Evidence of rescattering effect in Pb–Pb collisions at the LHC through production of K⁎(892)0 and ϕ(1020) mesons

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Physics Letters B

www.elsevier.com/locate/physletb

Evidence of rescattering effect in Pb–Pb collisions at the LHC through production of K ^∗ ( 892 ) ⁰ and φ ( 1020 ) mesons

.ALICE Collaboration

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

Articlehistory:

Received21November2019

Receivedinrevisedform10January2020 Accepted13January2020

Availableonline16January2020 Editor:L.Rolandi

MeasurementsofK^∗(892)⁰andφ(1020)resonanceproductioninPb–Pbandppcollisionsat√_s

NN=^5.02 TeV withthe ALICEdetector attheLargeHadronColliderare reported. The resonancesare measured at midrapidity (|^y| < 0.5) via their hadronic decay channels and the transverse momentum (pT) distributionsareobtainedforvariouscollisioncentralityclassesuptopT=^{20 GeV}/c.ThepT-integrated yield ratio K^∗(892)⁰/K in Pb–Pb collisions shows significant suppression relative to pp collisions and decreases towards more central collisions. In contrast, the φ(1020)/K ratio does not show any suppression. Furthermore, the measured K^∗(892)⁰/K ratio in central Pb–Pb collisions is significantly suppressedwithrespecttotheexpectationsbasedonathermalmodelcalculation,whiletheφ(1020)/K ratio agrees with the model prediction. These measurements are an experimental demonstration of rescatteringofK^∗(892)⁰ decayproductsinthe hadronicphaseofthecollisions.The K^∗(892)⁰/Kyield ratios in Pb–Pb and pp collisions are used to estimate the time duration between chemical and kinetic freeze-out,which is found to be ∼ ^4–7fm/c for central collisions. The pT-differential ratios of K^∗(892)⁰/K, φ(1020)/K, K^∗(892)⁰/π, φ(1020)/π, p/K^∗(892)⁰ and p/φ (1020) are also presented for Pb–Pb and pp collisions at √_s

NN = ^{5.02 TeV. These ratios show that the} rescattering effect is predominantlyalow-pTphenomenon.

©^{2020TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Several measurements in high-energy heavy-ion collisions at theLarge HadronCollider (LHC) [1–3] andthe Relativistic Heavy Ion Collider (RHIC) [4–9] have shown that a strongly-coupled Quark-GluonPlasma(QGP)isformedthatsubsequentlyhadronizes.

Resonances,shortlivedhadronsthatdecayviastronginteractions, playanimportantroleincharacterizingthepropertiesofhadronic matterformedinheavy-ioncollisions [10–16].Severalresonances havebeenobservedinppandnuclearcollisions [10–19]: f2(1270),

ρ

(770)⁰,(1232)⁺⁺, f0(980),K^∗(892)^0,±,(1385),(1520)and φ (1020) with lifetimes of the order of 1.1 fm/c, 1.3 fm/c, 1.6 fm/c,2.6fm/c,4.16fm/c,5.5fm/c,12.6fm/c and46.3fm/c,re- spectively [20]. The wide range oftheir lifetimes allows them to be good probes of the dynamics of the system formed in ultra- relativisticheavy-ioncollisions [21–27].

In the hadronicphase of the evolution of the system formed inheavy-ioncollisions,therearetwoimportanttemperaturesand corresponding timescales: the chemical freeze-out, when the in- elastic collisions among the constituents are expected to cease, and the later kinetic freeze-out, when all (elastic) interactions

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

stop [28–30]. If resonances decay before kinetic freeze-out,then theirdecayproductsaresubjecttohadronicrescatteringthatalters their momentum distributions. This leads to inability to recon- struct the parent resonance using the invariant mass technique, resulting ina decreasein themeasured yield relative to thepri- mordialresonanceyield, i.e.the yieldatchemicalfreeze-out.The fraction of resonances that cannot be recovered dependson the lifetimeofthehadronicphase(definedasthetimebetweenchem- icalandkinetic freeze-out),thehadronicinteractioncrosssection of resonancedecayproducts, the particle densityinthe medium andtheresonancephase spacedistributions.Forexample,a pion fromaK^∗(892)⁰ mesondecaycould scatter withanother pionin the medium as

π

⁻

π

⁺_→

ρ

⁰_→

π

⁻

π

⁺. At the same time, after thechemical freeze-out,pseudoelastic interactionscould regener- ateresonancesinthemedium,leadingtoanenhancementoftheir yields. Forexample, interactions like

π

K→ ^K∗(892)⁰ →

π

K and K⁻K⁺→φ (1020)→^{K−K+couldhappenuntilkinetic}freeze-out.

