Contents lists available atScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
3
H and 3 ¯
H production in Pb–Pb collisions at √
s NN = 2 . 76 TeV
.ALICE Collaboration
a r t i c l e i n f o a b s t ra c t
Articlehistory:
Received12July2015
Receivedinrevisedform21January2016 Accepted21January2016
Availableonline25January2016 Editor:L.Rolandi
The productionof thehypertritonnuclei 3H and 3¯
H has beenmeasured forthe firsttime inPb–Pb collisions at √s
NN=2.76 TeV with theALICE experiment atLHC. The pT-integrated 3H yieldin one unityofrapidity,dN/dy×B.R.3
H→3He,π−=(3.86±0.77(stat.)±0.68(syst.))×10−5inthe0–10% most central collisions,is consistentwith the predictionsfrom astatistical thermal model using the same temperature as for the light hadrons. The coalescence parameter B3 shows a dependence on the transverse momentum, similar tothe B2 of deuteronsand the B3 of3He nuclei.The ratio of yields S3=3H/(3He×/p)wasmeasuredtobeS3=0.60±0.13(stat.)±0.21(syst.)in0–10% centralityevents;
this value is comparedto different theoretical models.The measured S3 is compatiblewith thermal modelpredictions.Themeasured3H lifetime,τ=181+−5439(stat.)±33(syst.)ps isinagreementwithin1σ
withtheworldaveragevalue.
©2016CERNforthebenefitoftheALICECollaboration.PublishedbyElsevierB.V.Thisisanopen accessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introductionandphysicsmotivations
High-energy heavy-ion collisions offer a unique way to study thebehaviour ofnuclear matterunder conditionsofextremeen- ergydensities. AtLHCenergies, particlescarryingstrangenessare abundantly produced and light clusters of nucleons and hyper- ons,calledhypernuclei,areexpectedtobeformed[1].Sincetheir firstobservation[2],therehasbeenaconstantinterestinsearch- ing for new hypernuclei as they offer an experimental way to study the hyperon–baryon (Y N) and the hyperon–hyperon (Y Y) interactions, which are relevant for nuclear physics and nuclear astrophysics. For instance, the Y N interaction plays a key role in understanding the structure of neutron stars [3–6]. The pro- ductionof hypernuclei inheavy-ioncollisions has beenproposed andstudied fora long time [7,8] andat ultrarelativisticenergies it ispossible toproduce particles otherwise inaccessible,such as anti-hypernuclei.Infact,whilemany-hypernucleihavebeenob- served,the firstobservationof an anti-hypernucleusisratherre- cent and was reported from the analysis of Au–Au collisions at
√sNN=200 GeV bytheSTARCollaborationatRHIC [9].Sincehy- pernuclei are weakly bound nuclear systems, they are sensitive probes of thefinal stagesof theevolution of the fireballformed intheheavy-ioncollisions [10]. Theyieldofhypernuclei candis- tinguishbetweendifferentproductionscenarios,usuallydescribed usingtwo differenttheoretical approaches. The firstone isbased onacoalescencemodel[11],whilethesecondoneisbasedonthe
E-mailaddress:[email protected].
assumption that all theparticlespecies canbe described usinga statistical thermal model[12]. Inthe statistical thermal modela constantentropyoverbaryonratio[13]couldexplainwhyobjects with such a small binding energy (few MeV) could survive the high temperature (≈170 MeV) expanding fireball. On the other hand,ifhypernucleiareproducedthroughcoalescenceofprotons, neutronsandhyperonsatfreeze-out[14],theywillprovideamea- surement ofthe local correlation betweenbaryons andhyperons (strangeness)[15].
Thisletterpresentsastudyofhypertritonandanti-hypertriton productionat√
sNN=2.76 TeV Pb–PbcollisionsbytheALICECol- laboration. The paper is organised as follows. In Section 2 the ALICEdetector isbriefly described. The datasample, analysisde- tails and systematic uncertainties are presented in Section 3. In Section4theobtainedresultsarecomparedwiththeoreticalmod- els.FinallytheconclusionsaredrawninSection5.
