Multiplicity dependence of (anti-)deuteron production in pp collisions at √s=7 TeV

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Physics Letters B

www.elsevier.com/locate/physletb

Multiplicity dependence of (anti-)deuteron production in pp collisions at √

s = ^{7 TeV}

.ALICE Collaboration

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

Articlehistory:

Received5March2019

Receivedinrevisedform30April2019 Accepted20May2019

Availableonline22May2019 Editor:L.Rolandi

Inthisletter,theproductionofdeuteronsand anti-deuteronsinppcollisionsat√

s=^{7 TeVisstudied} as a function of the charged-particle multiplicity density at mid-rapidity with the ALICE detector at the LHC. Production yields are measured at mid-rapidity in five multiplicity classes and as a functionof thedeuterontransverse momentum(pT). Themeasurements are discussedinthe context ofhadron–coalescencemodels.Thecoalescenceparameter B2,extractedfromthemeasuredspectraof (anti-)deuterons and primary(anti-)protons,exhibitsnosignificantpT-dependenceforpT<3 GeV/c,in agreement with theexpectations ofasimple coalescencepicture.Atfixedtransverse momentumper nucleon,the B2parameterisfoundtodecreasesmoothlyfromlow multiplicitypp toPb–Pb collisions, in qualitative agreement with more elaborate coalescence models. The measured mean transverse momentum of (anti-)deuterons in pp is not reproduced by the Blast-Wave model calculations that simultaneouslydescribepion,kaonandprotonspectra,incontrasttocentralPb–Pb collisions.Theratio between the pT-integrated yield ofdeuteronsto protons, d/p,is foundto increasewiththe charged- particlemultiplicity,asobservedininelasticppcollisionsatdifferentcentre-of-massenergies.Thed/p ratiosarereportedinawiderange,fromthelowesttothehighestmultiplicityvaluesmeasuredinpp collisionsattheLHC.

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

1. Introduction

The production of light nuclei and anti-nuclei in elementary collisions has been described by phenomenological models in whichnucleonscoalesceintonuclei[1–4].Accordingtothesemod- els,a pair ofindependent final-statenucleons that are nearby in spaceand have similar velocities can transfer energyto therest of the system to form a deuteron or an anti-deuteron. The pro- ductionrateofthe(anti-)deuteronobtainedbycoalescenceisthus relatedtothose ofits constituentprotons andneutrons.Inorder to provide a quantitative description of this process the coales- cenceparameterB2,whichrelatesthedeuteronproductiontothe squareproduct ofnucleon yields,isextracted.Thesemodels have successfullybeentestedwithdeuteronandanti-deuteron produc- tionmeasuredinppcollisionsattheCERNISR[5,6] andTevatron [7],photo-productionanddeepinelasticscatteringofelectrons at HERA[8,9],electron-positroncollisionsatARGUS[10],BaBar[11], CLEO [12] and at LEP [13]. Results on the production of light (anti-)nuclei ininelasticppcollisionsat√

s=⁰.9,2.76 and7 TeV havebeenreportedby theALICECollaborationin [14,15] andthe validityofcoalescence models [1–4] at theLargeHadronCollider

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

(LHC) hasalso beendiscussed.Light nucleiandtheir anti-matter counterparts are rarely produced in elementary reactions. In pp collisionsatLHCenergies,thecosttoaddoneconstituentnucleon toanucleusamountstoareductionfactoroftheyield(alsocalled

“penalty factor”)of about1000[15]. Heavy-ion collisions, on the other hand,constitutea moreabundantsource oflight(anti-)nu- clei,asreportedbyALICE[14,16,17].Apenaltyfactorofabout300 hasbeenextractedincentralPb–Pb collisionsattheLHC[17].

In Pb–Pb collisions, the yields oflight (anti-)nucleiup to the massnumberA=4havebeensuccessfullydescribedtogetherwith otherlight-flavourhadronsinthethermal-statisticalapproachwith one commonchemical freeze-outtemperature[17–19].Compared tohydrodynamic-inspiredmodels(e.g.Blast-Wavemodel [20]),the measured deuteron p_T spectra and elliptic-flow coefficient (v₂) suggest common kinetic freeze-out conditions for deuterons and primary pions,kaons and protons[14,16]. Furthermore,the rela- tivedeuteron-to-protonyields(d/p)increasebyaboutafactortwo frominelasticpptocentralPb–Pbcollisions,wherethevalues[14]

are in agreement with thestatistical-thermal model [19]. A coa- lescence approach that neglects the size of the particle emitting source (hereafterdenoted as“simple coalescence”)failsinrepro- ducing thedeuteronB2 and v2 measuredinPb–Pb collisions[14, 16]. A formulation of the coalescence model that takes into ac- count the size oftheparticle-emitting source hasbeenproposed https://doi.org/10.1016/j.physletb.2019.05.028

0370-2693/©^{2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

todescribethebehaviourinlargesystems[4].Insmallersystems onehastoconsiderthatthesizeofthedeuteronmaybeaslarge asorevenlargerthanthesizeoftheemittingsource.

The abundances of nucleiare very sensitive to the freeze-out conditions,to thedynamics, andthesize of theemitting source.

Forthese reasons, a systematic comparison ofthe production of lightnucleiacrossdifferentcollisionsystemsand,inparticular,in eventswithsimilarfinal-statemultiplicitybutverydifferentinitial conditionsandcollisiongeometrycanshedlightontheproduction mechanisms.Thankstothehighstatisticsdatasamplecollectedby ALICE,thedeuteronandanti-deuteron productioninpp collisions canbe studieddifferentially asafunction ofthecharged-particle multiplicity andthe transverse momentum (p_T), complementing thepreviousmeasurementsinppandPb–Pbcollisions.