Hence,resonancesareprobesoftherescatteringandregeneration processesduringtheevolutionofthefireballfromchemicaltoki- neticfreeze-out.Indeed,transport-basedmodelcalculationsshow that both rescattering andregeneration processes affectthe final resonance yields [31,32]. Thermal statistical models, which have successfullyexplaineda hostofparticleyields inheavy-ioncolli- sions acrossawide rangeofcenter-of-massenergies [33–36],are https://doi.org/10.1016/j.physletb.2020.135225

0370-2693/©^{2020TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

abletoexplainthemeasuredresonanceyieldsonlyafterincluding rescatteringeffects [37,38].

Inthispaper,the measurementofthe productionofK^∗(892)⁰ andφ (1020)vector mesons atmidrapidity inPb–Pb and pp col- lisions at √

sNN = ^{5.02 TeV is presented. Although both vector} mesons have similar masses, their lifetimediffers by a factorof largerthan10.Thisaspectisexploitedtoestablishthedominance of rescattering in central Pb–Pb collisions at the LHC. The kaon andpion daughters of the short-lived K^∗(892)⁰ → ^K

π

rescatter withotherhadronsinthemedium.Themagnitudeoftheeffectis mainlydeterminedbythepion-pioninteractioncrosssection [39], whichismeasuredtobesignificantlylarger(factor 5)thantheto- talkaon-pioninteractioncrosssection [40].Thelatterdetermines themagnitudeoftheregenerationeffect [41].Thuswithrescatter- ing dominatingoverregeneration, theobservable K^∗(892)⁰ yields should decrease compared to the primordial yields, and there- fore, a suppression of the K^∗(892)⁰/K yield ratio is expected in heavy-ioncollisionsrelativeto ppcollisions.Furthermore,thisra- tioisexpectedtodecreasewithincreaseinsystemsize,which is determinedbythecollisioncentrality(maximumforcentralcolli- sions).Incontrast,becauseofalargerlifetimecomparedtothatof the hadronic phase, the φ (1020) meson yields are not expected to be affected by rescattering [14,32]. The φ (1020) mesons are also expectednot to be affectedby the regeneration dueto sig- nificantlylower KK crosssection compared to K

π

and

π π

cross sections [39,40].Hence theindependenceofthe φ (1020)/Kyield ratio ofthe systemsize will act as a baseline for corresponding K^∗(892)⁰/Kmeasurements,therebysupportingthepresenceofthe rescattering effect in heavy-ion collisions. The lower K^∗(892)⁰/K yieldratioinPb–Pb collisions comparedtopp atthesame √

sNN can then be used to estimate the time span between chemical andkineticfreeze-outinheavy-ioncollisions.Furthermore,dueto thescatteringofthedecayproducts,thelow-p_T K^∗(892)⁰ areless likelyto escapethe hadronicmedium beforedecaying,compared tohigh-pT K^∗(892)⁰ [32].ThiscouldaltertheK^∗(892)⁰ pT spectra in Pb–Pb collisions compared to pp, while no such effect is ex- pectedfor φ mesons.Therefore, studying pT-differential ratios of K^∗(892)⁰ andφ (1020)mesons withrespectto other non-strange (

π

) and strange (K) mesons, and baryons (p) in Pb–Pb and pp collisions will help to establish the pT dependence of rescatter- ingeffectsanddisentanglethemfromotherphysicsprocesseslike radialflowthatmodifiestheshapesofthe p_T distributionsatlow andintermediate transverse momenta. Inaddition, the measure- ments at √

sNN = ^{5.02 TeV are compared to results fromPb–Pb} collisions at√

sNN = ^2.76TeV [14,42]. Since productionofparti- clesandantiparticlesisequalatmidrapidityatLHCenergies,the averageoftheyieldsofK^∗(892)⁰andK^∗(892)⁰ispresentedinthis paper andis denoted by the symbol K^∗0 unless specified other- wise.Theφ (1020)isdenotedbythesymbolφ.

