at √s N
N
=2. 76TeVat t he LH
C
著者
. ALI CE Col l abor at i on, Bus c h O
. , Chuj o T. ,
M
i ake Y. , Sakai S.
j our nal or
publ i c at i on t i t l e
N
uc l ear phys i c s . A
vol um
e
971
page r ange
1- 20
year
2017- 12
権利
( C) 2018 Publ i s hed by El s evi er B. V.
Thi s i s an open ac c es s ar t i c l e under t he CC BY
l i c ens e
( ht t p: / / c r eat i vec om
m
ons . or g/ l i c ens es / by/ 4. 0/ ) .
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doi: 10.1016/j.nuclphysa.2017.12.004
ScienceDirect
Nuclear Physics A 971 (2018) 1–20
www.elsevier.com/locate/nuclphysa
Production
of
4
He
and
4
He in
Pb–Pb
collisions
at
√
s
NN
=
2
.
76 TeV at
the
LHC
.
ALICE
Collaboration
⋆Received 26October2017;receivedinrevisedform 20December2017;accepted 21December2017 Availableonline 27December2017
Abstract
Resultsontheproductionof4Heand4He nucleiinPb–Pbcollisionsat√sNN=2.76 TeV intherapidity range|y|<1,usingtheALICEdetector,arepresentedinthispaper.Therapiditydensitiescorrespondingto 0–10%centraleventsarefoundtobedN/dy4He=(0.8±0.4(stat)±0.3(syst))×10−6anddN/dy4He=
(1.1±0.4(stat)±0.2(syst))×10−6,respectively.Thisisinagreementwiththestatisticalthermalmodel expectationassumingthesamechemicalfreeze-outtemperature(Tchem=156 MeV)asforlighthadrons. Themeasuredratioof4He/4He is1.4±0.8(stat)±0.5(syst).
2018PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense
(http://creativecommons.org/licenses/by/4.0/).
Keywords:Pb–Pbcollisions;ALICEdetector;LHC;Anti-nuclei
1. Introduction
Theproductionof light (hyper-)nuclei,up toamassnumberA=3, hasbeen reported al-ready in Pb–Pb collisions at √sNN =2.76 TeV at the Large Hadron Collider (LHC). This includesdeuterons,3Heandthehypertritonaswellastheircorrespondinganti-particles[1,2]. Theobservedtotalyieldscanbedescribedwellbyequilibriumthermalmodels[3–9],withonly threefreeparameters:thechemicalfreeze-outtemperatureTchem,thevolumeV andthe baryo-chemicalpotentialμB.ThecurrentbestfittothemeasuredyieldsattheLHC,includingresults
ranginginmassfrompionsupto3He,resultsinaTchem=156 MeV[10].Themeasurementof theproductionyieldsof4Heand4He (A=4)willputadditionalconstraintsonTchem.Sincethe baryo-chemicalpotentialisconsistentwithzero(μB=0.7±3.8 MeV[11])atLHCenergies,
⋆ E-mailaddress:[email protected].
https://doi.org/10.1016/j.nuclphysa.2017.12.004
0375-9474/2018PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense
theexpectedanti-baryontobaryonratioisunity.Therefore,alsotheratioisexpectedtobeclose tounityforparticlescomposedof(anti-)baryons,namelytheanti-nucleiandnuclei[6].
Furthermore,4He istheheaviestanti-nucleuseverobserved.ItwasdiscoveredinAu–Au col-lisionsatRHICbytheSTARCollaboration[12].Outof109Au–Aucollisionsatcentre-of-mass energiespernucleonpair(√sNN)of 200 GeVand62.4 GeV,184He havebeendetected.The correspondingyieldatagiventransverse momentumpT iscomparedtothe predictionofthe thermalmodel[13]andthecoalescencenucleosynthesismodel[14]andfoundtobeconsistent withboth.Aconfirmationofthisobservationisstillpendingasnootherexperimenthasbeen abletodetectthe4He particlesincethen.
Coalescencemodelshavebeensuccessfullyusedtodescribethegeneraltrendsofdeuteron production[15–25]inrelativisticnuclearcollisions,albeitwithanumberofexternalparameters. Thesemodelsareclearlychallengedwiththeregularpatternobservedintheproduction proba-bilityforlightnucleimeasuredbytheSTAR[12]andALICE[1]Collaborations.Toextendthe studiestoA=4themeasurementatLHCenergiesisobviouslyofgreatinterest.
