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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√sNN = 5.02 TeV is presented. (Anti-)deuterons are identified via their specific energy lossdE/dx and via their time-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/d y isextracted. 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 theALICE collab-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
√
sNN=
5.02 TeV,beingasysteminbetweenthetwoextremesofppandPb–Pbcollisions,areofprominent in-terestandtheyarethesubjectofthisletter.Whiledeuteronshave been measured differentially in multiplicity,the 3He (3He) spec-trum was only obtained inclusively for all non-single diffractive eventsbecauseoftheirlowproductionrate.
Inadditiontotheevolutionoftheintegratedd/pratiofor var-iousmultiplicityclasses,thequestion whetherthetransverse mo-mentum distribution of deuterons is consistent with a collective radial expansion together with the non-composite hadrons is of particularinterest.Suchbehaviourhasbeenobservedforlight nu-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
2. Analysis
The results presented here are based on a low pile-up p–Pb datasamplecollectedwiththeALICEdetectorduringtheLHC run-ningcampaignat
√
sNN=
5.02 TeVin2013.Adetaileddescriptionofthedetectorisavailablein [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 of Sil-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. Inaddition,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 wascollectedexclusivelyinthebeamconfigurationwherethe pro-tontravelstowardsnegative
η
lab.Theminimum-biastriggersignalandthe 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-beamdirection) and
−
3.
7<
η
lab<
−
1.
7 (V0C, p-beam direction). Theeventselectionwas performedina similarwaytothat described in Ref. [18]. A coincidence of signals in both V0A and V0C was requiredonlineinordertoremovebackgroundfromsingle diffrac-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.Thepositionofthereconstructed pri-mary vertex was required to be located within±
10 cm of the nominalinteractionpointinthelongitudinaldirection.Intotal,an eventsample ofabout100million minimum-bias(MB)events af-terallselectionswasanalysed.Thecorrespondingintegrated lumi-nosity,Lint=
NMB/
σ
MB,whereσ
MB istheMBtriggercross-sectionmeasuredwithvan-der-Meerscans,amountsto47.8
μb
−1 witharelativeuncertaintyof3.7% [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 Nev 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-rapidityaresummarizedin Ta-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 ofπ
,K,andp [18] are found to be negligible forthe (anti-)deuteron and3He minimum-bias spectrawith 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 pT-rangeanda dE/dx resolutionof
about 6% forminimum ionisingparticles. The maximumallowed Distance-of-Closest-Approach(DCA)totheprimarycollisionvertex is0.12 cminthetransverse (DCAxy)and1.0 cminthe
longitudi-nal(DCAz) plane.Furthermore,itisrequiredthatthe
χ
2 perTPCclusterislessthan4andtracksofweak-decayproductswithkink topologyarerejected[29],astheycannotoriginatefromthetracks ofprimarynuclei.
Theparticleidentificationperformance oftheTPCandTOF de-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 3σ 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<
pT<
2.
4 GeV/
cisshownintherightpanelofFig.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
/
dx issufficientforaclean identificationusingonlythistechniqueover theentire mo-mentum range1
.
5 GeV/
c<
pT<
5 GeV/
c astheatomicnumberZ
=
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,inordertoaccountforthematerial be-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-drivenFig. 1. Energy lossdE/dx intheTPCandthecorrespondingexpectedenergylossfromaparametrizationoftheBethe-Blochcurve(left).Exampleofthefittothesquared TOFmassdifferencewhichshowsseparatelythesignalandthebackgroundfromtheexponentialtailofprotonsandfrommismatchedtracks(right).
Fig. 2. Tracking acceptance×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 Carlo simula-tion.SincetheTRDwasnotfullyinstalledin2013,thisstudywas repeatedfor regions in azimuthwith and without installed TRD modules.ThematchingefficienciesfortrackscrossingtheTRD ma-terialwere then scaledsuch that the correctedyield agrees with theone obtained fortracks that are not crossing anyTRD mate-rial.Thisprocedureresultsinafurtherreductionoftheacceptance
×
efficiencyof6% fordeuterons and11% foranti-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 secondariesamounts to about 45% to 55% in the lowest pT-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 correctionisestimatedbyrepeatingthetemplatefitprocedure un-der a variation of the DCAz 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 as well ason avariation of thesignal extractioninthe TOFwithdifferentfitfunctions. ThePID related uncertainties for 3He and 3He remain negligible over the entirepT-range dueto the background-free identificationbased on the
TPCdE/dx.Feed-downfromweaklydecayinghyper-tritons(3H)is negligiblefordeuterons [3,4].Sinceonlyabout4-8%ofall 3
de-Table 2
Mainsourcesofsystematicuncertaintiesfordeuteronsand3He aswellastheiranti-particlesforlowandhighp T.