The paperis organized asfollows: In section 2, the detectors usedintheanalysisarebrieflydescribed.Insection3,thedataset, theanalysistechniques,theprocedureforextractionoftheyields ofK^∗0 andφ mesons andthe studyofthesystematic uncertain- ties are presented.In section 4, the yields obtained by invariant massreconstruction ofK^∗0 andφ mesonsasa functionoftrans- versemomentuminPb–Pb andppcollisions at√

sNN =^5.02TeV, the pT-integrated ratios of K^∗0 andφ relative to chargedkaons, andpT-differentialratiosrelativetocharged

π

,Kandprotonsare reported.Finally,insection5thefindingsaresummarized.

2. Experimentalapparatus

Themeasurements of K^∗0 andφ meson productioninpp and Pb–Pbcollisions havebeenperformedusingthedatacollected by theALICEdetectorintheyear2015. Thedetails oftheALICEde-

tector can be found in Refs. [43–45]. So we briefly focus on the following main detectors used for this analysis. The forward V0 detector,a scintillatordetectorwitha timing resolutionlessthan 1ns,isusedforcentralityselection,triggering andbeam-induced background rejection. The V0 consists oftwo sub-detectors, V0A andV0C,placedatasymmetricpositions,oneoneach sideofthe interaction point with full azimuthal acceptance and cover the pseudorapidity ranges 2.8 <

η

< 5.1 and -3.7 <

η

< -1.7, re- spectively.ThecentralityclassesinPb–Pbcollisionsaredetermined fromthesumofthemeasuredsignalamplitudesinV0AandV0C, asdiscussedinRefs. [46,47].Thecollisiontimeinformationispro- vided by T0 which consist of two arrays of Cherenkov counters T0AandT0C,positionedonbothsidesoftheinteractionpoint [48].

TheZeroDegreeCalorimeter(ZDC)consistsoftwotungsten-quartz neutron andtwo brass-quartzprotoncalorimeterplacedata dis- tanceof113monbothsidesof theinteractionpoint.Itisusedto rejectthebackgroundeventsandtomeasurethespectatornucle- ons.

In the central barrel, the Inner Tracking System(ITS) andthe TimeProjectionChamber(TPC)areusedforcharged-particletrack- ingandprimarycollisionvertexreconstruction.TheITSconsistsof three sub-detectors of two layers each, covering a central pseu- dorapidity range |

η

| < 0.9: Silicon Pixel Detector (SPD), Silicon Drift Detector (SDD) andSilicon Strip Detector (SSD).The TPC is themainchargedparticletrackingdetector,andhasfullazimuthal coverage inthe pseudorapidity range|

η

|< 0.9. Alongwithtrack reconstruction,it alsoprovides ameasurementofthemomentum and excellent particle identification (PID). The TPC provides the measuredspecificenergyloss(dE/dx)toidentifytheparticles,es- pecially inlowmomentumrange(p<1GeV/c) wherethedE/dx ofparticlesarewellseparated.Toextendtheparticleidentification tohigher pT,theTimeofFlight(TOF)detectorisusedinaddition totheTPCinformation.TheTOFisbasedontheMultigapResistive PlateChamber(MRPC) technologyandmeasures thearrivaltimes of particles with a resolution of the order of 80 ps. It covers a pseudorapidityrange|

η

|<0.9andprovidesexcellentPIDcapabil- ities intheintermediate pT rangeby exploitingthetime-of-flight information.

3. Datasampleandanalysisdetails

Theppdatawerecollectedusingaminimumbias(MB)trigger.

The logic for MB trigger requiresat leastone hit in V0Aor V0C andonehitinthecentralbarreldetectorSPDincoincidencewith theLHCbunch crossing[49,50].Inppcollisions,a criterionbased on the offline reconstruction of multiple primary vertices in the SPD [45] isappliedtoreduce thepileup,whichiscausedbymul- tiple interactionsinthesamebunch crossing.Therejectedpileup events arelessthan 1% ofthetotal events.ThePb–Pb datawere also collectedusing aMB trigger withalogic thatrequires aco- incidenceofsignalsinV0AandV0C.TheMB-triggeredeventsare analyzed ifthey havea reconstructed collision vertexwhose po- sition alongthe beamaxis(Vz, z is thelongitudinal direction)is within 10cmfromthe nominalinteractionpoint inboth ppand Pb–Pb collisions.Backgroundeventsare rejectedusingthetiming informationfromtheZeroDegreeCalorimeters(ZDCs)andV0de- tectors.