In thispaper,themeasurementofthe productionyieldof the4Heand4He nuclei withthe ALICEapparatusispresented.Besidestheincreaseincollisionenergy,themaindifferencewith respecttothemeasurementbytheSTARCollaborationistheusageofasixlayersiliconvertex detectorinALICE.Togetherwiththeotherbarreldetectorsthisprovidesprecisioninformation onvertexposition,particleidentificationandmomentum.Thedeterminedyieldsarecompared tothermalmodelexpectations.
2. Detectorsetupanddata sample
Thetwomaindetectorsinvolvedintheidentificationofthe4Heand4He particlesaretheTime ProjectionChamber(TPC)[26]andtheTimeofFlight(TOF)detector[27],combinedwiththe starttimedetectorT0.Inaddition,V0detectors([28,29])areusedforcentralitydetermination andtheInnerTracking System(ITS)[30]isemployedfortrackingandthediscrimination be-tweenprimaryandsecondaryparticles[1,31].AfulldescriptionoftheALICEdetectorcanbe foundin[32],whereastheperformanceoftheALICEsub-detectorsisreportedin[33].
Themeasurementofthe4Heand4He particlesisperformedonthe2011datasetofPb–Pb collisionsat√sNN=2.76 TeV.Fromthiscampaign,38.7×106eventsinatriggermixofcentral, semi-centralandminimum-biaseventsareusedinthisanalysis.Thisleadsto20.7×106eventsin the0–10%centralityinterval,17.4×106eventsinthe10–50%centralityintervaland0.6×106 eventsinthe 50–80%centrality interval.The combinedyieldsare extrapolatedtothe0–10% centralityclasswiththeprocedurediscussedinsection4.
3. Analysis
Table 1
Selectioncriteriaappliedforthe4Heand4He analyses.
Track selection criteria value
Number of clusters in TPC ncl>80
Number of hits in ITS nhits>2
TPC track quality χ2/cluster<4 Acceptance in pseudo-rapidity |η|<0.8 Acceptance in rapidity |y|<1 DCAz DCAz<1cm
DCAxy DCAxy<0.1 cm
PID selection value
TPC PID cut ±3σ
TOF mass window ±3σ
ThedE/dxismeasuredintheTPCasafunctionoftherigidityp/z,wherepisthemomentum andzistheelectricchargeinunitsoftheelementarychargee.Thisdistributionofreconstructed chargedparticlesiswelldescribedbytheBethe–Blochformula[34,35]andisuniqueforeach particlespecies.
Primarily,alleventswithatleastoneparticlewithadE/dxcorrespondingtoa3Heand3He orahighermassareselected.ToensureagoodtrackmatchingbetweentheTPCandtheTOF detectors,onlycandidateswithin3standarddeviations(σ)aroundthemeaninthedE/dx(TPC) vs. βγ (TOF)plane are accepted.Here, β denotesthe relativisticvelocityβ =v/candγ is theLorentzfactor.Inordertoselect4Heor 4He particles,candidateswithina3σ bandofthe Bethe–Blochparametrisationinthe dE/dx versusp/z distributionare takenintoaccount. At highermomenta,thetwoBethe–Blochcurvesof4Heor4He andof3Heor3He approacheach other.Tostudyapossiblecontaminationfrom3Heand3He particles,differentnarrowercutsfor theTPCdE/dx selectionbandareinvestigated:whiletheuppercutof theband(3σ)isfixed, thelowercutisrestrictedprogressivelygoinginstepsof0.5unitsfrom−3σ upto0σ.Forall thesesevencuts theproceduredescribed inthefollowingiscarried outandayielddN/dy is determined.