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. Transverse momentumdistributionsofdeuterons(left)andanti-deuterons(right)forvariousmultiplicityclasses.Themultiplicityclassdefinitionisbasedonthesignal amplitudeobservedintheV0AdetectorlocatedonthePb-side.Theverticalbarsrepresentthestatisticalerrors,theemptyboxesshowthesystematicuncertainty.Thelines representindividualfitsusingamT-exponentialfunction.
cayinginto3He passthetrackselection criteriaforprimary 3He,
theremainingcontamination hasnotbeensubtractedandthe un-certainty related to it was further investigated by a variation of theDCAxy-cutindataandafinaluncertaintyof5%isassigned.The
influenceofuncertaintiesinthematerialbudgetonthe reconstruc-tionefficiencyhasbeen studiedby simulatingeventsvaryingthe amount of material by
±
10%. The estimates of the uncertainties relatedto thetrackingandITS-TPCmatchingarebasedona vari-ationofthetrackcutsandare foundtobe approximately5%.The uncertainties related to tracking, transport code, material budget andTPC-TOFmatching arefullycorrelated acrossdifferent multi-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 extractionofpTandpT-integratedyieldsdN/d y,thespectraarefittedindividuallyusingamT-exponentialfunction[42].
The values obtained for dN/d y for (anti-)deuterons are sum-marized in Table 3. They have been calculated by summing up
Table 3
Integrated yieldsdN/d y of(anti-)deuterons. Thefirstvalue isthe statisticaland thesecondisthetotalsystematicuncertaintywhichincludesboththesystematic uncertaintyonthemeasuredspectraandtheuncertaintyofthe extrapolationto lowandhighpT.
Multiplicity classes dN/d y (d) dN/d y (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-differentialyieldintheregionwherethespectrumis
mea-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], andpT-exponential).
Fig. 4 shows the d
/
d ratios as a function of pT for allmul-tiplicityintervals.Theratiosarefoundtobe consistentwithunity withinuncertainties.Thisbehaviourisexpected,sincethermaland coalescence models predict that the d
/
d ratiois givenby(
p¯
/
p)
2Fig. 4. Anti-deuteron todeuteronproductionratioforthefivemultiplicityclasses. Allratiosarecompatiblewithunity,indicatedasadashedgreyline.Thevertical barsrepresentthestatisticalerrorswhiletheemptyboxesshowthetotalsystematic uncertainty.
(seeforinstance [15])andthe p
¯
/
p ratio measured inp–Pb colli-sionsisconsistentwithunityforallmultiplicityintervals [18].Therareproductionof A
>
2 nucleionlyallowstheextraction ofminimum-biasspectrafor3He and3He withtheavailable statis-ticsandthusthe resultisnormalisedto allnon-singlediffractive (NSD) events. In total, 40 3He nuclei are observed, while about29400tracks fromd are reconstructed in thesame data sample. The corresponding spectra are shown in Fig. 5 together with a
mT-exponentialfit whichisused fortheextraction ofthedN/d y
and
pTofthespectra.Thefitisperformedsuchthattheresidualstoboththe3He 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/d y
=
(
1.
36±
0.
16(
stat)
±
0.
52(
syst))
×
10−6 andan averagetransversemomentum of
pT= (
1.
78±
0.
11(
stat)
±
0.
77(
syst))
GeV/
c areobtained.
Theyieldsofp,dand3He forNSDp–Pbeventsandnormalised
totheir spin degeneracyareshowninFig. 6asafunction ofthe massnumberA togetherwithresultsforinelasticppcollisionsand 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 observedforcentralPb–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. Transverse momentumdistributionof3He and3He forallNSDcollisions
(NNSD).Theverticalbarsrepresentthestatisticalerrorswhiletheemptyboxesshow
thetotalsystematicuncertainty.Thelinerepresentsaχ2fitwitham
T-exponential
function(seetextfordetails).
Fig. 6. Production yielddN/d y normalisedbythespindegeneracyasafunctionof themassnumberforinelasticppcollisions,minimum-biasp-PbandcentralPb-Pb collisions[12,13,18,48,49].Theemptyboxesrepresentthetotalsystematic uncer-taintywhilethestatisticalerrorsareshownbytheverticalbars.Thelinesrepresent fitswithanexponentialfunction.
phasespace. Inthispicture,the deuteronmomentumspectraare relatedtothoseofitsconstituentnucleonsvia [50,51]
Ed d3Nd dp3d
=
B2 Ep d3Np dp3p 2,
(1)wherethemomentumofthedeuteronisgivenby pd
=
2pp.Sincetheneutronspectraareexperimentallynotaccessible,theyare ap-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 andthe square of the proton yield at pT,p
=
0.
