Multiplicity dependence of light (anti-)nuclei production in p–Pb collisions at √sNN=5.02 TeV

.ALICE Collaboration

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

Articlehistory:

Received9July2019

Receivedinrevisedform10October2019 Accepted18October2019

Availableonline23October2019 Editor: L.Rolandi

The measurementofthe deuteronand anti-deuteronproductioninthe rapidityrange−¹<y<0 as afunction oftransverse momentum and event multiplicity inp–Pb collisions at√_s

NN = 5.02 TeV is presented. (Anti-)deuterons are identified via their specific energy lossdE/dx and via theirtime-of- flight. Their production in p–Pb collisions is compared to pp and Pb–Pb collisions and is discussed withinthe context ofthermal and coalescencemodels.The ratioofintegrated yields ofdeuteronsto protons(d/p)showsasignificantincreaseasafunctionofthecharged-particlemultiplicityoftheevent startingfromvaluessimilartothoseobservedinppcollisionsatlowmultiplicitiesandapproachingthose observedinPb–Pbcollisionsathighmultiplicities.Themeantransverseparticlemomentaareextracted from the deuteronspectra and the values are similar tothose obtained forp and particles.Thus, deuteronspectrado notfollow massordering.Thisbehaviourisincontrasttothetrendobserved for non-compositeparticlesinp–Pbcollisions.Inaddition,theproductionoftherare³He and³He nuclei hasbeenstudied.Thespectrumcorrespondingtoallnon-singlediffractivep-Pbcollisionsisobtainedin the rapiditywindow−¹<y<0 andthe pT-integrated yield dN/dyisextracted. Itis foundthat the yieldsofprotons,deuterons,and³He,normalisedbythespindegeneracy factor,followanexponential decreasewithmassnumber.

©^{2019PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

The energy densities reached in the collisions of ultra- relativistic particles lead to a significant production of complex (anti-)(hyper-)nuclei. The high yield of anti-quarks produced in thesereactions has led to the first observation ofthe anti-alpha particle [1] as well as of the anti-hyper-triton [2] by the STAR collaboration,andto detailedmeasurementsby theALICEcollab- oration[3–6] at energiesreachedatthe CERNLHC.However, the productionmechanismisnotfullyunderstood.In amoregeneral context, these measurements also provide input for the back- ground determination in searches for anti-nuclei in space. Such an observation of anti-deuterons or ³He of cosmic origin could carryinformationontheexistenceoflargeamountsofanti-matter inouruniverseorprovideasignature oftheannihilationofdark matterparticles [7–11].

Recentdatainppandinheavy-ioncollisionsprovideevidence foraninterestingobservationregardingtheproductionmechanism of(anti-)nuclei [3,5,6,12,13]: in Pb–Pb interactions, the d/p ratio doesnot vary with the collision centrality and the value agrees

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

withexpectationsfromthermal-statisticalmodelswhichfeaturea common chemical freeze-out temperature of all hadrons around 156 MeV [3,14,15]. In inelastic pp collisions, the corresponding ratio is a factor 2.2 lower than in Pb–Pb collisions [3,12]. With respecttothesemeasurements,theresultsofdand³Heproduced inp–Pb collisionsat√

s_NN =^{5.02 TeV,beingasysteminbetween} thetwoextremesofppandPb–Pbcollisions,areofprominentin- terestandtheyarethesubjectofthisletter.Whiledeuteronshave been measured differentially in multiplicity,the ³He (³He)spec- trum was only obtained inclusively for all non-single diffractive eventsbecauseoftheirlowproductionrate.

Inadditiontotheevolutionoftheintegratedd/pratioforvar- iousmultiplicityclasses,thequestion whetherthetransversemo- mentum distribution of deuterons is consistent with a collective radial expansion together with the non-composite hadrons is of particularinterest.Suchbehaviourhasbeenobservedforlightnu- clei inPb–Pb collisions [3,5]. Thepresence ofcollectiveeffects in p–Pb collisions at LHC energies has recently been supported by several experimental findings (see for instance [16–22] and re- cent reviews in [23,24]).These include a clear mass ordering of themeantransversemomenta oflightflavouredhadronsinp–Pb collisionsasexpectedfromhydrodynamicalmodels [18].

https://doi.org/10.1016/j.physletb.2019.135043

0370-2693/©^{2019PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

2. Analysis

The results presented here are based on a low pile-up p–Pb datasamplecollectedwiththeALICEdetectorduringtheLHCrun- ningcampaignat√

sNN=^{5.02 TeVin2013.Adetailed}description ofthedetectorisavailablein [25–29].Themaindetectorsusedin this analysis are the Inner Tracking System (ITS) [30], the Time Projection Chamber (TPC) [31], and the Time-Of-Flight detector (TOF) [32,33]. The two innermostlayers ofthe ITSconsist ofSil- iconPixelDetectors (SPD),followed bytwo layers ofSiliconDrift Detectors (SDD), andtwo layers of Silicon Strip Detectors (SSD).

