to theOSinvariantmassdistributionisperformedusingaMCshape forthesignal addedto apolynomial todescribe thebackground.

Asecond- or third-order polynomial function is used, depending onthe p_T range.ThenumberofJ/ψ isextractedbysummingthe dielectronyield inthebackground-subtracted invariant massdis- tribution in the mass interval 2.92<mee<3.16 GeV/c², which contains approximately 2/3 of the total reconstructed yield. The yieldfallingoutsideofthecountingwindowatlowinvariantmass isduetotheelectronbremsstrahlunginthedetectormaterialand totheradiativeJ/ψ decay,andiscorrectedforusingMonteCarlo simulations. Also, a correction forthe yield loss due to the lim- ited triggerandvertexﬁnding eﬃciencies atlow multiplicitiesis applied.

Duetothetriggerenhancement,theyields obtainedusingthe EMCal-triggeredeventswerecorrectedbythetriggerscalingfactor, whichisobservedtobeidenticalforalleventclasses.Thiscorrec- tionis necessaryto converttheyield per EMCal-triggered events intoayieldperMB-triggeredeventandisaccomplishedbyadata- drivenmethodusingtheratiooftheclusterenergydistributionin triggereddata dividedby thecluster energydistribution inmini- mumbiasdata.Theratioflattensabove thetriggerthresholdand thescalingfactoristhenobtainedby fittingaconstanttotheflat interval.

InthetoppanelsofFig.3areshowntheOSinvariantmassdis- tributionforMBevents(left),ahighmultiplicityintervalfromthe HM- (middle) and EMCal-triggered events (right), together with the estimated background distribution. The combinatorial background distribution from the track rotation method is shown in the left and middle panels with the blue lines, while the total backgroundis shownasblack squaresin all thepanels. The sig- nalobtainedafterbackgroundsubtractionisdescribedwellbythe signalshapeobtainedfromMonteCarlosimulations(discussedbe- low); these MC templates havebeen scaled and overlaid on the datapointsinthebottompanelsofFig.3.

The J/ψ measurement is performed integrated in transverse momentum and in the pT intervals 0<pT<4 GeV/c and 4<

pT<8 GeV/c, using the MB and HM triggers. At higher pT, the J/ψ mesons are reconstructed using the EMCal triggered events in the transverse momentum intervals 8<pT<15 GeV/c and

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15<pT<40 GeV/c.It was checkedthat theacceptance and ef- ﬁciency for J/ψ reconstruction are not dependent on the event multiplicity.Thiswasperformedusingppcollisionssimulatedwith the PYTHIA 8.2event generator withan injected J/ψ signal. The dielectrondecayissimulatedwiththeEvtGenpackage [33] using PHOTOS [34] todescribetheﬁnal-stateradiation.TheJ/ψ mesons are assumed tobe unpolarized consistentwith measurements in ppcollisionsattheLHC [35].

Toaccountforthemultiplicitydependenceofthe p_T spectrum oftheJ/ψ mesons,acorrection fortherelativeeﬃciency,namely the eﬃciency for a given pT value relative to the pT-integrated value, is applied toeach dielectronpair. Thisis containedin the invariantmassdistributionsshowninFig.3.

3.3. Systematicuncertainties

Normalizedmultiplicity:The systematic uncertaintyon the nor- malizedmultiplicitycontainscontributionsfromthetrigger,vertex finding, andSPDefficiencies.The firsttwo contributionsare estimated using alternative approaches:the trigger efficiencyis cal- culated inadata-drivenway,andforthevertexfindingefficiency Monte Carlo simulations are used. The differences to the values obtainedwiththedefaultmethodsaretakenasthesystematicun- certainties. The contribution fromthe vertexfinding efficiency is below1% (relativeuncertainty) inall eventclasses,theone from thetriggerefficiencyreachesamaximumvalueof1.3%forthelowestmultiplicityclass.