5pT,d. The obtainedB2-valuesareshowninFig.7.Initssimplestimplementation,the
coalescencemodelforuncorrelatedparticleemissionfroma point-like sourcepredicts that theobserved B2-valuesare independent
of pTandofeventmultiplicity (called“simplecoalescence”inthe
following).Withinuncertaintiesandgiventhecurrentwidthofthe multiplicityclasses,theobservedpTdependenceisstillcompatible
withtheexpectedflatbehaviour(foradetaileddiscussionsee[6]). Moreover,adecreaseofthemeasured B2 parameterwith
increas-ingeventmultiplicityforafixed pTisobserved.Thiseffectiseven
explana-Fig. 7. Coalescence parameterB2asafunctionofpTfordifferentV0Amultiplicity
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
pTvaluesaresimilartothoseof(
)andonly
slightlyhigherthanthoseofp(p).
¯
Note that simple coalescence models give a significantly dif-ferent prediction for the
pT of deuterons with respect tohy-drodynamicalmodels. This canbe best illustrated withtwo sim-plifying requirements which are approximately fulfilled in data. Firstly, thecoalescence parameter is assumedflatin pT and
sec-ondly the proton spectrum can be described by an exponential shape, i.e. C exp
(
−
pT/
T)
with two parameters C and T . In thiscase,the shapeofthe deuteronspectrumcan beanalytically cal-culated based on the definition of B2. Due to the self-similarity
featureoftheexponentialfunction,
(
exp(
x/
a))
a=
exp(
x)
,the spec-tral shape of the proton andthe deuteron are then found to be identical: 1 2πpd T d2Nd d y dpd T=
B2 1 2πppT d2Np d y dpTp 2=
B2 C exp(
−
p p T T)
2=
B2 C exp(
−
p d T 2T)
2=
B2C2exp(
−
pdT T) .
(2)Thus,thesame
pTforboth particlesisexpectedandthebe-haviour observed in p–Pb collisions is well described by simple coalescencemodels.Thisfindingcanbeevenfurthersubstantiated bydirectly calculatingthe
pTofdeuterons assuming aconstantvalueof B2 andusingthemeasuredprotonspectrumasinput.As
shownin Fig. 8 (right), in this case, a good agreement withthe dataisfoundconsideringthatalargefractionofthesystematic un-certaintyiscorrelatedamongdifferentmultiplicitybins.The Blast-Wave model [43] fails to describe the
pT valuesfor deuteronsusingthecommonkineticfreeze-outparametersfrom [18],which describesimultaneouslythespectraofpions,kaons,andprotons.
Fig. 8. Mean pT ofvariousparticle speciesasa functionofthemean
charged-particle densityat mid-rapidityfor differentV0Amultiplicityclasses. Theempty boxesshowthetotalsystematicuncertaintywhiletheshadedboxesindicatethe contributionwhichisuncorrelatedacrossmultiplicityintervals(left).Comparison ofpTofprotonsanddeuteronswiththesimplecoalescenceandtheBlast-Wave
modelexpectations.TheshadedareasshowtheexpectedpTfordeuteronsfroma
simplecoalescencemodelassumingapT-independentB2aswellasthecalculated
pTforprotonsanddeuteronsfromtheBlast-Wavemodel [43] usingthekinetic
freeze-outparametersforpions,kaons,protonsandfrom [18] (right).
Fig. 9. Deuteron-over-proton ratioasafunctionofcharged-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(red sym-bols).Suchatrendisconsistentwithathermal-statisticalapproach andthe magnitudeof themeasured valuesagreewithfreeze-out temperatures intherangeof150-160 MeV [3]. Thed/p ratio ob-tainedininelasticppcollisionsincreaseswithmultiplicity [6].The resultsinp–Pb collisionsbridgethetwomeasurementsintermsof multiplicityandsystemsizeandshowanincreaseofthed/pratio with multiplicity.Here, the low (high) multiplicity value is com-patible with the resultfrom pp (Pb–Pb) collisions. Note that the experimental significanceofthisenhancementisfurther substan-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 strangenessconservationinsmallersystemsgivesaqualitative ex-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–Pbcollisionsandsmallerthantheone mea-suredinpp collisions.The transversemomentum distributionsof deuteronsbecomeharderwithincreasingmultiplicity.Two intrigu-ingobservationsthathavebeenrecentlyreportedbyALICE[6] in highmultiplicitypp collisionsareconfirmedinthepresentpaper. Firstly,the
pTvaluesofdeuteronsarecomparabletothoseofthemuchlighter
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 andtechniciansfortheirinvaluablecontributionstothe construc-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 inbuildingand run-ningtheALICEdetector: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;MinistryofCommunications andHigh Tech-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 and Educa-tion,Croatia;CentrodeAplicacionesTecnológicasyDesarrollo Nu-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)KAKENHIandJapaneseMinistryof Ed-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,RussianScienceFoundationandRussian Foun-dation for Basic Research,Russia; Ministry of Education, Science, ResearchandSportofthe Slovak Republic,Slovakia; National Re-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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