As the maintracking device, the TPCprovides full azimuthal ac- ceptance fortracks in the pseudo-rapidity region |

η

lab|< 0.8. In addition,itprovidesparticleidentificationviathemeasurementof thespecific energy lossdE/dx. The TOFarray is located atabout 3.7m fromthe beamlineandprovides particle identificationby measuringtheparticlespeedwiththetime-of-flighttechnique.In p-Pbcollisions, theoveralltime resolutionisabout85 psforhigh multiplicity events. In peripheral events,where multiplicities are similar topp, itdecreases to about120 psdueto aworse start- time(collision-time)resolution [34].Alldetectorsarepositionedin asolenoidalmagneticfieldofB =^{0.5 T.}

Theeventsample usedfortheanalysispresentedinthisletter wascollectedexclusivelyinthebeamconfigurationwherethepro- tontravelstowardsnegative

η

lab.Theminimum-biastriggersignal andthe definitionofthemultiplicity classeswas providedbythe V0 detector consisting of two arrays of 32 scintillator tiles each covering the full azimuthwithin 2.8<

η

lab<5.1 (V0A, Pb-beam direction) and −³.7<

η

lab<−¹.7 (V0C, p-beam direction). The eventselectionwas performedina similarwaytothat described in Ref. [18]. A coincidence of signals in both V0A and V0C was requiredonlineinordertoremovebackgroundfromsinglediffrac- tive and electromagnetic events. In the offline analysis, further backgroundsuppressionwasachievedbyrequiringthatthearrival time ofthe signals inthe two neutronZero DegreeCalorimeters (ZDC), which are located ±^{112.5 m from the} interaction point, is compatible with a nominal p–Pb collision. The contamination frompile-up events was reducedto a negligible level (<1%) by rejecting eventsin which morethan one primary vertexwas re- constructedeitherfromSPDtrackletsorfromtracksreconstructed inthewholecentralbarrel.Thepositionofthereconstructedpri- mary vertex was required to be located within ±^{10 cm of the} nominalinteractionpointinthelongitudinaldirection.Intotal,an eventsample ofabout100million minimum-bias(MB)eventsaf- terallselectionswasanalysed.Thecorrespondingintegratedlumi- nosity,L_int=^NMB/

σ

MB,where

σ

MB istheMBtriggercross-section measuredwithvan-der-Meerscans,amountsto47.8

μ

b⁻¹ witha relativeuncertaintyof3.7% [35].

The final results are given normalised to the total number of non-single diffractive (NSD) events. Therefore, a correction of 3.6%±³.1% [36] is applied to the minimum-bias results, which corresponds to the trigger andvertex reconstruction inefficiency forthisselection.Forthestudyofdandd, thesampleisdivided into five multiplicity classes, whichare definedas percentilesof theV0Asignal. Thissignalis proportionalto thecharged-particle multiplicity in the corresponding pseudo-rapidity region in the direction of the Pb-beam. Following the approach in [37], the multiplicity dependent results are normalized to the number of events N_ev corresponding to the visible (triggered) cross-section.

The event sample is corrected for the vertex reconstruction effi- ciency. This correction is of the order of 4% for the lowest V0A multiplicity class (60-100%) and negligible (<1%) for the other multiplicity classes. The chosen selection and the corresponding charged-particlemultiplicityatmid-rapidityaresummarizedinTa- ble1.

Table 1

Multiplicity intervals and the correspond- ing charged-particle multiplicities at mid- rapidity. The uncertainties reported for the ^dNch/dηlab||ηlab|<0.5 arethesystematicones, statistical uncertainties are negligible. Values aretakenfrom[18].

V0A Class ^dNch/dηlab||ηlab|<0.5

0–10% 40.6±0.9

10–20% 30.5±0.7

20–40% 23.2±^0.5

40–60% 16.1±^0.4

60–100% 7.1±^0.2

In this analysis, the production of primary deuterons and 3He-nucleiandthatoftheirrespectiveanti-particlesaremeasured in a rapidity window −¹<y<0 in the centre-of-mass system.