In Fig. 1,the velocity (β) distributions of He candidates are plotted versus rigidity. One can clearly see the separation of 3He and 4He. From these data, the m2/z2 (m=mass of the particle) distributions are calculatedand displayed in the insert of this figure. From the insert, the separation of 3He and 4He can be quantitatively asserted. The m2/z2 is differ-ent for 3He (2.00 GeV2/c4) and4He (3.48 GeV2/c4).Candidates lying within awindowof 2.86 GeV2/c4< m2/z2<4.87 GeV2/c4areidentifiedas4Heor4He particles.Thiswindowis determinedbyafittothepeakinthem2/z2distributionoftheselectedtracks.Becauseof the lowstatistics,thefittingisdonesimultaneouslybothforparticlesandforanti-particles,including secondary4Heknockedoutfromthematerial.AGaussianwithanexponentialtailontheright sideisusedasthefitfunction.Forthebackground,thesumofafirst-orderpolynomialandan exponentialshapeisassumed.Thisisnecessarytodescribethetime-signalshapeof theTOF detector[27].Thepolynomialshapeisneededtocopewithmismatchedcandidatetracksinthe signalregion.Asimilarprocedureisusedin[1].
Fig. 1.VelocityβmeasuredwiththeTOFdetectorasafunctionoftherigidityp/z.Forthisfigureaselectionbandof
−1.5 to3σ aroundthemeanoftheTPCspecificenergy-lossdistributionisrequired.Negatively(positively)charged particlesareshownontheleft(right)side,withpositivetracksinblueandnegativetracksingreen.Thedashedvertical linerepresentsthecutontherigidityp/z=2 GeV/c(appliedonlyforpositivelychargedparticles).Theinsertshows them2/z2distributionsobtainedfromthedatapointsshowninthemainfigure.(Forinterpretationofthereferencesto colourinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)
abackground.Notethat thebackgroundduetoknockoutprocessesissteeplyfallingwith mo-mentumandthesignalisrisinginthismomentumrange.Therefore,only4Hecandidateswitha
p/zgreaterthan2GeV/careaccepted.Thecontaminationathighermomentaisestimatedtobe amaximumof0.13countsoutofatotalcountoftheorderof10,whichisaddedasasystematic uncertainty.
ThesmallnumberofclearsignalcountsobservedbycombiningtheTPCandTOFinformation doesnotgiveanyindicationofbackground.Inordertoestimateanupperlimitonthebackground countsfrommismatchedtracksintheTOFdetectorunderneaththe4Heor4He peakintheTOF mass window,alikelihoodfit under theassumption of aflat backgroundisperformed inthe dE/dxversusβγ planeoutsidethe±3σ matchingband.Inthisway,backgroundcandidatesare identifiedasmismatchedparticles.(Theseareusuallyrejectedandonlyusedforthispurpose.) Duetolimitedstatistics,thisprocedurecannotbeusedifastrongerselectioncriterionisapplied for theTPCdE/dx selection,sinceno4Heor 4He candidatesarelefttoapplythistechnique. Fortheseparticularcases,weassumeaconstantratioof3Hetobackgroundcountsandusethis toestimatethenumberof4Hebackground.
Thebackgroundstemmingfrommisidentificationof(anti-)3Heas(anti-)4Heisestimatedto be morethanoneorderofmagnitude smallerthanthe onefrom themismatch ofTPC tracks when extrapolatedtothe TOFdetectorandistherefore consideredtobe negligible.The esti-matedbackgrounddecreaseswithmorestringentTPC dE/dx cuts.The signal-to-background ratioimprovesdependingonthetightnessofthedE/dxcutfrom1.7to8.4for4Heandfrom1.7 to17.6for4He.
y andintransversemomentumpT.TheshapeofpTspectrainheavy-ioncollisionsistypically describedbyablast-wavemodel[36].Thismodelassumesanaverageradial-flowvelocityβ
andakineticfreeze-outtemperatureTkinasdescribedin[37].Generally,mosthadronpTspectra measuredinheavy-ioncollisionscanbedescribedwellbyonecommonsetofparameters[38]. Surprisingly,thisalsoworkswellforthedescriptionofdeuteronand3Hep
Tspectra[1].Hence thesameprescriptionisusedhereforthepTshapeof4Heand4He particles,namelythesame setofparametersisused,onlythemassischangedtothe4Hemass.
Sinceonlyasmallnumberof4Heand4He particles(144He and94HeforthewidestTPC dE/dxcut)areobserved,apTspectrumcannotbemeasured.Itisestimatedusingtheblast-wave parametersofdeuteronsand3He spectra[1].Thefinalacceptance×efficienciesareobtainedas describedin[39]andareoftheorderof15%for4Heand20%for4He.Thedifferenceoriginates fromthe2GeV/crigiditycutappliedto4Hecandidates.