This letter is organised as follows: in Sec. 2 the experimen- tal apparatus, the analysis technique and the estimation of the systematicuncertainties aredescribed. Theresultson multiplicity dependent pT-differential and pT-integrated yields and the anti- deuteron over deuteron ratio are reported in Sec. 3, which also containsadetaileddiscussionoftheresults.Conclusionsfollowin Sec.4.

2. Experimentaldetails 2.1.TheALICEdetector

A comprehensive description of the ALICE apparatus and its performance can be found in [21,22]. In this section, the detec- tors used for the analysis discussed in this paper are described.

Deuteronspectraaremeasured atmid-rapidity(|^y|<0.5) relying onthetrackingandparticleidentification(PID)capabilitiesofthe central-barrel detectors, which are located in a solenoid magnet providinga B =0.5Tfield, parallelto thebeamdirection(z-axis intheALICEreferenceframe).

From the innermostradius of 3.9cm (distance fromthe cen- tre ofthebeamvacuumpipe)to theoutermostradius of43cm, theInnerTrackingSystem(ITS)includestwolayersofSiliconPixel Detector(SPD),twoSiliconDriftDetector(SDD)layers,andtwoSil- iconStripDetector(SSD)layers.ThedifferentITSsub-systemshave fullazimuth anda commonpseudorapidity coverage of|

η

|<0.9 in the acceptance.The spatial precision of the ITS, its proximity tothebeampipe,anditsvery lowmaterialbudget [23] enablea precisedetermination oftheprimary vertexandofthe trackim- pactparameter(i.e.thedistanceofclosestapproachofthetrackto theprimaryvertex)inthetransverseplane,forwhicharesolution betterthan75 μmisachievedfortrackswithp_T > 1 GeV/c [23].

TheTimeProjectionChamber(TPC)isthemaintrackingdevice ofthe experiment and surrounds the ITSwith an active volume rangingfrom85cmto247cminradiuswithfullazimuthalcover- ageinthepseudorapidityinterval |

η

_|<0.9.Itprovidesupto159 spacepoints todetermine theparticle trajectoryandmeasure its momentum.Moreover,thespecificionisationenergy-lossofparti- clesinsidetheTPCvolumeismeasuredwitharesolutionof5%in ppcollisions,exploitedhereforPID.

TheTime-Of-Flight (TOF)system [24], anarray of1593Multi- gapResistivePlate Chambers,completesthesetofdetectorsused forPID in the analysispresented in thisletter. It is located at a radialdistanceofabout3.8m,coveringfullazimuthinthepseu- dorapidity interval |

η

|<0.9. The event time of the collision is obtainedonanevent-by-eventbasiseitherusingtheTOFdetector, ortheT0detector,oracombinationofthetwo[25].TheT0detec- torconsistsoftwoarraysofCherenkovcounters,located onboth sidesoftheinteractionpointatz=^{350 cmandz}= −^{70 cmfrom} thenominalvertex position.The time-of-flightof theparticles is determinedwitharesolutionofabout120psinppcollisions.

BetweentheTOF andtheTPC, theTransitionRadiationDetec- tor (TRD) is positioned at a radial distance between 2.9and 3.7 mfromthebeamaxis,withpseudorapiditycoverageof|

η

_|<0.8.

Since 2014, all eighteen TRD supermodules are installed, cover- ing full azimuth. In 2010, when the data used for the analysis presented here were collected, only seven sectors were present.

AlthoughtheTRDisnotusedinthisanalysis,itsdetectormaterial playsaroleintheefficiencycorrections,describedinSec.2.5.

TheV0detectorconsistsoftwoscintillatorarraysbuiltaround the beampipe oneither side ofthe interaction pointat z=³²⁹ cmandz= −^{88 cm,andcoveringthe}pseudorapidityranges2.8≤

η

_≤5.1 (V0-A) and-3.7≤

η

_≤ -1.7 (V0-C). Thisdetector is used fortriggeringandbackgroundsuppression.Itisalsoemployedfor classifyingevents accordingto multiplicity, asfurther detailedin thenextsection.

2.2. Eventselectionandmultiplicityclasses

Theanalysisisbasedonadatasampleof237millionminimum- bias triggered pp collisions at √

s=^{7 TeV. The} minimum-bias trigger requiresa hit ineitherthe V0or theSPD, incoincidence with the crossing of proton bunches from the two beams. The timinginformationprovidedbytheV0detectoraswellasthecor- relationbetweentheSPDhitmultiplicity andthenumberofSPD tracksegments pointingto theprimary vertexare usedoffline to rejectthecontaminationfrombeam-gasevents,achievingapurity oftheminimum-biaseventsampleof99.7% asestimatedin[22].

The pileup rejection is performed by rejecting offline the events with more than one reconstructed vertex in the SPD. The resid- ualfractionofeventswithpileuprangesfromabout10⁻⁴ to10⁻² forthelowestandhighestmultiplicity classes,respectively.Events are also required to havea primary vertex reconstructed by the SPDwithin±^{10cmfromthenominal}interactionpointalongthe beamdirection. Thesample selected withtheabove criteriacon- tains172millionevents.

The results are reported for an event class (INEL>0) charac- terised by at least one charged particle being produced in the pseudorapidity interval |

η

_| < 1, corresponding to about 75% of thetotalinelasticcross-section.INEL>0eventsareselectedexper- imentally by requiring that atleast one track segment (tracklet) isreconstructed inthe SPD. Thisselection can beaffected by in- efficiencies associated with the tracklet reconstruction. Thus the selectednumberofeventsusedforthenormalisationoftheyields iscorrectedforthe8.5%lossduetoinefficiencyinthelowestmul- tiplicity class andfor lessthan 1.2% loss for all other classes,as estimatedin[26].