In order toestimate uncertainties dueto the SPDtracklet re- constructioneﬃciency,thenumberofcorrectedtrackletsisscaled upanddownby3%,whichisthemaximumobserveddiscrepancy ofthe averagenumber ofSPDtrackletsbetweendata andMonte Carlosimulations.Thisuncertaintyamountsto3.6%inthelowest multiplicity class, and to less than 1.5% in all other classes.The uncertainty fromthe unfolding of the charged-particle multiplicity distribution is estimatedby varying the numberof iterations usedintheBayesianunfolding,aswellasbyusingan alternative unfolding method [36]. Theuncertainty isfound tobe negligible.

All theaforementioned uncertainty sources are addedin quadrature, leadingtoatotal uncertaintyonthenormalizedmultiplicity of3.7%forthelowestmultiplicityclass,andtolessthan2%forall otherclasses.

NormalizedJ/ψyield:Thesystematicuncertaintiesofthenormal- izedJ/ψ yieldareduetothesignalextraction,bin-flowcausedby thePoissoniansmearingappliedforthe zvtx-dependentcorrection of the SPD acceptance and vertex finding, trigger and SPD efficiencies. For the analysis of the EMCal-triggered events, there is an additionalcomponentduetothe matchingoftracksto EMCal clustersandtheelectron identificationvia the E/p measurement, which hasa non-negligible multiplicity dependence.The E/p interval andthevalue of E used toselectonlyelectrons above the EMCaltriggerthresholdarevariedtodeterminethesystematicun- certainty oftheelectronidentificationwiththeEMCal,leading to valuesfrom1%to12%,dependingonthemultiplicitybin.

The uncertainty ofthe J/ψ signal extraction isdetermined by varyingthefunctionsusedtofitthebackground(first- orsecond- degreepolynomialsorexponential)andthefittingranges,withthe RMSofthe distributionofnormalizedyieldsobtainedfromthese variationsbeingtakenasasystematicuncertainty(thenormalized yield corresponds to thedefault selection). The bin-floweffect is estimatedfromthe RMSofthe resultsobtainedby repeating the analysis severaltimes withdifferent seeds forthe random num- bergenerator.Theuncertaintiesfromthesignalextractionandthe bin-floweffectarethedominantones.Theyareofcomparablesize, withvaluesbetween1%and8%dependingonthemultiplicityand pT interval. The uncertainties of the vertex finding, trigger and

Fig. 4.NormalizedinclusivepT-integratedJ/ψ yieldatmidrapidityas afunction ofnormalizedcharged-particlepseudorapiditydensityatmidrapidity(|η|<1)with theeventselectionbasedonSPDtrackletsatmidrapidityandonV0amplitudeat forwardrapidityinppcollisionsat√

s=^{13 TeV.}^Top:^normalized^J/ψyield(diag- onaldrawnfor reference).Bottom:doubleratioofthenormalizedJ/ψ yieldand multiplicity.Theerrorbarsshowstatisticaluncertaintiesandtheboxessystematic uncertainties.

SPD tracklet efficiencies affect the estimated number of INEL>0 collisions,andhence theevent-averagedminimumbias J/ψ yield ^dNJ/ψ/dy^,âs^wellâs^the^J/ψ yieldinthelowmultiplicityclasses.

TheuncertaintiesofthevertexfindingandSPDefficienciesarebe- low 1% in mostclasses,while the uncertaintydue tothe trigger efficiencyreachesupto4%,dependingonthemultiplicityclass.

All the mentioned sources are added in quadrature to obtain the totalsystematic uncertainty, which,for the pT-integratedre- sults, varies between 3% and 7% with the multiplicity class. For theselected pT intervals,the uncertaintiesare larger, varyingbe- tween 3% and10% withmultiplicity and p_T interval, mainly due tothesignalextraction,whichisaffectedbystatisticalﬂuctuations ofthe background.The results athigh pT, employing the EMCal, haveuncertainties upto13%,whicharelargerbecauseofthead- ditionalselection requirementsonthe track-clustermatching and theEMCalelectronidentiﬁcationselections.