Forthe4He analysis,theabsorptioninthedetectormaterialistakenintoaccountusingtwo differenttransportcodes,namelyGEANT3[40]andGEANT4[41].Thesetwocodesuse differ-entmodelsfortheestimationoftheabsorptioncrosssection.InGEANT4,aGlaubermodelbased onthewellknownhadronicinteractioncrosssectionsfor(anti-)protonsisimplemented[42].The versionof GEANT3usedinthisanalysisismodified[1]such thatitcalculatestheabsorption basedonanempiricalparameterisation[43],basedonthemeasurementsofanti-deuterons car-riedoutatSerpukhov[44].ThebaselineisgivenbytheabsorptioncalculatedwithGEANT4, whiletheGEANT3basedcorrectionisusedinthesystematicuncertaintyevaluation.The maxi-mumabsorptionprobabilitytowardslowp/zisabout20%.IncontrasttoGEANT4,whichstill showsanabsorptionofabout5%atpT=10 GeV/c,GEANT3exhibitsbasicallynoabsorption above3.5GeV/c.
Themaincontributionstothesystematicuncertaintyonthedeterminedproductionyieldsare:
– TheuncertaintyduetotheunknownshapeofthepTdistributions,whichisdeterminedby usingtheblast-wavemodelbasedonthemeasureddeuteronand3He spectra[1].Thisleads toasystematicuncertaintycontributionofaround13%.
– Only for 4He: The rigidity cut on p/z greaterthan 2 GeV/c itselfhas a systematic un-certainty of 4 to 13% depending on the TPC PID cut. As mentioned before, the sec-ondarycontamination abovethis cutis estimated tobe amaximumof 0.13 counts. This leads to a systematic uncertainty of at minimum 20% and at maximum 49% grow-ing with stricter TPC PID cut. As the number of observed candidates shrinks with stricterTPC dE/dx selection,the systematicuncertainty onthesecondarycontamination grows.
– Onlyfor4He:Theabsorptioncorrectionhasanuncertaintyof7%,estimatedfromthe dif-ferenceofthetwoGEANTimplementations.
Othersystematicuncertaintiesareestimatedbyvaryingthecutsinthelimitsconsistentwith thedetectorresolution.Thecontributionsof thesesystematicuncertainties aretypicallyfound tobebelow thepercentrange. Thesystematic uncertaintyon thechosenTPC PIDcut varies between1%for themostloosecutsand19% for strictercuts.Thisiscausedbythe stronger sensitivityofthestrictercuts,namelytheevenfurtherreducedlownumberofcandidates,which isnotreflectedintheMonteCarlosimulation.
Fig. 2.dN/dyforprotons(A=1)upto4He(A=4)andthecorrespondinganti-particlesincentral(0–10%)Pb–Pb collisionsat√sNN=2.76 TeV.Thebluelinesarefitswithanexponentialfunction.Statisticaluncertaintiesareshown
aslines,whereasthesystematicuncertaintiesarerepresentedbyboxes.
4. Results
Themeasurementisperformedonadatasetincludingcentral,semi-centralandminimum-bias triggeredevents.Tomakeuseofallthedataanalysed,thesemi-centralandminimum-biasevents havebeenextrapolatedto0–10%centralityintervalassumingthattheparticleandanti-particle yieldsscalelinearlywiththecharged-particlemultiplicitydNch/dη.Thisprocedurehasalready been testedto workwellfor the(anti-)hypertritonproduction[2].In addition,d/p and3He/p ratiosaremeasuredtobeapproximatelyflatversusmultiplicitywithinuncertainties[1].Thus,for eachcentralityclass,thenumberofanalysedeventsismultipliedbythecorrespondingmeasured charged-particle densitydNch/dη [28].Ifthisisaddedupanddividedby thetotalnumberof measured eventsit leads to aweighting factor of 1034.To get the final yieldin the 0–10% centralityclassthemeasuredyieldismultipliedwiththedNch/dηfor0–10%centrality(1447.5) anddividedbytheweightingfactor,asdN/dy0−10%=dN/dymeasured×1447.5/1034.