2. TheALICEdetector
A detailed description of the ALICE detector can be found in [16] andreferences therein.Forthe presentanalysisthe main sub-detectorsusedaretheV0detectors,theInnerTrackingSystem (ITS) and the Time Projection Chamber (TPC), which are located inside a 0.5 T solenoidal magnetic field. The V0 [17] detectors areplacedaroundthebeam-pipeoneithersideoftheinteraction point:onecoveringthepseudorapidityrange2.8<
η
<5.1 (V0-A) andtheotheronecovering −3.7<η
<−1.7 (V0-C).Thecollision centrality isestimated by usingthe multiplicity measured in the V0 detectors along with a Glauber modelsimulation to describe http://dx.doi.org/10.1016/j.physletb.2016.01.0400370-2693/©2016CERNforthebenefitoftheALICECollaboration.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
themultiplicitydistributionasafunctionoftheimpactparameter [18,19].TheITS[20] hassixcylindricallayers ofsilicondetectors withradii between3.9 and43 cmfrom thebeam axis,covering thefullazimuthalangleandthepseudorapidityrangeof|
η
|<0.9.ThesamepseudorapidityrangeiscoveredbytheTPC[21],which isthemaintrackingdetector.HitsintheITSandfoundclustersin theTPCare usedtoreconstructcharged-particletracks.Theseare usedtodeterminetheprimarycollisionvertexwitharesolutionof about10 μmin thedirectiontransverseto thebeams forheavy- ioncollisions. The TPC is used forparticle identification through thedE/dx(specificenergyloss)intheTPCgas.
3. Analysis
The (anti-)hypertriton (3¯
H) 3H is the lightest observed hy- pernucleus and is a bound state formed by a (anti-)proton, a (anti-)neutron and a (anti-). The 3H and 3¯
H production yields were measured by detecting their mesonic decay (3H→
3He+
π
−) and(3¯H→3He+
π
+) via the topological identifica- tionof secondary verticesandthe analysisof theinvariant mass distributionsof(3He+π
−)and(3He+π
+)pairs.The analysis was done using Pb–Pb collisions at √ sNN = 2.76 TeV taken in 2011. The events were collected with an in- teraction trigger requiring a signal in both V0-A andV0-C. Only eventswithaprimaryvertexreconstructedwithin±10 cm,along thebeamaxis,fromthenominalpositionoftheinteractionpoint were selected.The analysed sample, collected withtwo different centrality trigger configurations corresponding to the 0–10% and 10–50% centralityintervals,containedapproximately20×106 and 17×106events,respectively.
The 3H can be identified via the invariant mass of its de- cay products and, since it has a lifetime similar to the free (c
τ
∼8 cm), inmostcases it ispossible to identifyits decay up toafewcmawayfromtheprimaryvertex.The decayvertexwas determinedbyexploitingasetofgeometricalselections:i)thedis- tanceof closest approach (DCA) betweenthe two particle tracks identified using dE/dx in the TPCas 3He andπ
, ii) the DCAof theπ
± tracksfromtheprimaryvertex,iii)thecosineoftheangle betweenthetotalmomentumofthedecaypairsatthesecondary vertexand a vector connecting the primary vertex and the sec- ondaryvertex(pointing angle),andiv) a selection onthe proper lifetime(cτ
) of thecandidate.An additionalselection onthe 3H (3¯H)rapidity(|y|<0.5)wasapplied.
Fig. 1 shows the invariant mass distribution of (3He,
π
−) on theleft and (3He,π
+) onthe rightfor eventswith10–50% cen-tralityinthepairtransversemomentumrange2≤pT<10 GeV/c.
In order toestimate thebackground, foreach event the
π
track detected atthe secondary vertexwas rotated20 timesby a ran- dom azimuthal angle. The shape of the corresponding (3He,π
) invariant mass distributionwas foundto reproduce theobserved backgroundoutsidethesignal region.Thedata pointswere fitted withafunctionwhichisthesumofaGaussianandathirddegree polynomial, used to describe the signal and the background, re- spectively.Thebackgroundwasnormalizedtothemeasuredvalues inthe 3.01–3.08 GeV/c2 region. Thefit tothe backgrounddistri- bution was used to fix the parameters of the polynomial inthe combinedfit.In the 0–10% most central collisions, a signal was extracted in three transverse momentum intervals(2≤pT<4 GeV/c, 4≤ pT<6 GeV/c, 6≤pT<10 GeV/c), for both 3H and 3¯
H. In the 10–50% centrality class a signal both for 3H and 3¯
H was ob- tained for the full pT range under study (2≤pT<10 GeV/c).