4. Resultsanddiscussion

The top panel of Fig. 4 shows the normalized J/ψ yield as a functionofthenormalizedcharged-particlepseudorapiditydensity atmidrapidity,dNch/d

η

/^dNch/d

η

.Thedashedlinealsoshownin theﬁgureisalinearfunctionwiththeslopeofunity.

These results include both the MB and HM triggered events, whichallowfora coverageofupto7timestheaveragecharged- particlemultiplicity,wheneventsareselectedbasedon themea- suredmidrapidity multiplicity.Thisisasigniﬁcantextension with respecttoourprevious resultsinpp collisionsat√

s=^{7 TeV [5],} where only the range up to 4 was covered and with larger uncertainties. Using the event selection based on the V0 forward multiplicity (green squares), whichshould largely remove a pos- sibleauto-correlationbias,themeasurementextendsonlyupto5 timesthe^dNch/d

η

^.^The^results^for^the^two^event^selection^meth- ods are in very good agreement. In both cases, the normalized

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Fig. 5.NormalizedinclusiveJ/ψyieldatmidrapidityasafunctionofnormalizedcharged-particlemultiplicity inppcollisionsat√

s=13 TeV,fordifferentrangesofpTof theJ/ψ meson.Left:eventselectionbasedonmultiplicityatmidrapidity.Right:eventselectionbasedonmultiplicityatforwardrapidity.Theerrorbarsshowstatistical uncertaintiesandtheboxessystematicuncertainties.

J/ψ yield grows signiﬁcantly fasterthan linearwith the normalizedmultiplicity.

IncludedinFig.4isalsothedoubleratioofthenormalizedJ/ψ yield tothe normalizedmultiplicity (bottompanel).Tworegimes could be identiﬁed, with a stronger increase of the double ra- tio for events with small multiplicity and a weaker increase for high-multiplicityevents.Itisnotedthat the“energycost”forthe production of a J/ψ meson, characterized by a transverse mass mT=

m²_J_/ψ+p²_T/c²5 GeV/c²,issimilartotheoneforparticle productionperunitrapidityoftheunderlyingMBevent,estimated as^dNch/d

η

_·pT^.^A^linear^(diagonal)correlationwithmultiplic- ity is then expected to ﬁrst order and observed in PYTHIA 8.2 simulations[18].AsseeninFig.4,thedataexhibitricherfeatures thanthisbaselineexpectation.

Thedatainintervalsofp_ToftheJ/ψ mesonareshowninFig.5.

ThedataexhibitasigniﬁcantincreaseofthenormalizedJ/ψ yield withthenormalizedmultiplicitybetweentheJ/ψ pTintervals0–4 and4–8GeV/c.Thiseffectcouldbeattributedtovariouscontribu- tions [18],likeassociatedJ/ψ productionwithotherhadronsinjet fragmentationorfrombeauty-quarkfragmentation,asthefraction ofJ/ψ fromb-hadrondecaysincreaseswithp_T [37].

Measurements of the correlation with the event multiplicity for inclusive charged-particle production have identiﬁed similar trends [11] asfortheJ/ψ p_Tdependence.Thestrengthofthiscor- relationissimilarforJ/ψ andforinclusivechargedparticles(dom- inatedby pions)for pT valuesgivingacomparable mT value. The production ofstrange hyperonsatmidrapidity was also observed to exhibit a correlation with event multiplicity in proportion to theirmass [38];astrongcorrelationwas alsomeasuredfortheϒ mesons [7].

The theoretical models currently available attribute the observed behavior todifferent underlying processes.In the PYTHIA 8.2eventgenerator [17],multipartoninteractions(MPI)areanim- portantfactorincharm-quarkproduction.Indeed,fromMPIsalone astrongerthanlinearscalingisexpectedforopen-charmproduc- tion, as was demonstrated in Ref. [6] with PYTHIA8.157. Taking into account all sources of heavy-quark production, however, a

closeto linear increase is predicted [18]. PYTHIA8.2 reproduces well theobservationin datawitha very similar correlation with multiplicityforthetwodifferentrapidityintervalsusedformulti- plicitymeasurement,asseen intheleft panel ofFig. 6,although theoverall slopeof thetrendis underestimated.Toillustrate the effectofnon-promptJ/ψ intheinclusiveproduction,inFig.6the caseofpromptJ/ψ mesonproductionaspredictedbyPYTHIA8.2 isshowninaddition. Asigniﬁcant reduction ofthecorrelation is observed,whichappearstobestrongerfortheSPDeventselection case.