Since the energyper nucleonof the protonbeam ishigher than that of the Pb beam, the nucleon-nucleon system moves in the laboratoryframewitharapidity of-0.465.Potentialdifferencesof thespectralshapeornormalisationduetothelarger y-rangewith respect to themeasurement of

π

,K,andp [18] are found to be negligible forthe (anti-)deuteron and³He minimum-bias spectra with respect to the overall statistical and systematic uncertain- ties. Inorder to selectprimary tracksof suitable quality, various trackselectioncriteriaareapplied.Atleast70clustersintheTPC and two hits in the ITS (out of which at least one in the SPD) are required.These selections guarantee a trackmomentum res- olution of2% inthe relevant p_T-rangeanda dE/dx resolutionof about 6% forminimum ionisingparticles. The maximumallowed Distance-of-Closest-Approach(DCA)totheprimarycollisionvertex is0.12 cminthetransverse (DCAxy)and1.0 cminthelongitudi- nal(DCAz) plane.Furthermore,itisrequiredthatthe

χ

² perTPC clusterislessthan4andtracksofweak-decayproductswithkink topologyarerejected[29],astheycannotoriginatefromthetracks ofprimarynuclei.

Theparticleidentificationperformance oftheTPCandTOFde- tectors inp–Pb collisionsis shownin Fig.1. Forthemass deter- mination with the TOF detector, the contribution of tracks with a wrongly assigned TOF cluster is largely reduced by a 3

σ

pre- selectionintheTPCdE/dx,where

σ

correspondstotheTPCdE/dx resolution.Nevertheless,duetothesmallabundanceofdeuterons the background is still significant and it is removed using a fit to the squared mass distribution. An example of a fit for anti- deuterons withtransverse momenta 2.2 GeV/c<p_T<2.4 GeV/c isshownintherightpanelofFig.1.Thesquaredrestmassofthe deuteronhasbeensubtracted tosimplifythefittingfunction. The signal hasaGaussian shapewithanexponential tailontheright side.Thistailisnecessarytodescribethetime-signalshapeofthe TOF detector [33]. Forthe background,thesumof two exponen- tial functionsis used. One of the exponential functionsaccounts for themismatched tracks andthe other accounts forthe tailof theprotonpeak.For(anti-)³He nuclei,thedE/dxissufficientfora clean identificationusingonlythistechniqueover theentiremo- mentum range1.5 GeV/c< pT <5 GeV/c astheatomicnumber

Z=^{2 for3Heleadstoaclearseparationfromotherparticles.}

Thetrackingacceptance×^efficiencydeterminationisbasedon a Monte-Carlo simulationusing theDPMJET eventgenerator [38]

andafulldetectordescriptioninGEANT3 [39].Asdiscussedin [3], the hadronicinteraction of(anti-)nucleiwithdetectormaterial is notfullydescribedinGEANT3,thereforetwoadditionalcorrection factorsareapplied.Firstly,inordertoaccountforthematerialbe- tween the collision vertex and the TPC, the trackreconstruction efficienciesextractedfromGEANT3arescaledtomatchthosefrom GEANT4 [40,41]. Secondly, fortracks which crossin addition the material between the TPC and the TOF detectors, a data-driven

Fig. 1.EnergylossdE/dxintheTPCandthecorrespondingexpectedenergylossfromaparametrizationoftheBethe-Blochcurve(left).Exampleofthefittothesquared TOFmassdifferencewhichshowsseparatelythesignalandthebackgroundfromtheexponentialtailofprotonsandfrommismatchedtracks(right).

Fig. 2.Trackingacceptance×efficiencycorrectionfor(anti-)deuterons(left)andfor³Heand³He (right)intheminimum-biasclass.Theefficienciesforanti-nucleiarelower duetothelargercross-sectionforhadronicinteractions.

correction factorhas been evaluated by comparing the matching efficiencyof tracks to TOF hits in data andMonte Carlosimula- tion.SincetheTRDwasnotfullyinstalledin2013,thisstudywas repeatedfor regions in azimuthwith and without installed TRD modules.ThematchingefficienciesfortrackscrossingtheTRDma- terialwere then scaledsuch that the correctedyield agrees with theone obtained fortracks that are not crossing anyTRDmate- rial.Thisprocedureresultsinafurtherreductionoftheacceptance

× ^{efficiencyof6% fordeuterons and11% for}anti-deuterons. The acceptance and efficiency corrections are found to be indepen- dentoftheeventmultiplicityandareshowninFig.2forprimary deuterons andanti-deuterons, withand without requiring a TOF match,aswellasfor³He and³He.