From thecombinedfitresultsthemeanvalue,thewidthandthe yieldofthesignalwereextracted. Themeaninvariantmass(
μ
= 2.991±0.001(stat.)±0.003(syst.)GeV/c2) is compatible within uncertainties with the mass from the literature [22]. The signal width,σ
=(3.01±0.24(stat.))×10−3GeV/c2 obtained as the mean value ofall the measured widths, is reproduced by Monte Carlo simulations and is driven by detector resolution. The raw yieldofthesignalwasdefinedastheintegraloftheGaussianfunc- tion ina±3σ
regionaround themeanvalue. The significanceof bothmatterandanti-mattersignalsvariesinthedifferent pT bins inthe rangeof 3.0–3.2σ
forthe mostcentral collisions (0–10%) andrangesfrom3to3.5σ
forthesemi-centralones(10–50%).A correction factor which takes into account the detector ac- ceptance,the reconstruction efficiency, andtheabsorption of 3H (3¯
H) bythematerialcrossedwasdeterminedasafunctionofpT. Detector acceptanceand reconstruction efficiencywere evaluated usinga dedicatedHIJINGMonte Carlosimulation [23], wherethe onlyallowed decaywas thetwo-bodydecaytochargedparticles, (3H→3He+
π
−)and(3¯H→3He+
π
+).Thesimulatedparticles werepropagatedthroughthedetectorusingtheGEANT3transport code[24]andthenprocessedwiththesamereconstruction chain asforthedata.Sincetheabsorptionof(anti-)(hyper)nuclei isnotproperlyim- plementedinGEANT3,acorrection basedonthep(p)absorption was applied in order to take into account the absorption of 3H (3¯
H) and3He(3He)by thematerialoftheALICEdetector.Inthis approach,the3Heand3H weretreatedasstatesofthreeindepen- dentp(p).The3Hewasconsideredasaboundstateof3protons
Fig. 1.Invariantmassof(3He,π−)(left)and(3He,π+)(right)foreventswith10–50%centralityinthepair2≤pT<10 GeV/cinterval.Thedatapointsareshownasfilled circles,whilethesquaresrepresentthebackgrounddistributionasdescribedinthetext.Thecurverepresentsthefunctionusedtoperformthefitandusedtoevaluatethe backgroundandtherawsignal.Thesignificancein±3σaroundthepeakis3.5and3.0fortheinvariantmassdistributionof(3He,π−)and(3He,π+),respectively.
Table 1
SummaryofsystematicuncertaintiesforthethreepTintervalsandinthefullrange(F.R.)considered.Theseuncertaintiesarethesameforeventswith0–10%and10–50%
centrality.Forthefinalsystematicuncertaintyevaluationtheywereaddedinquadrature.
3
H 3¯
H
pTintervals (GeV/c) pTintervals (GeV/c)
2–4 4–6 6–10 F.R. 2–4 4–6 6–10 F.R.
Absorption 5.4% 5.3% 5.4% 5.4% 13% 10% 8.9 % 10.6%
Tracking efficiency 10% 10% 10% 10% 10% 10% 10% 10%
3
H lifetime 8.5% 8.5% 8.5% 8.5% 8.5% 8.5% 8.5% 8.5%
Signal extraction method 9% 9% 9% 9% 9% 9% 9% 9%
Extrapolation at lowpT – – – 5% – – – 5%
Total 16.8% 16.8% 16.8% 17.5% 20.5% 18.8% 18.2% 19.8%
Fig. 2.Left:TransversemomentumspectramultipliedbytheB.R.ofthe3H→3He+π−decayfor3H (filledcircles)and3¯H (squares)forthemostcentral(0–10%)Pb–Pb collisionsat√
sNN=2.76 TeV for|y|<0.5.Symbolsaredisplacedforbettervisibility.Thedashedlinesaretheblast-wave curvesusedtoextracttheparticleyieldsintegrated overthefullpTrange.Inordertotakeintoaccountthelargebinningusedintheanalysisandthelimitednumberofbins,thecentre ofeachbinwasevaluatedweighting theactualbincentre withtheblast-wave function.Right:3¯H to3H ratioasafunctionofpT.Inbothpanelsstatisticaluncertaintiesarerepresentedbybarsandsystematic uncertaintiesarerepresentedbyopenboxes.
becausetheprotonabsorptioncorrectionintheALICEdetectorwas measured [25]. The direct measurement offers the advantage of havingaprobabilitydensitywhichtakesintoaccounttheeffective material ofthedetector crossed by acharged particle.The effect of using protons instead of neutrons was tested withdeuterons, whichwereconsideredasaboundstateof2protonsandtheab- sorption correctionwas evaluatedwith thesame modelused for 3He. The result was compared with the one obtained with the absorptioncorrectionofGEANT3patchedwithhadroniccrosssec- tionsfordandd.Thetwocalculatedabsorptioncorrectionswhere found tobe consistent within uncertainties. Totake into account thesmallseparationenergy(B(3H)=0.13±0.05 MeV[26]), theabsorptioncrosssectionofthe3H wasincreasedby50%with respecttotheoneofthe3He.Thischoicewas basedonthetheo- reticalcalculationof3H absorptioncross-section[27]on238Uand its ratiowiththeextrapolationof 3Hecross section onthesame target [28].Using thesame extrapolationitwas possible toeval- uatethesameratioonALICEmaterials.The correctionappliedto theextractedyieldwas about12% for3H andabout22% for3¯H.