In orderto studydeuteronproduction asa functionof multi- plicity,theselectedeventsareclassifiedusingthe“V0M”forward multiplicityestimator,basedonthetotalenergydepositedinboth theV0scintillator arrays(V0-AandV0-C).The V0Mamplitude is linearlyproportionaltothetotalnumberofchargedparticlespro- ducedin theV0 detectorsacceptance. Sincedeuteron production ismeasuredatmid-rapidity,anindependentestimatorispreferred as an event classifier to avoid auto-correlation biases. In each V0M eventclassthe averagecharged-particle multiplicity density (^dNch/d

η

^{) ismeasured at}mid-rapidityandresultsare reported inthefollowingasafunctionof^dNch/d

η

.

For the event classes relevant for this analysis, the values of ^dNch/d

η

^{and the fraction of the INEL>0 cross section are re-} portedinTable1.Romannumeralsareusedtoindicateeachofthe teneventclassesinwhichthemeasurementofotherlight-flavour hadron yields, andprotonsin particular,have beenperformedas reportedin[26,27].Consideringthedeuteronstatisticsneededfor thepresentanalysis,someoftheseclasseshavebeencombinedas indicatedinthetable.

Table 1

Charged-particlemultiplicity(^dNch/dη)measuredatmid-rapidity(|η|< 0.5)and itscorrespondingfractionoftheINEL>0crosssection(σ/σINEL>0)foreachofthe multiplicityclassesselectedwiththeV0Mestimatorandrelevantforthisanalysis, indicatedbyromannumerals[26].Theuncertaintiesarethesquare-rootofthesum inquadratureofstatisticalandsystematiccontributionsandrepresentonestandard deviation.

Multiplicity class σ/σINEL>0 ^dNch/dη

I+II 0 - 4.7 % 17.47±⁰.52

III 4.7 - 9.5 % 13.50±⁰.40

IV+V 9.5 - 19 % 10.76±0.30

VI+VII 19 - 38 % 7.54±0.23

VIII+IX+X 38 - 100 % 3.30±0.13

I to X 0 - 100 % 5.96±⁰.23

2.3. Trackselectionandparticleidentification

In orderto ensure good quality, tracks are selected according tothefollowingcriteria.Foreachtrack,atleasttworeconstructed points arerequired intheITS(including atleastone intheSPD) and70 out ofa maximumof 159in theTPC. The track-fit qual- ityisassuredbyrequiringthe

χ

²perspacepointintheTPCtobe lessthan 4.Daughtertracks fromreconstructed kinksinthe TPC volume are rejectedinorder to keep only trackspointing tothe primary vertex. To limit the contamination from secondary par- ticles from material (see Sec. 2.4), requirements are imposed on theDistanceofClosestApproachofeachtracktotheprimaryver- tex alongthe beamdirection(DCAz) andin thetransverse plane (DCAxy) to be lessthan 1 cmand0.1 cm, respectively. The fidu- cialpseudo-rapidityregionisdefinedas|

η

|<0.8,whichensuresa uniformacceptanceinthedetectorsinvolved.

The identification of (anti-)deuterons is achieved by exploit- ingthe measurementoftheir specificionisationenergy-loss, pro- videdby the TPC, andvia themeasurement of thetime-of-flight oftheparticles,performedwiththe TOF.Duetothe differentac- ceptance of the two detectors, the TPC is used without the TOF for p_T < 1 GeV/c, where the separation of deuterons from light hadrons is very effective. Deuterons and anti-deuterons are se- lected by requiringan energy losscompatible, within ±³

σ

, with the value expected for particles having the mass and charge of the deuteron, where

σ

is the resolution of the particle energy lossintheTPC.For pT>1 GeV/c,TOFinformationisrequiredto- getherwiththatfromtheTPC. Thesquaredmassoftheparticles, m²_TOF=^p2(t²_TOF/L²−¹/c²),isthendeterminedfromthemeasured time-of-flight(tTOF), themomentum (p) andthetracklength (L), afterthe3

σ

selectionontheparticleenergy-lossintheTPC.Fig.1 showsan example of the obtainedm²_TOF distribution around the anti-deuteron peak for a selected pT interval and in the high- estmultiplicity class(I+II). Them²_TOF distribution isfittedusinga Gaussianfunctionwithanexponentialtailtowardshighermasses for the signal that reflects the TOF detector time response [24].

Todescribethebackgroundthesumoftwo exponentialfunctions isused.Theyaccount forthosetrackserroneouslyassociatedtoa TOF hit and forthe tail of the(anti-)proton signal. Forboth the TPC-onlyandTOF-TPC analyses theyields of deuterons andanti- deuteronsareseparatelyextractedineach p_Tintervalandforeach multiplicityclass.

2.4. Rejectionofsecondarydeuterons

The sample of identified deuterons is contaminated by those that originatefrominteractions ofprimary particles withthede- tector material, e.g. knock-outor pick-up, which are highly sup- pressedforanti-deuterons. Thecorrespondingcorrection, onlyfor matter, is estimated as in [15] and is based on a fit to the dis- tribution of the DCA_xy. The latter is determined as the sum of

Fig. 1.TOFsquared-massdistribution(m²_TOF)aroundtheanti-deuteronpeakfora selectedpTintervalandinthehighestmultiplicityclass.Thesolidredlinerepre- sentsafitofaGaussianfunctionplusanexponentialrighttailtotheanti-deuteron signal,thegreydashedlinethefitofthebackgroundperformedusingthesumof twoexponentialfunctions,andthesolidbluelineisthesumofthesignalandback- groundcomponents.

two contributions: the signal of primary deuterons appears as a Gaussian-like peakcentredaroundzerowhereassecondarynuclei contribute to theflatunderlying background.Thefractionofsec- ondary deuteronsis about40% at pT ^{0.6 GeV}/c anddecreases exponentially as thetransverse momentum increases until it be- comes smallerthan 5% above 1.4 GeV/c. It is observed that this doesnot dependonmultiplicity andthereforeacorrection based onthemultiplicity-integrateddatasampleisusedtominimisethe statisticaluncertainties.