The raw yields of deuterons and ³He also include secondary particles which stem from the interactions of primary particles withthe detector material.To subtract this contribution,a data- drivenapproachasin [3,18] isused.ThedistributionoftheDCAxy isfitted withtwo distributions (called“templates” inthe follow- ing) obtained from Monte-Carlo simulations describing primary andsecondarydeuterons,respectively. Thefitisperformedinthe range|^DCAxy|<0.5 cmwhichallowsthecontributionfrommate- rialto be constrainedby theplateauof thedistribution atlarger distances (|^DCAxy|>0.15 cm). The contamination of secondaries amounts to about 45% to 55% in the lowest p_T-interval and de- creasesexponentiallytowardshigherpTuntilitbecomesnegligible (<1%)above2 GeV/c.Thelimitednumberof³He candidatetracks doesnotallow a backgroundsubtractionbased ontemplates, in-

steadabincountingprocedureintheaforementionedDCAxysignal andbackgroundregionsisused.

The systematic uncertainties of the measurement are sum- marised for deuterons and ³He as well asfor their antiparticles inTable2.Fordeuterons,theuncertaintyrelatedtothesecondary correctionisestimatedbyrepeatingthetemplatefitprocedureun- der a variation of the DCA_z cut. The corresponding uncertainty for ³He nucleiis determinedby varying theranges in DCAxy for thesignal andbackgroundregions inthebincountingprocedure.

For d and ³He the systematic uncertainty on the cross-section forhadronicinteractionisdeterminedbyasystematiccomparison ofdifferent propagationcodes(GEANT3 andGEANT4).The mate- rial between TPC and TOF needs to be considered only for the (anti-)deuteron spectrum and increases the uncertainty by addi- tional 3% and 5% for deuterons and anti-deuterons, respectively.

This corresponds to the half of the observed discrepancy in the TPC-TOFmatchingefficiencies evaluatedindataandMonteCarlo.

Forboth deuterons andanti-deuterons, theparticle identification procedure introduces only a smalluncertainty which slightly in- creasesathighpT andisestimatedbasedonthevariation ofthe n

σ

-cutsinthe TPCdE/dx aswell ason avariation of thesignal extractioninthe TOFwithdifferentfitfunctions. ThePID related uncertainties for ³He and ³He remain negligible over the entire pT-range dueto the background-free identificationbased on the TPCdE/dx.Feed-downfromweaklydecayinghyper-tritons(³H)is negligiblefordeuterons [3,4].Sinceonlyabout4-8%ofall ³H de-

Table 2

Mainsourcesofsystematicuncertaintiesfordeuteronsand³He aswellastheiranti-particlesforlowandhighpT.

d d ³He ³He

pT(GeV/c) 0.9 2.9 0.9 2.9 2.2 5.0 1.8 5.0

Tracking (ITS-TPC matching) 5% 5% 5% 5% 6% 4% 6% 4%

Secondaries material 1% negl. negl. negl. 20% 1% negl. negl.

Secondaries weak decay negl. negl. negl. negl. 5% negl. 5% negl.

Material budget 3% 3% 3% 3% 3% 1% 3% 1%

Particle identification 1% 3% 1% 3% 3% 3% 3% 3%

Transport code 3% 3% 3% 3% 6% 6% 18% 11%

TPC-TOF matching 3% 3% 5% 5% – – – –

Total 7% 8% 8% 9% 23% 8% 20% 12%

Fig. 3.Transversemomentumdistributionsofdeuterons(left)andanti-deuterons(right)forvariousmultiplicityclasses.Themultiplicityclassdefinitionisbasedonthesignal amplitudeobservedintheV0AdetectorlocatedonthePb-side.Theverticalbarsrepresentthestatisticalerrors,theemptyboxesshowthesystematicuncertainty.Thelines representindividualfitsusingamT-exponentialfunction.

cayinginto³He passthetrackselection criteriaforprimary ³He, theremainingcontamination hasnotbeensubtractedandtheun- certainty related to it was further investigated by a variation of theDCA_xy-cutindataandafinaluncertaintyof5%isassigned.The influenceofuncertaintiesinthematerialbudgetonthereconstruc- tionefficiencyhasbeen studiedby simulatingeventsvaryingthe amount of material by ±^{10%. The estimates of the} uncertainties relatedto thetrackingandITS-TPCmatchingarebasedonavari- ationofthetrackcutsandare foundtobe approximately5%.The uncertainties related to tracking, transport code, material budget andTPC-TOFmatching arefullycorrelated acrossdifferentmulti- plicityintervals.