Thetotal systematicuncertaintytakesinto account,aslower and upperlimits ofthe 3H (3¯
H) absorption cross section, valuesre- spectivelyequaltoortwotimeshigherthantheabsorptioncross section of 3He (3He). This uncertainty is pT dependent, and its valuesarereportedinTable 1.Othersources ofsystematicuncer- taintiesintheyieldevaluationwereestimated:
– The systematicuncertainty dueto the single-track efficiency, andthe differentchoices of the track quality selections was takenfrom[29].A10%uncertaintyisquotedforthetwobody decayof3H.
– 3H lifetime:sincethe3H lifetimeisnotaccuratelyknown,the influenceofvaryingthe3H lifetimeontheefficiencywaseval- uated by variation of theproper lifetime of the injected 3H intheMonteCarlosimulation.Theassociateduncertaintywas estimatedusingtwoadditionaldedicatedMonteCarlosimula- tionswithdifferentlifetimes.Theinjectedlifetimeof3H (3¯
H) was varied (±1
σ
) withrespectto theresultobtainedinthis analysis,leadingtoanuncertaintyof8.5%.– Theuncertaintyrelatedtothesignalextractionprocedurewas evaluatedbyconstrainingfitparameters(
μ
andσ
)indifferent ways.Thissourceledtoa9%uncertainty.ThesystematicuncertaintyduetotheuncertaintyoftheALICEde- tectormaterialbudgetandpTdistributionintheMonteCarloused fortheefficiencyestimationledtoa1%systematicuncertainty.
The 3H and3¯
H spectra areshowninFig. 2 (leftpanel),mul- tipliedbythebranchingratio(B.R.)ofthe3H→3He+
π
−decay.The anti-hypertriton to hypertriton ratio as a function of pT is shownin Fig. 2(right panel).Itis consistentwithunityover the wholeconsideredpTrange,asexpectedfromzeronetbaryonden- sity atLHC energies. Inthe ratio,the commonsystematicuncer- tainties(trackingefficiency,lifetime,andsignalextractionmethod) canceloutandhavethereforebeenremoved.
In order to take into account the unmeasured pT region and toextracttheparticleyieldsintegratedoverthefull pT range,the spectrawerefittedusingablast-wavefunction[30]whoseparam- etervaluesweretakenfromthedeuteronanalysis[31]leavingthe normalization free. The function fits the data with a
χ
2/NDF of 0.92.TheextrapolationinthepT<2 GeV/cregioncontributes28%to thefinalyield forboth3H and3¯
H,whilethecontributionfor
Table 2
Summaryofsystematicuncertaintiesforthedetermi- nationoftheproperlifetimeof3H+3¯H.
Source Value
Signal extraction method 9%
Tracking efficiency 10%
Absorption 12%
Total 18%
Fig. 3.Measured dN/d(ct)distributionandanexponentialfitusedtodetermine thelifetime. Thebarsandboxesarethe statisticalandsystematicuncertainties, respectively.
pT>10 GeV/c is negligible. Differenttransverse momentum dis- tributionswereusedtoevaluatethesystematicuncertaintyrelated totheextrapolation,whichwasfoundtobe5%.
Todeterminethe lifetime, the(3H+3¯ H) sample was divided into four intervals in ct=M Lc/p, where M is the mass, L the decay length, c is the speed of light, and p is the total mo- mentum. The mass was fixed to the value from the literature M=2.991 GeV/c2[22].Forthedeterminationofthelifetime,both centrality classes 0–10% and 10–50% were used. The signal was extractedintheintervals: 1≤ct<4 cm, 4≤ct<7 cm, 7≤ct<
10 cm and10≤ct<28 cm.Toestimatethelifetime,therawsig- nalwas corrected by the detectoracceptance, the reconstruction efficiencyandtheabsorptionof3H (3¯
H)inthematerial.Thesame dedicatedHIJINGMonteCarlosimulationandthesameprocedure usedtodeterminethe pT dependenceoftheefficiencywereused.
ThesourcesofsystematicuncertaintyareshowninTable 2.
Anexponentialfitwasperformedtodeterminethelifetime.The dN/d(ct) distributionandtheexponentialfitare showninFig. 3.
Thevertical bars show thestatisticaluncertainties andthe boxes representthesystematicuncertainties.Theslope ofthefitresults inaproperdecaylengthofc
τ
=5.4+−11..62(stat.)±1.0(syst.)cm.