2.5. Acceptanceandefficiency

After subtracting the contamination fromsecondary particles, raw yields are corrected for acceptance and tracking efficiency (Acc×

ε

). This correction allows one to account for the limited acceptanceofthedetectors,theparticleabsorptioninthedetector material–mainlyduetoenergylossandmultiple-scatteringpro- cesses –andthepartial inefficienciesduetodetectordeadzones andinactive readoutchannels.The Acc×

ε

iscomputedby using MonteCarlo(MC)generatedevents.Standardeventgeneratorsfor ppcollisions, e.g.PHOJET [28] orPYTHIA [29] donotconsiderthe production of nuclei. To include light (anti-)nuclei, these are in- jectedintounderlyingPHOJETeventswithflatmomentumandra- piditydistributions.TheALICEdetectordescriptionisbasedonthe GEANT3particletransportcode [30].Asdiscussedin[14],GEANT3 includes only an approximate description of the interactions of light nucleiwiththedetectormaterial.The Acc×

ε

isreducedby 6% when TOF PID isused, due to the extra(anti-)deuterons lost because of hadronic interactions that GEANT3 does not account for.Thiscorrectionisbasedonthefractionof(anti-)deuteronsab- sorbedintheTRDmodulesinstalledbetweenTPCandTOF,studied indataandMCsimulations.Moredetailscanbefoundin[15].

As alreadymentionedinSec.2.2,the pT-differentialyields are normalised to INEL>0 events.Rawyields needto be further cor- rected for the amount of (anti-)deuteron signals lost because of theeventselection.Thiscorrectionisexpectedtobedependenton multiplicity.Simulations enrichedwithnuclei,such asthoseused to determine Acc×

ε

, are not appropriate for its estimation, be- causethemeannumberofchargedparticlespereventisnotwell described. In this respect,a MC simulation (based on PYTHIAas eventgenerator) that reproducesthe charged-particlemultiplicity measured in the datacan be safely used.Since such simulations

donot contain nuclei, thefractionof signal lostin theeventse- lectionisestimatedfor(anti-)deuteronsbyextrapolating theones determinedfor pions,kaons andprotons. This hasbeen done by exploitingthelineardependenceofthelostsignalasafunctionof themassoftheparticles, whichwasobservedinsimulations.For thelowestmultiplicityclass,theresultingfractionofdeuteronloss isabout4%at p_T ^{0.6 GeV}/c andrapidlydecreasesasthetrans- versemomentumincreasesuntilitbecomessmallerthan1%above 1 GeV/c.Forhighermultiplicities,thecorrectionisnegligible.

2.6.Systematicuncertainties

There are several contributions to the total systematic uncer- tainty.Twocontributionsarisefromtheparticularsetofselections appliedtothesample oftracksfortheanalysisandfromthepar- ticleidentificationprocedure.Therejectionofsecondarydeuterons alsointroducesanuncertainty.Othersignificantuncertaintiesorig- inatefromthelimitedknowledgeoftheabsorptionoflight(anti- )nuclei in the detector material and of the amount of material itself. The ITS-TPC track matching efficiency is also known with finiteprecision. The normalisationof the pT-differential yields to INEL>0eventsisanadditionalsourceofuncertainty.Allcontribu- tionstothetotalsystematicuncertaintyaresummarisedinTable2 forthehighestmultiplicityclass(I+II). Moredetailsarepresented inthefollowing.

The systematic uncertainty related to PID is smaller at low transversemomenta,down to3% at0.6GeV/c,becauseofaclear separationof the deuteron andanti-deuteron signals in theTPC.

Athigherp_T,thepresenceofthebackground,whichcontaminates thesignal intheTOFsignificantly,introduces anadditionaluncer- tainty.Thelatterincreasesgraduallyfromabout3%at1GeV/c to about22–23%forpT≈^{3 GeV}/c.Theuncertaintyathightransverse momentum,at p_T≈^{3 GeV}/c,originatesmainlyfromtherighttail oftheprotonsquared-mass distribution,which stronglycontami- natesthe(anti-)deuteronsignalintheTOF.

InthecaseoftheTPCPID,thesystematicuncertaintyestimate isbased on a variation of themaximum accepted difference be- tweenthemeasuredandexpectedenergy-lossvalueforthe(anti- )deuteron-masshypothesis.In thecaseofTOF PID,thebinwidth ofthesquared-massdistributionandtherangeofthefithavebeen varied.Atintermediatetransversemomenta(1<pT<1.6 GeV/c), wherethebackgroundunderthe(anti-)deuteronsignalpeakinthe m²_TOFdistributionisalmostnegligible,theyieldisextractedbybin counting.Thisresultiscomparedtotheoneobtainedwiththefit proceduredescribed inSec. 2.3 inorder to estimate the system- aticuncertainty.Theuncertaintyresultingfromthetrackselection hasbeenestimatedthroughvariationsofthespecificrequirements usedintheanalysis. The rejectionofsecondarydeuterons isalso a source ofuncertainty atlow p_T while it isnegligible for anti- deuterons.Theuncertaintyisestimatedby varyingthemaximum

|^DCAz|^{of the acceptedtracks, which hasa significant impact on} theestimatedfractionofprimary particles.A p_T-independentun- certaintyof3%isassociatedwiththedifferencebetweentheITS- TPC track matching efficiency in data and MC simulations [27, 31].Thesystematicuncertaintyrelatedtothenormalisationofthe spectratotheINEL>0eventclassisfoundtobenotlargerthan1%

forall multiplicities andtransverse momenta.This uncertaintyis estimatedasthedifferencebetweenthecorrespondingprotonand deuteroncorrections(seeSec.2.5).

The limited knowledge of the hadronic interaction cross sec- tion of the primary particles in the detector material leads to a systematicuncertaintyof6% uniformin p_T, asestimatedin[15].