3. Resultsanddiscussion 3.1. Spectraandyields

The transverse momentum spectra of deuterons and anti- deuterons inthe rapidity range −¹ < y < 0 are presented in Fig.3forseveralmultiplicityclasses.The spectrashowa harden- ingwithincreasingeventmultiplicity.Thisbehaviourwas already observedforlower massparticles inp–Pb collisions[18].Forthe extractionof^pT^andpT-integratedyieldsdN/dy,thespectraare fittedindividuallyusingamT-exponentialfunction[42].

The values obtained for dN/dy for (anti-)deuterons are sum- marized in Table 3. They have been calculated by summing up

Table 3

Integrated yieldsdN/dyof(anti-)deuterons. Thefirstvalue isthe statisticaland thesecondisthetotalsystematicuncertaintywhichincludesboththesystematic uncertaintyonthemeasuredspectraandtheuncertaintyofthe extrapolationto lowandhighpT.

Multiplicity classes dN/dy(d) dN/dy(d)

0-10% (2.86±0.03±0.30)×10⁻³ (2.83±0.03±0.35)×10⁻³ 10-20% (2.08±⁰.02±⁰.22)×¹⁰⁻³ (1.94±⁰.03±⁰.24)×¹⁰⁻³ 20-40% (1.43±⁰.01±⁰.15)×¹⁰⁻³ (1.43±⁰.02±⁰.17)×¹⁰⁻³ 40-60% (8.93±⁰.08±⁰.93)×¹⁰⁻⁴ (9.06±⁰.15±¹.09)×¹⁰⁻⁴ 60-100% (2.89±⁰.05±⁰.30)×¹⁰⁻⁴ (3.02±⁰.07±⁰.36)×¹⁰⁻⁴

the pT-differentialyieldintheregionwherethespectrumismea- sured andby integratingthe fit resultin theunmeasured region at low and high transverse momenta. While the fraction of the extrapolatedyield athigh pT is negligible,thefractionatlow pT ranges from23% at highto 38%at low multiplicities.The uncer- tainty introducedbythisextrapolationisestimatedby comparing theresultobtainedwiththemT-exponential fitto fitresultsfrom several alternative functional forms (Boltzmann, Blast-wave [43], andp_T-exponential).

Fig. 4 shows the d/d ratios as a function of p_T for all mul- tiplicityintervals.Theratiosarefoundtobe consistentwithunity withinuncertainties.Thisbehaviourisexpected,sincethermaland coalescence models predict that the d/d ratiois givenby (^p¯/p)²

Fig. 4.Anti-deuterontodeuteronproductionratioforthefivemultiplicityclasses.

Allratiosarecompatiblewithunity,indicatedasadashedgreyline.Thevertical barsrepresentthestatisticalerrorswhiletheemptyboxesshowthetotalsystematic uncertainty.

(seeforinstance [15])andthe p¯/p ratio measured inp–Pb colli- sionsisconsistentwithunityforallmultiplicityintervals [18].

Therareproductionof A>2 nucleionlyallowstheextraction ofminimum-biasspectrafor³He and³He withtheavailablestatis- ticsandthusthe resultisnormalisedto allnon-singlediffractive (NSD) events. In total, 40 ³He nuclei are observed, while about 29400tracks fromd are reconstructed in thesame data sample.

The corresponding spectra are shown in Fig. 5 together with a m_T-exponentialfit whichisused fortheextraction ofthedN/dy and^pT^{ofthespectra.Thefitisperformedsuchthattheresiduals} toboththe³He and³He spectrumareminimisedsimultaneously.

The fractionof the extrapolated yield corresponds to about 58%.

Theuncertaintyintroduced bythisextrapolationisalsoestimated bycomparingtheresultobtainedwiththemT-exponentialfittofit resultsfromseveralalternativefunctionalforms(Boltzmann,Blast- wave [43], and pT-exponential).A pT-integratedyield ofdN/dy= (1.36±⁰.16(stat)±⁰.52(syst))×^{10−6 andan averagetransverse} momentum of^pT = (1.78±⁰.11(stat)±⁰.77(syst)) GeV/c are obtained.