Thelifetimesoflight-hypernuclei(A≤4)areexpectedtobe very similar to that of the free , ifthe in the hypernucleus isweaklybound[33].Themeasuredlifetimesoflight hypernuclei suchas3H[9,34–40]arenotknownaspreciselyasthelifetime, andtheoretical predictions [33,41–48] are scatteredover a large
Fig. 4.3H lifetime(τ)measuredbyinthisanalysis(reddiamond)comparedwith published results. The bandrepresents the world averageof 3H lifetime mea- surements
τ=215+−1816
ps,whilethedashedlinerepresentthelifetimeofas reportedbytheParticleDataGroup[32].(Forinterpretationofthereferencesto colourinthisfigurelegend,thereaderisreferredtothewebversionofthisarti- cle.)
range,too.Recently, astatisticalcombinationoftheexperimental lifetime estimations of 3H available in literature was published, resultinginanaveragevalue
τ
=216+−1918
ps[49].
With the present data, a lifetime of
τ
=181+−5439(stat.)± 33(syst.)
ps has been obtained. It is compared with the previ- ously published results in Fig. 4. Our result, together with the previous ones, was used to re-evaluate the world average of the existingresultsusingthesameprocedureasdescribedin[49].The obtainedvalue,
τ
=215+−1816ps
,isshownasabandinFig. 4.The resultobtained inthis analysisis compatiblewiththe computed average.
4. Comparisonbetweenexperimentalyieldsandtheoretical models
The product of the pT-integrated yield and the B.R. of the 3
H→(3He+
π
−)decayfor3H and3¯H fortwocentralityclasses (0–10%and10–50%)arereportedinTable 3.Thesystematicuncer- taintiesalsoincludethecontributionduetothelow pT extrapola- tionasdescribedinSection3.
It ispossibleto comparethe pT-integrated3H yieldat differ- entcentralities by scaling themaccordingto thecharged-particle densities dNch/d
η
. For central (0–10%) collisions dNch/dη
= 1447±39,whileforsemi-central(10–50%)dNch/dη
=575±12.Theratio
3H+3¯H
(0−10%) 3
H+3¯H
(10−50%)
dNch/dη(0−10%) dNch/dη(10−50%)
=
1.
34±
0.
35(
stat.) ±
0.
24(
syst.)
(1) is compatible with unity within 1σ
. The 3H (3¯H) production scaleswithcentralitylikethecharged-particleproduction.
Table 3
pT-integrated3H yieldtimestheB.R.ofthe 3H→(3He+π−)decay,for3H and3¯H inPb–Pbcollisionsat
√sNN=2.76 TeV fordifferentcentralityclassesin|y|<0.5.ForeachcentralityintervaltheaveragedNch/dηis alsoreported[18].
Centrality dNch/dη 3H dN/dy×B.R.×105 3¯H dN/dy×B.R.×105 0–10% 1447±39 3.86±0.77(stat.)±0.68(syst.) 3.47±0.81(stat.)±0.69(syst.) 10–50% 575±12 1.31±0.37(stat.)±0.23(syst.) 0.85±0.29(stat.)±0.17(syst.)
Fig. 5.pT-integrated3H yieldtimesbranchingratioasafunctionofbranchingratio (dN/dy×B.R.vsB.R.).Thehorizontal lineisthe measuredvalue andthe band representsstatisticalandsystematicuncertaintiesaddedinquadrature.Linesare differenttheoreticalexpectationsasexplainedinthetext.
4.1. Comparisonbetweenthermalmodelsandexperimentalyields Since the decay branching ratio of the 3H→3He+
π
− was estimatedonlyrelativetothecharged-pionchannels[39],thecor- responding value (B.R.=35%) provides an upper limit for the absolute branching ratio. On the other hand, a theoretical esti- mation for the 3H→3He+π
− decay branching ratio, which alsotakes into account decayswith neutralmesons decays,gave a B.R. = 25% [33]. Assuming a possible variation on the B.R. in the range 15–35%, we show in Fig. 5 a comparison of our re- sult with different theoretical model calculations [1,50,51]. The measured dN/dy×B.R.is shownasa horizontalline, wherethe band represent statistical and systematic uncertainties added in quadrature while the different theoretical models are shown as lines.The dataarecomparedwiththefollowingmodels:twover- sions of the statistical hadronization model [1,50] and the hy- bridUrQMD model [51], which combines the hadronictransport approach with an initial hydrodynamical stage for the hot and densephaseofaheavy-ioncollision.Thetwoversionsofthesta- tistical hadronization model used are the equilibrium statistical model (GSI-Heidelberg), described in [1] and references therein, withatemperature Tch=156 MeV andthenon-equilibriumther- malmodel(SHARE),describedin[50]andreferencestherein,with Tch=138.3 MeV,γ
q=1.63 andγ
s=2.08,whereγ
q andγ
s rep- resent the quark and strangeness phase space occupancy of the systemcreatedafterthecollision,respectively.Thenon-equilibriumthermalmodel(SHARE)[50]overestimates the(anti-)hypertriton pT-integratedyield by afactor from2to 5 depending on the branching ratio (B.R.). For the branching ra- tio expected following [33] (B.R.=25%) the equilibrium thermal model[1](GSI-Heidelberg)andthehybridUrQMDmodel[51]de- scribethedatabest.