Moreover,theuncertaintyofthematerialbudgetcontributeswith anadditional3% tothetotaluncertainty.Foritsevaluation,theef- fectofvaryingtherelativeamountofmaterialby ±^{10% hasbeen}

Table 2

Systematic uncertainties on deuteron and anti-deuteron transverse-momentum spectraatlowandhighpTforthehighestmultiplicityclass(I+II).Thevaluesin parenthesesapplytoanti-deuteronsandareonlygivenwheretheydifferfromthose relatedtodeuterons.Otherwise,whereitisnotexplicitlyspecified,thevaluesare commontoparticlesandanti-particles.

Source d (d)

pT 0.6 GeV/c 3 GeV/c

Particle identification 3% 24% (26%)

Track selection 1% 5%

Secondary nuclei 7% (negl.) negl.

ITS-TPC matching 3% 3%

Norm. to INEL > 0 events 1% negl.

Hadronic interactions 6% 6%

Material budget 3% 3%

Total 11% (8%) 26% (27%)

studiedthroughsimulations.Allthementionedcontributionshave beensummedinquadrature.Thetotalsystematicuncertaintyde- pendsmoderatelyonmultiplicity: therelative differencebetween differentmultiplicityclassesis20–30%atmost.

3. Resultsanddiscussion 3.1. Transversemomentumspectra

The transverse momentum spectra of deuterons and anti- deuterons in the considered multiplicity classes are shown in Fig. 2, in the left and right panels, respectively. In order to ex- trapolate the spectra to low and high pT, the distributions are individuallyfittedwiththeLévy-Tsallisfunction [31,32],

d²N dp_Tdy

=

^dN

dy

p_T

(

n

−

¹

)(

n

−

²

)

nC

[

^nC

+

^m0

(

n

−

²

)]

1

+

^mT

−

^m0

nC

₋n

,

(1)

wherem_T=

p²_T+^m2₀ ^{isthetransversemass,m}0istherestmass of the particle (deuteron for the present analysis) and n, C and dN/dyarethefreefitparameters.Asobservedalreadyin [14] for inelastic collisions and in [27] for light hadrons, the Lévy-Tsallis function describes the spectra in all multiplicity classes rather well.The pT-integratedyieldper unitofrapidity(dN/dy) atmid- rapidityandthemeantransversemomentum^pT^{arereportedin} Table3.TheseareobtainedbyintegratingthepT-differentialyields inthe measured pT regionand thefittedLévy-Tsallis function in theextrapolatedregionsatlowandhigh pT.Thefractionofyield containedin thesetwo regions is alsoreportedin the table.The firstuncertaintyofdN/dyand^pT^{reportedinTable3represents} the statistical uncertainty, whereas the second is the systematic uncertainty.Thelatterincludestheuncertaintyduetotheextrap- olationofthespectra,whichamountstoabout4to9% (fromhigh to low multiplicity)of the integratedyield andto about1to 5%

of the mean p_T. Both these estimates are derived by fitting the spectra withother functional forms,which describe the low and the high pT regions of the spectra in a different way. These in- clude Boltzmann, Fermi-Dirac, Bose-Einstein,m_T-exponential and pT-exponentialdistributions[33].

Table 3 showsthat the yield ofdeuterons and anti-deuterons increaseswithmultiplicity,mirroringthe factthat thenumberof constituent nucleons per event isalso rising [27]. The multiplic- itydependenceofthe^pT^{reflectstheobservedhardeningofthe} deuteronandanti-deuteronspectrafromlowtohighmultiplicity.

The anti-deuteronto deuteronratiois showninFig.3 forthe considered multiplicity classes. These ratios are compatible with unity within 2

σ

(where

σ

is the uncertainty ineach pT bin) in themeasured p_T rangeandforallmultiplicity classes,andare in

Fig. 2.Transverse-momentumspectraofdeuterons(left)andanti-deuterons(right)measuredatmid-rapidityinppcollisionsat√

s=7 TeV intheconsideredmultiplicity classes.Theverticalbarsarethestatisticaluncertainties,theopenboxesrepresentthesystematicones.Thedashedlinescorrespondtoindividualfitstothedataperformed withtheLévy-Tsallisfunction(seeEq. (1)).Thespectrahavebeenscaledwiththeindicatedfactorsforbettervisibility.

Table 3

pT-integratedyield,dN/dy,andmeantransversemomentum,pT,alongwiththe extrapolatedfraction(Extr.)ofdeuterons(top)andanti-deuterons(bottom)inpp collisionsat √

s=^{7TeV indifferent}multiplicityclasses. Thefirstuncertaintyis statistical,thesecondoneisthesuminquadratureofthesystematicerrorandthe uncertaintyduetothespectrumextrapolation,asdescribedinthetext.

Multiplicity class dN/dy(×¹⁰⁻⁴) ^pT^(GeV/c) Extr. (%) d

I+II 10.14±⁰.15±¹.17 1.28±⁰.01±⁰.06 23 III 7.01±⁰.13±⁰.81 1.19±⁰.02±⁰.07 27 IV+V 5.76±⁰.08±⁰.64 1.11±⁰.01±⁰.05 29 VI+VII 3.55±0.04±0.39 1.05±0.01±0.05 30 VIII+IX+X 1.15±0.01±0.17 0.82±0.01±0.05 39

d

I+II 10.87±0.18±1.47 1.47±0.02±0.16 31 III 7.44±⁰.15±⁰.82 1.16±⁰.02±⁰.06 29 IV+V 5.68±⁰.13±⁰.68 1.17±⁰.02±⁰.10 31 VI+VII 3.88±⁰.06±⁰.44 1.05±⁰.01±⁰.07 35 VIII+IX+X 1.07±⁰.02±⁰.15 0.85±⁰.01±⁰.05 39

Table 4

Anti-deuterontodeuteronratioaveragedoverallmea- suredpTbinsineachmultiplicityclassinppcollisions at√

s=^{7 TeV.Thefirst}uncertaintyisstatisticalandthe secondisthesystematiccontribution.