IntheEPOS3eventgenerator [15,39],initialconditionsaregen- eratedaccordingtotheparton-basedGribov-Reggeformalism [40].

Sources of particle productionin this framework are partonlad- ders, each composed of a pQCD hard process with initial- and ﬁnal-state radiation. This model already predicted the stronger than linear increase with multiplicity observed for open-charm mesons [6], originating from a collective (hydrodynamical) evo- lution of the system. The predictions from EPOS3, here without thehydrodynamic component, are similar in magnitudeto those fromPYTHIA8.In thepercolationmodel [14],spatially extended colorstringsarethesources ofparticleproductioninhigh-energy hadronic collisions. In a high-density environment they overlap;

such a decrease in the effective number of strings leads to a reduction in particle production. Since the transverse size of a string is determined by its transverse mass, lighter particles are affected in a stronger way than heavier ones. This results in a linearincrease ofheavy-particle productionat low multiplicities, gradually changing to a quadratic one athigh multiplicities. The coherent particle production (CPP) model [13,41] employs phe- nomenologicalparametrizationsforlight hadronsandJ/ψ derived fromp–Pb collisions, andpredicts a strongerthan linear relative increase of J/ψ production with the normalized eventmultiplicity. In the Color Glass Condensate (CGC) approach, the NRQCD framework is employed for J/ψ production. This effective ﬁeld theory predicts, both for J/ψ and D mesons, a relative increase with the normalized multiplicity that is faster than linear, both for pp and p–Pb collisions [16]. In a CGC saturation model, a

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Fig. 6.Left:ComparisonofdataandPYTHIA8.2predictionsforthetwomethodsofeventselection.ForPYTHIA8.2,thecaseofpromptJ/ψmesonproductionisincluded forillustration.Right:comparisonofdata(withSPDeventselection)withmodelpredictionsfromthecoherentparticleproductionmodel[13],thepercolationmodel[14], theEPOS3eventgenerator[15],theCGCmodel[16],the3-PomeronCGCmodel[19],andPYTHIA8.2predictions.Exceptforthelatter,noneofthemodelsincludethe non-promptcomponent.

Fig. 7.NormalizedinclusiveJ/ψ yieldatmidrapidityasafunctionofnormalizedcharged-particlepseudorapiditydensityatmidrapidityfordifferentpTintervals;thedata arecomparedtotheoreticalmodelpredictionsfromPYTHIA8.2.

faster thanlinear trendgenerically arisesfromthe Bjorken-xde- pendent saturation scale which would suppress more the soft- particlemultiplicity,produced atlow-x,compared toJ/ψ production which is sensitive to larger values of x. In the 3-Pomeron fusion model[19],the correlationarisesasJ/ψ productionvia 3- gluon fusion processes from various Pomeron configurations are considered. The larger configurationspace forthe particularcase of the overlapping rapidity interval for J/ψ and charged particles leads to a significantly stronger correlation. Gluon saturation is implemented in this model; its effect, interestingly a re- duced correlation, becomes significant for normalized multiplici- tiesabove 7.

All models predict an increase which is faster than linear, as shownintherightpanelofFig.6.Inall modelsthisiseffectively the resultofa (N_ch-dependent) reductionof thecharged-particle multiplicity,realizedthroughratherdifferentphysics mechanisms in the various approaches (color string reconnection or percola- tion,gluonsaturation,coherentparticleproduction,3-gluonfusion

in gluon ladders/Pomerons). The PYTHIA 8.2 and EPOS3 models underpredictthe data,whilethe percolationmodelslightlyover- predictsthemathighmultiplicity;goodagreementisseenforthe CGC,the coherentparticle production,and the 3-Pomeron models.