Afit,basedonthethermalfitdescribedin[1],was performed to the hypertriton yield and to yields from other light flavour hadrons, except K∗, previously measured by our Collaboration at
√sNN=2.76 TeV [31,52–55]. The inclusion of the deuteron, 3He [31] and 3H in the thermal fit [56] inaddition to lighter parti- cles,doesnot changetheresultingfreeze-outtemperature(Tch= 156±2 MeV)andthemeasuredyieldsofthenucleiandthehyper- tritonagreewiththemodelpredictionswithin1
σ
.Theresultson thehypertritonyieldsdiscussedabovewerealsousedtodetermine the3H/3He and3¯H/3He ratios,whichareshowninTable 4.Inor- derto computetheratios,ourprevious measurementof3Heand
Table 4
Ratiosof3H/3He and3¯H/3He assumingaB.R.=25%forthe3H→3He+πde- cay[33].Theresultsfrom3Heand3He analysismeasuredbytheALICEexperiment wereused[31].
Centrality 3H/3He 3¯H/3He
0–10% 0.47±0.10(stat.)±0.13(syst.) 0.42±0.10(stat.)±0.13(syst.) 10–50% 0.40±0.11(stat.)±0.11(syst.) 0.26±0.09(stat.)±0.08(syst.)
Fig. 6.Theratios3H/3He and3¯H/3He determinedbythepresentanalysis(filled circles)formatterandanti-mattercomparedwithSTARresults(squares)[9]and theoreticalpredictions(lines)[1,50,57,58]asdescribedinthelegend.
3He yields[31]wereused.Theseresultswerecomparedwithdif- ferenttheoreticalmodels[50,57,58]andresultsfromtheSTARex- periment[9]at√
sNN=200 GeV,whichusethesameB.R.=25%.
The comparison is shownin Fig. 6. STAR resultsare higher than ALICEresults,butstillcompatiblewithinuncertainties.
4.2. DatacomparisontocoalescencemodelsandS3ratio
At the moment no prediction of the 3H and 3¯
H yields in a non-trivialdynamical coalescencemodelisavailable atLHCener- gies.Neverthelesswithinasimplecoalescencemodelitispossible to evaluatesome parameters whicharesensitive tothe existence ofcoalescence mechanismsforhypernucleiformation.Intheem- piricalcoalescencemodel[11]thecrosssectionfortheproduction ofaclusterwithmassnumber A isrelatedtotheprobability that Anucleonshaverelativemomentalessthanp0,whichisafreepa- rameterofthemodel.Thisprovidesthefollowingrelationbetween theproductioncrosssectionsofthenuclearclusteremittedwitha momentum pA andthenucleonemittedwithamomentum pp
EA
d3NA
d3pA
=
BA Epd3Np
d3pp
A,
(2)where pA=App. Fora givennucleus, thecoalescence parameter BAshouldnotdependonthemomentumsinceitdependsonlyon theclusterparameters:
BA
=
4π
3 p30
(A−1) M
mA (3)
whereMandmarethenucleusandtheprotonmass,respectively and p0 is the relative momentum between the constituent nu- cleons of the nucleus. The parameter B3 was computed for 3H accordingtoEquation(2)usingthespectrumshowninFig. 2and ourpreviousmeasurementoftheproton[52]and[54]spectra.
Fig. 7.Left:B2asafunctionofpT/A ford (filledcircles)[31],3He(emptycircles)[31],and3H (filledsquares).The B(2d,3H)and B(2d,3He)wereevaluatedasexplainedin thetext.k1=m3 Hem2dmp,andk2=mm22dm
pm3 H
.Right:S3 ratiomeasuredinthisanalysiscomparedwithpreviousexperimentalresults(E864[8]andSTAR[9](triangleandstar, respectively))anddifferenttheoreticalmodelsasindicatedinthelegend.
Parameters Bd2 and B33He obtainedin [31] are compared with thehypertriton B
3 H
3 fromthisanalysisusingtherelations B32He
=
m2dm3HempB33He
,
(4)B
3 H 3
=
B33Hempm3 H
m3Hem
,
(5)andfinally
B32H
=
m2dmm2pm3 H
B33H
.