Multiplicity class d/d

I+II 0.93±⁰.03±⁰.13

III 1.01±0.04±0.15

IV+V 0.92±0.03±0.13

VI+VII 0.96±⁰.03±⁰.13

VIII+IX+X 0.93±⁰.03±⁰.14

agreementwithresultsforprotons [27].Accordingtocoalescence models,d/d isequal to(p/p)² andthe anti-proton toproton ra- tioisindeedcompatiblewithunity [27],independentofpTandof charged-particle multiplicity.Foreachmultiplicity class,the aver- ageoftheanti-deuterontodeuteronratiooverall pTbinsinFig.3 isreportedinTable4.

3.2. CoalescenceparameterB2

Theproductionoflightnucleiandanti-nucleiinppcollisionsis expectedto be theresultofthe coalescenceof protonsandneu- trons that are nearby inspace andhave similar velocitiesat the laststageofthecollision.Thisprocessisdescribedbymodelswith theparameterBA,whereAisthemassnumberofthenucleusun- der study.Here, itcorresponds to B2, whichrelatesthe invariant differentialyieldofdeuteronstotheoneofprotonsviathefollow- ingequation[1,4]

1 2

π

p^d_T

d²N^d dp^d_Tdy

=

B2

1 2

π

p^p_T

d²N^p dp^p_Tdy

₂

.

(2)

InEq. (2) theprotonyieldismeasuredatavalueofhalfofthe deuteron transverse momentum i.e. p^p_T=^pd_T/2 andneutrons are assumedto havethe sameinvariant differential yield asprotons.

Fig.4showstheB₂ parametercomputedaccordingtoEq. (2) asa functionofthetransversemomentumper nucleon(pT/A)forthe differentmultiplicityclasses,scaledbyconstantfactors.Thediffer- ential yieldsfordeuterons andanti-deuteronsshowninFig.2are used.The pT spectraof(anti-)protonsarethosepublishedin [27].

The statistical uncertainties in Fig. 4 are dominated by those of (anti-)deuterons, while the systematic uncertainties by those of (anti-)protons,becausetheprotontermenterstothesquarepower inEq. (2).Inanyoftheconsideredmultiplicity classes,withinthe experimental precision B₂ doesnot showa significant p_T depen- dence as expected in a simple coalescence model [1], where a point-likesourceisassumedthatemitsnucleonswithoutanycor- relationbetweenprotonandneutronmomenta.

In [15], where the results have been reported for inelastic pp collisions without anyselection on theevent multiplicity,the B₂ parameter (red circles in Fig. 5) was found to increase with thetransversemomentum.Thistrendwasreproducedbyanafter- burnermodel [34],whichlooksforcorrelationsbetweennucleons produced by QCD-inspired event generators, and explained as a hard scattering effect [15]. In thiswork the coalescenceparame- terisre-evaluatedforthemultiplicity-integratedsample,indicated hereafterasB₂,bymeansofthefollowingequation

Fig. 3.Anti-deuterontodeuteronratioasafunctionofpTintheconsideredmultiplicityclassesinppcollisionsat√

s=7 TeV.Theverticalbarsrepresentthestatistical uncertaintyandtheopenboxesthesystematicones.

Fig. 4.CoalescenceparameterB2of(anti-)deuteronsasafunctionofthetransverse momentumpernucleon,pT/A,intheconsideredmultiplicity classesinppcolli- sionsat √

s=^{7 TeV.Theverticalbarsrepresentthe}statisticaluncertainties,the openboxesthesystematicones.Thedistributionsineachclassarescaledbycon- stantfactorstoimprovevisibility.

B₂

=

VIII to X

i=^I+^II

(

N_i

/

N

)

Bⁱ₂

(

S_pⁱ

)

²

VIII to X

i=^I+^II

(

Ni

/

N

)

Sⁱ_p

₂

,

(3)

where S_pⁱ =¹/(2

π

pT)d²N_pⁱ/(dpTdy) is the invariant differential yield of protons or anti-protons [27], and Ni/N the fraction of eventsinthei-thmultiplicityclass.Thesetofthep_T-independent Bⁱ₂ measuredin thisworkare alsoused asinputsofEq. (3). The resultford isshownin Fig.5 asa redshaded band, afterbeing normalisedtoinelasticcollisions viathescalingfactor0.852 [35].

Thewidthofthebandrepresentsanuncertaintyofabout4%.This uncertainty includes a 2-3% contribution obtained by consider- ingfinermultiplicityclassesthanthoseusedintheanti-deuteron analysis (anti-proton spectra are measured in [27], B₂ has been

Fig. 5.CoalescenceparameterB₂ofanti-deuteronsasafunctionofthetransverse momentumpernucleonpT/A(redshadedband,seetextfordetails).Theresultis comparedwiththeexperimentaldataforB2measuredininelasticppcollisionsat

√s=7 TeV [15].

interpolated), summed in quadrature to a 3% difference between deuteron and anti-deuteron results. The level of agreement with theexperimentalpoints from[15] indicatesthatpartoftheriseof B2,inthemeasured pT/A range,canbeexplainedwithinasimple coalescencepictureasaconsequenceofthehardeningofthepro- ton spectrawithincreasing multiplicity.The hintfordeviationat high pT leavesroom foradditionalhard scatteringeffects,asthe oneinvokedin [15,34].

Itisworth notingthat oncethe B2 parameterismeasureddi- rectly from the multiplicity-integratedsample andnormalised to inelasticcollisions, the resultobtainedhereisinagreement with the onepublished in[15]. Incentral Pb–Pb collisionsthe coales- cence parameterexhibits an increasing trendwiththe transverse momentum [14] that mightbe attributedtothe presenceof col- lectiveflow [36].