Theyieldsofp,dand³He forNSDp–Pbeventsandnormalised totheir spin degeneracyareshowninFig. 6asafunction ofthe massnumberAtogetherwithresultsforinelasticppcollisionsand central Pb-Pb collisions. An exponential decrease with increasing A isobserved in all cases,yet withdifferentslopes. The penalty factor,i.e.the reduction ofthe yield foreach additionalnucleon, isobtainedfromafittothedataandavalue of635±^{90 inp-Pb} collisions isfound whichis significantly largerthan the factorof 359±^{41 whichwas observedforcentral}Pb–Pb collisions [3].The penaltyfactorobtainedfortheinelasticppcollisions[12] isfound tobe942±^107.Suchanexponentialdecreaseofthe(anti-)nuclei yieldwithmassnumberhasalsobeenobservedatlowerincident energiesinheavy-ion[1,44–46] aswellasinp–Acollisions[47].

3.2.Coalescenceparameter

Inthetraditionalcoalescencemodel,deuteronsandother light nuclei are formed by protons and neutrons, which are close in

Fig. 5.Transversemomentumdistributionof³He and³He forallNSDcollisions (NNSD).Theverticalbarsrepresentthestatisticalerrorswhiletheemptyboxesshow thetotalsystematicuncertainty.Thelinerepresentsaχ²fitwithamT-exponential function(seetextfordetails).

Fig. 6.ProductionyielddN/dynormalisedbythespindegeneracyasafunctionof themassnumberforinelasticppcollisions,minimum-biasp-PbandcentralPb-Pb collisions[12,13,18,48,49].Theemptyboxesrepresentthetotalsystematicuncer- taintywhilethestatisticalerrorsareshownbytheverticalbars.Thelinesrepresent fitswithanexponentialfunction.

phasespace. Inthispicture,the deuteronmomentumspectraare relatedtothoseofitsconstituentnucleonsvia [50,51]

E_dd³N_d dp³_d

=

^B2

E_pd³N_p

dp³_p

2

,

(1)

wherethemomentumofthedeuteronisgivenby pd=^2pp.Since theneutronspectraareexperimentallynotaccessible,theyareap- proximated by the proton spectra. The value of B₂ is computed asa function of eventmultiplicity andtransverse momentum as the ratiobetweenthe deuteronyield measured at pT=^pT,d and the square of the proton yield at pT,p =⁰.5pT,d. The obtained B₂-valuesareshowninFig.7.Initssimplestimplementation,the coalescencemodelforuncorrelatedparticleemissionfromapoint- like sourcepredicts that theobserved B2-valuesare independent of pTandofeventmultiplicity (called“simplecoalescence”inthe following).Withinuncertaintiesandgiventhecurrentwidthofthe multiplicityclasses,theobservedp_Tdependenceisstillcompatible withtheexpectedflatbehaviour(foradetaileddiscussionsee[6]).

Moreover,adecreaseofthemeasured B2 parameterwithincreas- ingeventmultiplicityforafixed pTisobserved.Thiseffectiseven morepronounced in Pb–Pb collisions[3] and apossible explana-

Fig. 7.CoalescenceparameterB2asafunctionofpTfordifferentV0Amultiplicity classes.Theverticallinesrepresentthestatisticalerrorsandtheemptyboxesshow thetotalsystematicuncertainty.

tionis anincreasing source volume,whichcan effectivelyreduce thecoalescenceprobability [7,51].

3.3. Meantransversemomenta

InFig.8 (left),themeanvaluesof thetransversemomenta of deuterons are compared with the corresponding results for

π

^±, K^±, p(^p),¯ ^and () [18]. As for all other particles, the ^pT ^of deuterons shows an increase with increasing event multiplicity, which reflects the observed hardening of the spectra. However, itis strikingthat deuterons violatethe massordering whichwas observed fornon-composite particles [18,52]:despite their much largermass,the^pT^{valuesaresimilartothoseof}()andonly slightlyhigherthanthoseofp(^p).¯

Note that simple coalescence models give a significantly dif- ferent prediction for the ^pT ^{of deuterons with respect to hy-} drodynamicalmodels. This canbe best illustrated withtwo sim- plifying requirements which are approximately fulfilled in data.