(6)In a simple coalescence model the BA parameter for all the lightnucleishouldhavethesamebehaviour.Thecoalescence pa- rameterofdeuteron (Bd2) andthe coalescence parameters of3He and 3H (B33He and B
3 H
3 ) can be directly compared deriving the B32He and the B
3 H
2 using equation (4), equation (5) and equa- tion (6). The comparison of the three coalescence parameters is shownintheleftpanelofFig. 7.The3H coalescenceparameteris notflatasafunctionofpTcontrarytothepredictionofthesimple coalescencemodel[11],whichdoesnottakeintoaccountthechar- acteristicsoftheemittingsource.Thisisthesamebehaviourasob- servedfordeuteronsand3Henuclei[31].Atlow pTthe B2values arecompatible,suggestingthat p0 issimilarforA=2andA=3.
Usingthemeasured 3H yieldtheratio S3=3H/(3He×/p), alsoknownasthe strangenesspopulation factor[59], was evalu- ated. This ratio was first suggested by the authors of [8] in the expectationthat dividing thestrange tonon-strangebaryon yield shouldresultinavaluenearunityinasimplecoalescencemodel.
Accordingtotheauthorsof[59],S3shouldbealsoavaluabletool to probe the nature of the matter created in the collision, since itissensitivetothelocalbaryon-strangenesscorrelation [60–62]:
a valueof S3 close tounity wouldindicate that thephase-space populations for strange and light quarks are similar and would support the formation of high-temperature matter of deconfined quarks.Inthethermalmodelapproach the S3 ratiodoesnot de- pendon thechemical potential ofparticles andwas found to be almost energy independent [1,63], while in a dynamical coales- cencepicture itincreaseswithdecreasing beamenergyandisin generallargerthanthethermalmodelpredictions[63].Thisleads to the conclusion that the informationon correlations of baryon
Table 5
S3formatterandanti-matter.TocomputetheratioaB.R.of25%wasassumedfor the3H→3He+πdecay.
Centrality 33HeH×p 33HeH×p
0–10% 0.60±0.13(stat.)±0.21(syst.) 0.54±0.13(stat.)±0.19(syst.)
numberandstrangenessislostinthethermalcalculationbecause S3 essentially depends only on the temperature. The /p ratio used in the present analysiswas taken from [52] and [54]. The S3 valuesobtainedforparticles(anti-particles)aresummarisedin Table 5andtheaverageofthetwomeasurementsisshowninthe right panel ofFig. 7.These values were compared withdifferent theoreticalmodelsandtotheresultsfromexperimentsatBNL-AGS [8]andRHIC[9].
Themodelsusedforthecomparisonarethestatisticalhadroni- zationmodel[1],thehybridUrQMDmodel[63]anditsextension atthe LHCenergy [51],the DCM(DubnaCascade Model) coales- cence model (described in [63]) and two versions – default and stringmelting–oftheAMPT(A Multi-PhaseTransportModelfor Relativistic Heavy IonCollisions) [64] plus coalescence described in [59]. The presentresult at √
sNN=2.76 TeV is comparable to that measuredatE864 experiment[8]at√
sNN∼5 GeV,while it doesnotconfirm therising behaviourshownby STAR[9]andby theAMPTwithstringmeltingpluscoalescencemodel[59].Thisre- sultisconsistentwiththethermalmodelapproach,whichpredicts aconstantS3 valuefrom√
sNNaboveafewGeV.
5. Conclusions
Measurements of 3H and 3¯
H in Pb–Pb collisions at √ sNN= 2.76 TeV werepresentedinthisletter.The 3H lifetimewasmea- suredandwasfoundtoagreewithpreviousmeasurementswithin uncertainties. The measured value was included inthe computa- tionofthe worldaverage ofthe3H lifetime.Transversemomen- tumyields atmid-rapidity forcentral (0–10%)Pb–Pbcollisions at
√sNN=2.76 TeV weremeasured inthree pT intervals. Theyields of particles and anti-particles were measured in two centrality classes(0–10% and 10–50%) andcomparedwithdifferenttheoret- icalmodels.Theratio3¯
H/3H isconsistentwithunity,asexpected at the LHC energy. The measured yields indicate that hypernu- clei in high-energy heavy-ion collisions are produced within an equilibratedthermalenvironmentinwhichthetemperatureisthe sameasfortheotherparticlesproduced attheLHC.The3H/3He
(3¯
H/3He) ratio was also measured andcompared withdifferent theoretical models and results from the STAR experiment. STAR results are higher than ALICE results,but compatiblewithin un- certainties.The 3H coalescence parameter wasalsoevaluated. Its valueincreaseswithpT,andwithintheuncertainties,isconsistent withthose extractedfor deuteronand3Henuclei [31]. The ratio S3=3H/(3He×/p)was evaluatedandcomparedwithdifferent theoreticalmodelsandmeasurements fromprevious experiments.