ThisleadstofinalvaluesofdN/dy4He=(0.8±0.4(stat)±0.3(syst))×10−6for4Heand dN/dy4He=(1.1±0.4(stat)±0.2(syst))×10−6for4He.Fortheratio4He/4He weobtain1.4± 0.8(stat)±0.5(syst)(“stat”and“syst”indicatethestatisticalandthesystematicuncertainty).
Themeasuredyieldsinthe0–10%centralityintervalareshowninFig. 2togetherwiththose of (anti-)protons,(anti-)deuteronsand(anti-)3He[1,38](detailsontheextrapolationto0–10% centrality canbefoundin[10]).Thebluelinesareexponentialfitswiththefit functionKeBA
resultinginB= −5.8±0.2,whichcorrespondstoapenaltyfactor(suppressionfactorof pro-ductionyieldfornucleiwithoneadditionalbaryon)ofaround300.Thesamepenaltyfactoris alsoobtainedifthefitisdoneupto3Heonly[1].
The obtainedpenalty factor of around 300 for each additional nucleon is consistent with
Tchem≈160 MeV in the equilibrium thermal models. The measured yields for 4He and 4He nucleiareconsistent withthepredictions from thevarious(equilibrium) thermalmodels
(THERMUS [45], GSI[5,46,47] andSHARE [48–50])with Tchem=156 MeV,as shown in
Fig. 3.Thermalmodelfits,withthreedifferentimplementations,tothelightflavourhadronyieldsincentral(0–10%) Pb–Pbcollisionsat√sNN=2.76 TeV.Thedatapointsaretakenfrom[1,2,38,51–54]anddetailsofthefitscanbefound
in[10,11].Theupperpanelshowsthefitresultstogetherwiththedata,whereasthemiddlepanelshowsthedifference betweenmodelanddatanormalisedtothemodelvalueandthelowerpanelthedifferencebetweenmodelanddata normalisedtotheexperimentaluncertainties.
particlesonlynuclei(deuterons,3Heand4Heand4He)areconsideredforthefit,theresulting temperaturesare154±4MeV.Thepuremeasuredyieldsfor4Heand4He nucleiagree, depend-ingonthemodelimplementation,withinthedetermineduncertaintieswithtemperaturesfrom 135 MeVto177 MeV.Takentogethertheseobservationssuggestthattherelativelyheavy4He and4He nucleiarealsoproducedstatisticallyatthesametemperatureasthelighterparticles.
5. Summaryandconclusion
The ALICE Collaboration has measured the production yieldsof 4He and 4He in central (0–10%)Pb–Pbcollisionsat√sNN=2.76 TeV.Theratio ofthetwoyieldsisconsistentwith unityandtheresultsareingoodagreementwiththepredictionofthestatisticalthermalmodel assumingthesametemperatureof156 MeVasisobtainedfromthefittotheotherlightflavour hadrons.
theratioof4He/4He willbesignificantlyimproved.Inaddition,amassdifferencemeasurement similartowhatwasdonein[56]willbepossible.
Acknowledgements
MinistryofEducation,Science,ResearchandSportoftheSlovakRepublic,Slovakia;National ResearchFoundationofSouthAfrica,SouthAfrica;CentrodeAplicacionesTecnológicasy De-sarrolloNuclear(CEADEN),Cubaenergía,Cuba,MinisteriodeCienciaeInnovacionandCentro deInvestigacionesEnergéticas,Medioambientales yTecnológicas(CIEMAT),Spain;Swedish ResearchCouncil(VR)andKnutandAliceWallenbergFoundation (KAW),Sweden;European OrganizationforNuclearResearch,Switzerland;NationalScienceandTechnologyDevelopment Agency(NSDTA),SuranareeUniversityofTechnology(SUT)andOfficeoftheHigher Educa-tion Commissionunder NRUprojectof Thailand,Thailand; Turkish AtomicEnergy Agency (TAEK),Turkey;NationalAcademyofSciencesofUkraine,Ukraine;ScienceandTechnology FacilitiesCouncil(STFC),UnitedKingdom;NationalScienceFoundationoftheUnitedStates ofAmerica(NSF)andU.S.DepartmentofEnergy,OfficeofNuclearPhysics(DOENP),United StatesofAmerica.
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