Firstly, thecoalescence parameter is assumedflatin pT andsec- ondly the proton spectrum can be described by an exponential shape, i.e. Cexp(−^pT/T) with two parameters C and T. In this case,the shapeofthe deuteronspectrumcan beanalytically cal- culated based on the definition of B2. Due to the self-similarity featureoftheexponentialfunction,(exp(x/a))^a=^exp(x),thespec- tral shape of the proton andthe deuteron are then found to be identical:

1 2

π

p^d_T

d²N^d dydp^d_T

=

^B2

₁

2

π

p^p_T d²N^p dydp_T^p

2

=

^B2

Cexp

( −

^p

p T

T

)

2

=

^B2

Cexp

( −

^pdT 2T

)

2

=

^B2C²exp

( −

^pdT

T

) .

(2) Thus,thesame^pT^{forboth particlesisexpectedandthebe-} haviour observed in p–Pb collisions is well described by simple coalescencemodels.Thisfindingcanbeevenfurthersubstantiated bydirectly calculatingthe^pT^{ofdeuterons assuming aconstant} valueof B2 andusingthemeasuredprotonspectrumasinput.As shownin Fig. 8 (right), in this case, a good agreement withthe dataisfoundconsideringthatalargefractionofthesystematicun- certaintyiscorrelatedamongdifferentmultiplicitybins.TheBlast- Wave model [43] fails to describe the ^pT ^{valuesfor deuterons} usingthecommonkineticfreeze-outparametersfrom [18],which describesimultaneouslythespectraofpions,kaons,andprotons.

Fig. 8. Mean pT ofvariousparticle speciesasa functionofthemeancharged- particle densityat mid-rapidityfor differentV0Amultiplicityclasses. Theempty boxesshowthetotalsystematicuncertaintywhiletheshadedboxesindicatethe contributionwhichisuncorrelatedacrossmultiplicityintervals(left).Comparison of^pT^{ofprotonsanddeuteronswiththesimple}coalescenceandtheBlast-Wave modelexpectations.Theshadedareasshowtheexpected^{pTfordeuteronsfroma} simplecoalescencemodelassumingapT-independentB2aswellasthecalculated pTforprotonsanddeuteronsfromtheBlast-Wavemodel [43] usingthekinetic freeze-outparametersforpions,kaons,protonsandfrom [18] (right).

Fig. 9.Deuteron-over-protonratioasafunctionofcharged-particlemultiplicityat mid-rapidityforpp,p–Pb andPb–Pb collisions[3,6,12].Theemptyboxesshowthe systematicuncertaintywhiletheverticallinesrepresentthestatisticaluncertainty.

3.4. Deuteron-over-protonratio

The deuteron-over-proton ratio is shown in Fig. 9 for three collision systems asa function of thecharged-particle densityat mid-rapidity.InPb–Pb collisionsithasbeenobservedthatthed/p ratiodoesnotvarywithcentralitywithin uncertainties(redsym- bols).Suchatrendisconsistentwithathermal-statisticalapproach andthe magnitudeof themeasured valuesagreewithfreeze-out temperatures intherangeof150-160 MeV [3]. Thed/p ratioob- tainedininelasticppcollisionsincreaseswithmultiplicity [6].The resultsinp–Pb collisionsbridgethetwomeasurementsintermsof multiplicityandsystemsizeandshowanincreaseofthed/pratio with multiplicity.Here, the low (high) multiplicity value iscom- patible with the resultfrom pp (Pb–Pb) collisions. Note that the experimental significanceofthisenhancementisfurthersubstan- tiated by considering only thepart ofthe systematicuncertainty whichisuncorrelatedacrossmultiplicityintervals.

A similar rise with multiplicity is observed for the ratios of the yieldsof multi-strangeparticles tothat ofpionsin p–Pb col- lisions [53]. In this case the canonical suppression due to exact strangenessconservationinsmallersystemsgivesaqualitativeex- planation [54]. An interpretation of the d/p ratio within thermal

inp–Pb collisionsat sNN = ^{5.02TeV hasbeen studiedatmid-} rapidity. The results on deuteron production in p–Pb collisions exhibit a continuous evolution withmultiplicity betweenpp and Pb–Pb collisions.The productionof complexnucleishowsan ex- ponential decrease with mass (number). The penalty factor (de- creaseofyieldforeach additionalnucleon) islargerthantheone observedincentralPb–Pbcollisionsandsmallerthantheonemea- suredinpp collisions.The transversemomentum distributionsof deuteronsbecomeharderwithincreasingmultiplicity.Twointrigu- ingobservationsthathavebeenrecentlyreportedbyALICE[6] in highmultiplicitypp collisionsareconfirmedinthepresentpaper.