The value of S3 suggests that the production of nuclei and hy- pernucleiattheLHCcanbe describedwithathermodynamicap- proach,andissimilartotheonecalculatedbytheHybridUrQMD model[51].No conclusionscanbedrawnabouttheAMPT+ coa- lescencemodel[59],sincenopredictionofdynamicalcoalescence modelsisavailable attheLHCenergy.Themeasured S3 valueex- cludestherisingtrendinAMPT seenup toRHICenergiesextends toLHCenergies.The S3 measuredatAGS,RHICandLHCarecom- patible within uncertainty witha value which is independent of thecentreofmassenergyofthecollision.
Acknowledgements
The ALICE Collaboration would like to thank all its engineers andtechnicians fortheir invaluablecontributionstotheconstruc- tionoftheexperimentandtheCERNacceleratorteamsfortheout- standingperformanceoftheLHCcomplex.TheALICECollaboration gratefully acknowledges the resources and support provided by all Gridcentres andtheWorldwide LHCComputing Grid(WLCG) Collaboration. The ALICE Collaboration acknowledges the follow- ing funding agencies for their support in building and running theALICEdetector:StateCommitteeofScience,World Federation of Scientists (WFS) andSwiss Fonds Kidagan, Armenia, Conselho Nacionalde DesenvolvimentoCientífico e Tecnológico (CNPq), Fi- nanciadorade Estudose Projetos(FINEP),Fundação de Amparoà Pesquisa do Estado de São Paulo (FAPESP); National Natural Sci- enceFoundation ofChina (NSFC), theChinese MinistryofEduca- tion(CMOE)andtheMinistryofScienceandTechnologyofChina (MSTC); Ministry of Education andYouth of the Czech Republic;
Danish Natural Science Research Council, the Carlsberg Founda- tionandthe DanishNationalResearchFoundation;The European ResearchCouncilundertheEuropeanCommunity’sSeventhFrame- work Programme; Helsinki Institute of Physics and the Academy of Finland; French CNRS-IN2P3, the ‘Region Pays de Loire’, ‘Re- gionAlsace’,‘RegionAuvergne’ andCEA,France; GermanBundes- ministeriumfurBildung,Wissenschaft,ForschungundTechnologie (BMBF)andtheHelmholtzAssociation;GeneralSecretariatforRe- searchandTechnology,MinistryofDevelopment,Greece;Hungar- ianOrszagosTudomanyosKutatasiAlappgrammok(OTKA)andNa- tionalOfficeforResearchandTechnology (NKTH); Departmentof AtomicEnergy andDepartmentofScienceandTechnology ofthe Governmentof India;Istituto Nazionale diFisica Nucleare(INFN) and Centro Fermi – Museo Storico della Fisica e Centro Studi e Ricerche“EnricoFermi”,Italy;MEXTGrant-in-AidforSpeciallyPro- motedResearch,Japan;JointInstituteforNuclearResearch,Dubna;
National Research Foundation of Korea (NRF); Consejo Nacional de Cienca yTecnologia(CONACYT),Direccion Generalde Asuntos del Personal Academico (DGAPA), México, Amerique Latine For- mation academique – European Commission (ALFA-EC) and the EPLANETProgram (EuropeanParticle PhysicsLatin AmericanNet- work);StichtingvoorFundamenteelOnderzoekderMaterie(FOM) andtheNederlandseOrganisatievoorWetenschappelijkOnderzoek (NWO),Netherlands; ResearchCouncil ofNorway (NFR); National Science Centre, Poland; Ministry of National Education/Institute forAtomic Physics andNational Council of Scientific Research in Higher Education (CNCSI-UEFISCDI), Romania; Ministry of Educa- tion and Science of the Russian Federation, Russian Academy of
Sciences, Russian Federal Agency of Atomic Energy, Russian Fed- eral Agency for Science and Innovations and The Russian Foun- dation for Basic Research;Ministry of Educationof Slovakia; De- partment of Science and Technology, Republic of South Africa, South Africa; Centro de Investigaciones Energeticas, Medioambi- entales y Tecnologicas(CIEMAT),E-Infrastructure sharedbetween EuropeandLatinAmerica(EELA),MinisteriodeEconomíayCom- petitividad (MINECO) of Spain, Xunta de Galicia (Consellería de Educación), Centrode Aplicaciones Tecnológicasy DesarrolloNu- clear(CEADEN),Cubaenergía,Cuba,andIAEA(InternationalAtomic EnergyAgency);SwedishResearchCouncil(VR)andKnutandAlice WallenbergFoundation (KAW);UkraineMinistryofEducationand Science;UnitedKingdomScienceandTechnologyFacilitiesCouncil (STFC);TheUnitedStatesDepartmentofEnergy,theUnitedStates National Science Foundation, the State ofTexas, andthe State of Ohio; Ministry of Science, Education and Sports of Croatia and Unity through Knowledge Fund,Croatia; Council ofScientific and IndustrialResearch(CSIR),NewDelhi,India.
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