The B2 parameter forone selected interval of transverse mo- mentumpernucleon(0.7 < p_T/A< 0.8 GeV/c)isshowninFig.6as

Fig. 6.Coalescence parameter B2 of (anti-)deuterons as a functionof charged- particlemultiplicityatmid-rapidityinppandPb–Pb collisions [14] attheLHCat thetransversemomentumpernucleonof0.7 <pT/A< 0.8 GeV/c.Theopenboxes representthesystematicuncertainties.

afunction ofcharged-particle multiplicitydensityatmid-rapidity andcomparedtothemeasurementsinPb–Pb collisionsat√

sNN = 2.76 TeV [14].Inasimplecoalescencemodel [1,3],the B2param- eteris expected to be dependent only on themaximum relative momentum of the constituent nucleons coalescing in the bound stateandthereforenomultiplicitydependenceispredicted.Inpp collisions(darkgreencirclesinFig.6),theextractedB2isobserved tovary by about25% fromthelowest tothe highestmultiplicity reachedinthepresentanalysis.Thiseffectismorepronouncedin Pb–Pb collisions and suggests that the increasing volume of the particle-emitting source – which reduces the coalescence proba- bility– has tobe taken into account,as done inmore elaborate coalescencemodels [4].

3.3. Meantransversemomentum

The mean transverse momenta of deuterons and protons are shownasafunctionofthecharged-particlemultiplicityinppcol- lisionsinFig.7.Thedifferencebetweendeuteronandprotonmean momenta is significant, exceptat extremelylow charged-particle multiplicity. In high-multiplicity pp collisions, the ratio between the^pT^{ofdeuteronsandprotonsisabout1.2andissmallerthan} the value (about 1.6) measured in central Pb–Pb collisions [14], wheretheestablishedmassorderingisingeneralattributedtothe emissionofparticlesfromaradiallyexpandingsource.

In pp collisions the multiplicity dependence of the deuteron meantransversemomentumiswellreproducedbycomputingthe deuteron spectra using Eq. (2) with the proton spectra as input andassuming,asinasimplecoalescencemodel,apT-independent B2 value. Note that in central Pb–Pb collisions the Blast-Wave model [20] –ahydrodynamic-inspiredmodelwhichdescribespar- ticleproductionassumingthattheseareemittedfromanexpand- ingthermalisedsource–simultaneouslyfitslightnuclei(deuterons and³He)together withlight hadrons [14]. Onthecontrary,inpp collisions,the^pT^{ofdeuteronsisnotcorrectlyreproducedbyus-} ingthe Blast-Waveparametersthat simultaneouslydescribe pion, kaon and proton spectra from [27], as clearly shown in Fig. 7.

SincetheBlast-Wavemodelisabletoreproduceexperimentaldata solelyin Pb–Pb collisions, we have evidencethat a full hydrody- namicapproachdoesnotconcurrently describethe productionof light hadronsand nucleiin pp collisions. The latteris consistent withacoalescence picturewheretheformation ofweaklybound compositeparticles is expectedtooccur only atthe last stage of

Fig. 7.Meantransversemomentum^pT^{ofdeuteronsandprotonsasafunctionof} charged-particlemultiplicityatmid-rapidityinppcollisionsattheLHC.Theopen boxesrepresentthetotalsystematicuncertaintywhilethecontributionthatisun- correlatedacrossmultiplicity(whereestimated)isshownwiththeshadedboxes.

ThefullshadedareacorrespondstotheexpectedmeanpTofdeuteronsfroma simple coalescencemodelassuminga pT-independent B2 value.Thehollow and dashedareascorrespondtothemeanpT ofprotonsanddeuteronscalculatedby usingtheBlast-Waveparametersthatsimultaneouslyfittothepion,kaonandpro- tonspectra.

the system evolution afterthe collision, namely afterthe kinetic freeze-out.

3.4. Deuteron-to-protonratio

Fig. 8 shows the ratio between the pT-integrated yield of deuterons and protons asa function ofmultiplicity, includingall the presently available measurements performed atthe LHC. For computing the multiplicity-dependent ratio in pp collisions at

√s=^{7 TeV, the deuteron yields reported in Table 3 are used.}

The dN/dy ofprotons are those reportedin [26]. In a naive ap- proach, one wouldpredict an increase ofthe deuteron-to-proton ratio since the number of nucleons increases with the charged- particlemultiplicity.Inppcollisions,theobservedtrendofthed/p ratioisinqualitativeagreementwiththisexpectation,furthersup- portedbythefactthatthesystematicuncertaintiesareexpectedto be largelycorrelatedacrossmultiplicity.Inmoresophisticatedco- alescencemodels [4],thesourcevolumeisalsotakenintoaccount and the rise of the d/p ratio is expected to be the result of an enhanced nucleon density,andnotsimply relatedtothe nucleon abundances.Thepredictionof [4] qualitativelydescribesthedataif theriseinthenucleonabundancedominatesovertheincreasein thevolumesizeinppcollisions.Nosignificantmultiplicitydepen- dence ofthed/p ratio isobserved inPb–Pb collisions within the achievedexperimental precision [14], inagreementwithexpecta- tionsfromthermal-statisticalmodels [18,37].

4. Conclusions

The transverse-momentum spectra of deuterons and anti- deuterons inpp collisions at√

s= 7 TeVhavebeen presentedin fivemultiplicityclasses.Theyarecombinedwiththeprimarypro- tonspectratoextractthecoalescenceparameterB2.Thelatter ex- hibits an approximately constant behaviour with the transverse momentum per nucleon in multiplicity classes in the measured p_T/Arange,inagreementwithasimplecoalescencemodel,where

Fig. 8.RatiobetweenthepT-integratedyieldofdeuteronsandprotonsasafunction ofcharged-particlemultiplicityatmid-rapidityinpp(thiswork)andPb–Pb colli- sions [14] attheLHC.Thedeuteron-to-protonratiomeasuredininelasticppcolli- sionsat√

s=⁰.9,2.76 and7 TeV [15] hasalsobeenreported.

uncorrelatedparticleemissionfromapoint-likesourceisassumed.