Firstly,the^pT^{valuesofdeuteronsarecomparabletothoseofthe} muchlighter baryonsandthusdo notfollowa massordering.

Thisbehaviourisobservedforallmultiplicityintervalsanditisin contrastto the expectationfrom simple hydrodynamical models.

Theseobservationsmadeinp–Pb collisionssupportacoalescence mechanism, whileinPb–Pb collisions the deuteronseems to fol- lowthecollectiveexpansionofthefireball.Secondly,thed/pratio rises stronglywithmultiplicity, whilethis ratioremains approxi- matelyconstant as a function of multiplicity in Pb–Pb collisions, whereitsvalueagreeswiththermal-modelpredictions.

Acknowledgements

The ALICECollaboration wouldlike to thank all its engineers andtechniciansfortheirinvaluablecontributionstotheconstruc- tion of the experiment and the CERN accelerator teams for the outstandingperformance of the LHC complex. The ALICE Collab- oration gratefully acknowledges the resources and support pro- videdbyallGridcentresandtheWorldwideLHCComputingGrid (WLCG) collaboration. The ALICECollaboration acknowledges the followingfundingagenciesfortheir support inbuildingandrun- ningtheALICEdetector:A.I.AlikhanyanNationalScienceLabora- tory(YerevanPhysicsInstitute)Foundation (ANSL),StateCommit- teeofScienceandWorldFederationofScientists(WFS), Armenia;

Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung,Austria;MinistryofCommunications andHighTech- nologies, National Nuclear Research Center, Azerbaijan; Conselho NacionaldeDesenvolvimentoCientíficoeTecnológico(CNPq),Uni- versidadeFederal doRioGrandedo Sul(UFRGS), Financiadorade EstudoseProjetos(Finep)andFundaçãodeAmparoàPesquisado Estadode São Paulo(FAPESP),Brazil; MinistryofScience &Tech- nology of China (MSTC), National Natural Science Foundation of China (NSFC) andMinistry ofEducation ofChina (MOEC), China;

Croatian Science Foundation and Ministryof Science andEduca- tion,Croatia;CentrodeAplicacionesTecnológicasyDesarrolloNu- clear(CEADEN), Cubaenergía, Cuba; Ministryof Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish CouncilforIndependentResearch|NaturalSciences,theCarlsberg FoundationandDanishNationalResearchFoundation(DNRF),Den- mark;HelsinkiInstitute ofPhysics (HIP),Finland; Commissariatà

e Ricerche Enrico Fermi and Istituto Nazionale di Fisica Nucle- are (INFN), Italy; Institute forInnovative Science andTechnology, Nagasaki Institute ofApplied Science (IIST),Japan Societyfor the PromotionofScience(JSPS)KAKENHIandJapaneseMinistryofEd- ucation, Culture, Sports, Science and Technology (MEXT), Japan;

Consejo Nacional de Ciencia (CONACYT) y Tecnología, through FondodeCooperación InternacionalenCienciayTecnología(FON- CICYT)andDirección GeneraldeAsuntos delPersonalAcademico (DGAPA), Mexico; NederlandseOrganisatievoor Wetenschappelijk Onderzoek(NWO), Netherlands; TheResearch CouncilofNorway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Uni- versidad Católica del Perú, Peru; Ministry of Science andHigher Education andNationalScienceCentre, Poland;Korea Institute of Science andTechnology InformationandNationalResearch Foun- dation of Korea (NRF), Republic of Korea; Ministry of Education andScientificResearch,InstituteofAtomicPhysicsandMinistryof ResearchandInnovationandInstituteofAtomicPhysics,Romania;

Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation, National Research Centre KurchatovInstitute,RussianScienceFoundationandRussianFoun- dation for Basic Research,Russia; Ministry of Education, Science, ResearchandSportofthe Slovak Republic,Slovakia; NationalRe- searchFoundationofSouthAfrica,SouthAfrica;SwedishResearch Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden;EuropeanOrganizationforNuclearResearch,Switzerland;

National Science and Technology Development Agency (NSDTA), SuranareeUniversityofTechnology(SUT)andOfficeoftheHigher Education Commission under NRU project of Thailand, Thailand;

Turkish Atomic EnergyAgency (TAEK), Turkey;NationalAcademy ofSciences ofUkraine, Ukraine;Science andTechnology Facilities Council (STFC), United Kingdom; National Science Foundation of theUnitedStatesofAmerica(NSF) andUnitedStatesDepartment of Energy, Office of Nuclear Physics (DOE NP), United States of America.

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