Theseobservationsneedtobeconsidered havinginmindthat inall models exceptPYTHIA8.2only the promptJ/ψ production isincluded.AsillustratedinFig.6forPYTHIA8.2,thepromptJ/ψ mesonproductionexhibitsaweaker relativeincrease withmulti- plicitycompared totheinclusiveproduction.The agreementwith data will improvein case of EPOS3 and will degrade for all the other models, ina consistent comparison. Thatcould be realized eitheroncethedataforthepromptcomponentwillbecomeavail- able oras soon asthe non-prompt component will be added to thecurrentmodelpredictions.

Thecontributionfromdecaysofbeautyhadronsincreasessig- niﬁcantly with pT [37] and might also have a different depen- dency on multiplicity; the existing measurement of charm and

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beautyproduction [6] isnotpreciseenoughtobeconclusive,buta studyinPYTHIA8.2 [18] showedthat thefeed-downfrombeauty hadronsinﬂuencestheresult.Thetrendofstrongerincreaseinthe p_T intervalsabove4GeV/c seeninthedataisqualitativelyrepro- ducedbyPYTHIA8.2,which,however,underestimatesthedatafor pT<8 GeV/c,asshowninFig.7.

5. Summaryandconclusions

Wehavepresentedacomprehensivemeasurementofinclusive production ofJ/ψ mesons asa function ofthe eventmultiplicity in pp collisions at √

s=13 TeV performed withthe ALICEappa- ratus. The J/ψ production at midrapidity is studied using a data sample including minimum bias, high event activity, and EMCal triggered events. The event selection is performedbased on the charged-particle measurement atmidrapidity andin the forward region. The J/ψ yield in a given multiplicity interval normalized to the J/ψ yield in INEL > 0 collisions is presented as a function ofthecharged-particle multiplicitysimilarly normalized.The advantageofsucharepresentationisthatmostoftheexperimen- tal systematic uncertainties cancel; also, some of the theoretical modeluncertaintiesaremitigatedforsuchnormalizedyields.

AstrongerthanlinearincreaseoftherelativeproductionofJ/ψ asa function ofmultiplicity is observed for p_T-integratedyields;

this increase is stronger for high-pT J/ψ mesons. The trends are qualitatively, and for some of the models quantitatively, repro- duced by theoretical models, buta critical appraisal of the sim- ilarity or difference between the physics mechanisms at play in variousmodelsisyettobeperformed.Morestringenttestsofthe modelsare neededtoo.Disentanglingthefeed-downfrombeauty hadrons, not included in mostof the current theoretical predictions, will be an important step towards shedding light on the mechanismofhadronizationofcharm(andbeauty)quarks,inpar- ticularintheenvironmentofahighdensityofcolorstringscreated inhigh-multiplicity pp collisions.Data which willbe collected in Run3attheLHCwillbeasigniﬁcantadditionforsuchstudies.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompetingﬁnan- cialinterestsorpersonalrelationshipsthatcouldhaveappearedto inﬂuencetheworkreportedinthispaper.

Acknowledgements

We aregratefulto E.Ferreiro,B. Kopeliovich,E.Levin, M.Sid- dikov,R.Venugopalan,K.Watanabe,andK.Wernerforsendingus thepredictionsofandclariﬁcationsabouttheirmodels.

The ALICE Collaboration would like to thank all its engineers andtechniciansfortheirinvaluablecontributionstotheconstruc- tion of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collab- oration gratefully acknowledges the resources and support pro- videdbyallGridcentresandtheWorldwideLHCComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the following fundingagenciesfortheir supportinbuildingandrun- ningthe ALICEdetector:A.I. AlikhanyanNationalScience Labora- tory(YerevanPhysicsInstitute)Foundation (ANSL),State Commit- teeofScienceandWorldFederationofScientists(WFS),Armenia;

Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung,Austria;MinistryofCommunicationsandHighTech- nologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de DesenvolvimentoCientíﬁco e Tecnológico (CNPq), Fi- nanciadora de Estudose Projetos(Finep), Fundação de Amparoà