Asimplecoalescence picture cannot, however,explain themulti- plicity dependence of the B₂ parameter at fixed transverse mo- mentum (p_T/A = 0.75GeV/c), observed also in Pb–Pb collisions.

Instead,theseobservationspointtowardadependenceofthecoa- lescenceprocessonthevolumeoftheparticle-emittingsource.In fact, the increasing volume of the particle-emitting source with multiplicity plays an effective role in reducing the coalescence probability as predicted by more elaborate models. These mod- elsareabletodescribedataeveninthesmallestcollidingsystem attheLHC,asreportedinthisletter,wherethespatialextensionof thesourceiscomparabletothedeuteronsize.Coalescencemodel calculations,preciselycorrelatingthesizeofthehadronicemission region with the multiplicity, need to be performed to quantita- tivelysupportthecurrentinterpretationoftheresults.

Themean transversemomentum of deuterons hasbeenmea- sured as a function of the charged-particle multiplicity. In pp collisions, the hydrodynamic-inspired Blast-Wave model, which assumes that the particles are emitted thermally from an ex- panding source,does not describe the production of nucleiwith identical freeze-out conditions as lighter hadrons. While in cen- tralPb–Pb collisions thereisevidencethat nucleiandanti-nuclei participate in the expansion of the fireball together with non- compositelighthadrons,inpp collisionssuchevidenceismissing.

Allpresently available measurements of the pT-integratedd/p ratioattheLHChavebeendiscussedasafunctionofthecharged- particlemultiplicity.The observedmultiplicity dependenceofthe d/p ratio suggests that the rise with multiplicity ofthe number of nucleons available for coalescence is faster than the increase ofthe source volume in smallcolliding systems atthe LHC. The multiplicity dependenceof d/p, aswell asthat of B2, hints ata continuousevolutionofdeuteronproductionfromlow-multiplicity pp to Pb–Pb collisions. Measurementsat intermediate multiplici- ties,suchasthosereachedinp–Pb collisions,arebeingperformed toconfirmthispicture.

Theobserved similarities betweenpp andheavy-ion collisions canbetracedbacktocommonunderlyingproductionmechanisms oflight(anti-)nuclei.Thedifferences,suchastheoneappearingin themeantransversemomentumofdeuterons,areextremelyinter- esting because they can shed light on the possibility that nuclei mayemergeatdifferentstagesof thecollision depending onthe initialconditions.

Acknowledgements

The ALICE Collaboration would like to thank all its engineers andtechniciansfortheir invaluablecontributions totheconstruc- tion of the experiment and the CERN accelerator teams for the outstanding performance ofthe LHC complex.The ALICECollab- oration gratefully acknowledges the resources and support pro- videdbyallGridcentresandtheWorldwideLHCComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the followingfunding agenciesfortheir supportinbuildingandrun- ningtheALICEdetector:A.I.AlikhanyanNationalScienceLabora- 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 NacionaldeDesenvolvimentoCientíficoeTecnológico(CNPq),Uni- versidade FederaldoRio GrandedoSul (UFRGS),Financiadorade EstudoseProjetos(Finep)andFundaçãodeAmparoàPesquisado Estado de SãoPaulo (FAPESP),Brazil;Ministryof Science& Tech- nology of China (MSTC), National Natural Science Foundation of China (NSFC) andMinistry ofEducation of China (MOEC), China;

Croatian Science Foundation and Ministry of Science and Educa- tion,Croatia;CentrodeAplicacionesTecnológicasyDesarrolloNu- clear (CEADEN),Cubaenergía, Cuba; Ministry of Education,Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research — Natural Sciences, the Carls- bergFoundationandDanishNationalResearchFoundation(DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commis- sariat à l’Energie Atomique (CEA), Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre Na- tional de la Recherche Scientifique (CNRS) and Rlégion des Pays de laLoire,France; Bundesministerium fürBildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI Helmholtzzentrum fürSchwerionenforschungGmbH,Germany;GeneralSecretariatfor ResearchandTechnology,MinistryofEducation,ResearchandRe- ligions, Greece; National Research, Development and Innovation Office,Hungary;DepartmentofAtomicEnergyGovernmentofIn- dia (DAE), Department of Science and Technology, Government of India(DST), University Grants Commission, Governmentof In- dia(UGC)andCouncil ofScientific andIndustrialResearch(CSIR), India; Indonesian Institute of Science, Indonesia; Centro Fermi - MuseoStorico dellaFisicae CentroStudi eRicerche EnricoFermi andIstitutoNazionalediFisicaNucleare(INFN),Italy;Institute for Innovative Science and Technology, Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion of Science (JSPS) KAKENHIandJapaneseMinistryofEducation,Culture, Sports,Sci- enceandTechnology (MEXT), Japan;Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Interna- cional enCienciay Tecnología(FONCICYT)andDirección General deAsuntosdelPersonalAcademico(DGAPA),Mexico;Nederlandse OrganisatievoorWetenschappelijkOnderzoek(NWO),Netherlands;

TheResearchCouncilofNorway,Norway;CommissiononScience andTechnology forSustainable Developmentin theSouth(COM- SATS),Pakistan;PontificiaUniversidadCatólicadelPerú,Peru;Min- istry ofScience and Higher Education andNational Science Cen- tre, Poland; Korea Institute of Science and Technology Informa- tion and National Research Foundation of Korea (NRF), Republic of Korea; Ministry ofEducation and Scientific Research, Institute of Atomic Physics and Ministry of Research and Innovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research(JINR), MinistryofEducationandScienceofthe Russian Federation, NationalResearch Centre Kurchatov Institute, Russian Science Foundation and Russian Foundation for Basic Research,