Pesquisa doEstado de São Paulo (FAPESP)andUniversidade Fed- eraldoRioGrandedoSul(UFRGS),Brazil;MinistryofEducationof China (MOEC),MinistryofScience & Technologyof China(MSTC) andNational NaturalScience Foundation ofChina (NSFC),China;

Ministry of Science and Education and Croatian Science Foun- dation, Croatia; Centro de Aplicaciones Tecnológicas yDesarrollo Nuclear (CEADEN),Cubaenergía,Cuba;The Ministryof Education, Youth and Sports of the Czech Republic, Czech Republic; Dan- ishCouncilforIndependentResearchNaturalSciences,theVillum Fonden and Danish National Research Foundation (DNRF), Den- mark;Helsinki InstituteofPhysics (HIP),Finland; Commissariatà l’Énergie Atomique (CEA) and Institut National de Physique Nu- cléaire etdePhysique desParticules (IN2P3)andCentre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum fürSchwerionenforschungGmbH,Germany;GeneralSecretariatfor ResearchandTechnology,MinistryofEducation,ResearchandRe- ligions,Greece;NationalResearchDevelopmentandInnovationOf- fice,Hungary;DepartmentofAtomicEnergy,GovernmentofIndia (DAE),DepartmentofScienceandTechnology,GovernmentofIndia (DST),University Grants Commission, Governmentof India(UGC) andCouncil ofScientificandIndustrial Research(CSIR),India;In- donesian Institute of Science, Indonesia; Centro Fermi - Museo StoricodellaFisicaeCentroStudieRicercheEnricoFermiandIsti- tutoNazionalediFisicaNucleare(INFN),Italy;InstituteforInnova- tiveScienceandTechnology,NagasakiInstitute ofAppliedScience (IIST),JapaneseMinistryofEducation,Culture,Sports,Scienceand Technology(MEXT)andJapanSocietyforthePromotionofScience (JSPS)KAKENHI, Japan;ConsejoNacionalde Ciencia(CONACYT) y Tecnología, through Fondode Cooperación Internacional enCien- ciayTecnología(FONCICYT)andDirecciónGeneraldeAsuntosdel PersonalAcademico(DGAPA,UNAM),Mexico;NederlandseOrgan- isatievoor WetenschappelijkOnderzoek(NWO),Netherlands; The ResearchCouncilofNorway, Norway;CommissiononScience and TechnologyforSustainableDevelopmentintheSouth(COMSATS), Pakistan;PontificiaUniversidadCatólicadelPerú,Peru;Ministryof Science andHigher Education,National Science Centre and WUT ID-UB,Poland;KoreaInstituteofScienceandTechnologyInforma- tion and National Research Foundation of Korea (NRF), Republic of Korea;Ministry of Education and Scientific Research, Institute of Atomic Physics and Ministry of Research and Innovation and InstituteofAtomicPhysics,Romania;JointInstituteforNuclearRe- search (JINR), Ministry of Education and Science of the Russian Federation, National Research Center “Kurchatov Institute”, Rus- sianScienceFoundationandRussianFoundationforBasicResearch, Russia;Ministry ofEducation, Science,Research andSportofthe Slovak Republic, Slovakia; National ResearchFoundation ofSouth Africa,SouthAfrica;SwedishResearchCouncil(VR)andKnut&Al- iceWallenbergFoundation(KAW),Sweden;EuropeanOrganization forNuclearResearch,Switzerland;SuranareeUniversityofTechnol- ogy(SUT), NationalScience andTechnology DevelopmentAgency (NSDTA) and Office of the Higher Education Commission under NRUprojectofThailand,Thailand;Turkish AtomicEnergyAgency (TAEK),Turkey;NationalAcademyofSciencesofUkraine,Ukraine;

ScienceandTechnology FacilitiesCouncil (STFC),UnitedKingdom;

NationalScienceFoundationoftheUnitedStatesofAmerica(NSF) andUnitedStatesDepartmentofEnergy, OﬃceofNuclearPhysics (DOENP),UnitedStatesofAmerica.

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