ThePb–Pb analysisisperformedin8centralityclassesdefined in Ref. [46]: 0–10%, 10–20%, 20–30%, 30–40%, 40–50%, 50–60%, 60–70% and 70–80%. The 0–10% class corresponds to the most central Pb–Pb collisions, with smallimpact parameter, while the 70–80%classcorrespondstoperipheralPb–Pbcollisions,withlarge impact parameter. The total number of events that are analyzed after passingthe eventselectioncriteriaare ∼^{110million forpp} and∼^{30millionforPb–Pb} collisions.Charged tracksare selected

foranalysisbasedontrackselectioncriteriathatensuregoodtrack quality,asdoneinpreviouswork [42].Inparticular,atrackinthe TPCisrequestedtohaveaminimumof70crossedrows(horizon- tal segments along the transverse readout plane of the TPC) out of a maximum possible 159 [51]. A pT-dependent selection cri- terionon the distanceof closest approachto the collisionvertex inthetransverse(xy)plane(DCAxy)andalongthelongitudinaldi- rection(DCAz)isusedtoreducethecontaminationfromsecondary chargedparticlescomingfromweakly decayinghadrons. Inaddi- tionto these selection criteria, tracks are requiredto have pT >

0.15GeV/c inbothppandPb–Pbcollisions.Charged particlesare acceptedinthe pseudorapidity range |

η

| < 0.8, which ensures a uniformacceptance.

The particle identificationexploits both the TPCand the TOF.

ForK^∗0 and φ reconstruction in Pb–Pb collisions, charged parti- clesareidentifiedaspionorkaonifthemeanspecificenergyloss (^dE/dx^{) measured by the TPC fallswithin two standard devia-} tions(2

σ

TPC)fromtheexpecteddE/dxvaluesfor

π

orKoverthe entire momentum range. If the TOF information is available for thetrack, inaddition to the TPC, a TOF-based selection criterion 3

σ

TOF isappliedoverthemeasuredmomentumrange,where

σ

TOF is the standard deviation from the expected time-of-flight for a givenspecies.Theserequirementshelpinreducingthebackground underthe signalpeakover alargemomentum rangeandprovide a better separation between signal and backgroundwith respect toTPCPID only.ForK^∗0 reconstructioninpp collisions,thesame PID selection criteriaare applied to identify pion andkaon can- didatesas are usedin Pb–Pb collisions. Forthe φ reconstruction inppcollisions, thekaoncandidatesare identifiedusinga 6

σ

TPC, 4

σ

TPCand2

σ

TPC selectiononthemeasureddE/dxdistributionsin themomentumrangesp<0.3GeV/c,0.3<p<0.4GeV/candp

>0.4GeV/c,respectively. Ontop ofthis, theTOF-basedselection criterionof3

σ

TOF isappliedovertheentiremeasuredmomentum rangeinppcollisionsiftheTOFinformationisavailable.

3.1.Yieldextraction,correctionsandnormalization

TheK^∗0 andφ resonancesarereconstructedbycalculatingthe invariantmassoftheirdecayproductsthroughthehadronicdecay channelsK^∗0(K^∗0)→^K+

π

⁻(K⁻

π

⁺)(BranchingRatio,BR=66.666

± 0.006% [20])and φ→^{K+K− (BR =49.2} ± 0.5% [20]), respec- tively.OppositelychargedKand

π

(orK)fromthesameeventare paired to reconstruct the invariant mass distributions of K^∗0(φ).

TheK

π

andKK pairsareselectedintherapidity range|^y|< 0.5 inboth pp and Pb–Pb collisions. The invariant mass distribution exhibits a signal peak and a large combinatorial background re- sulting from the uncorrelated K

π

(KK) pairs. The combinatorial background is estimated using a mixed-event technique in both collision systems.The mixed-event background is constructed by combiningkaonsfromoneeventwiththeoppositelycharged

π

(K) fromdifferenteventsforK^∗0(φ).The eventswhicharemixedare requiredto havesimilar characteristics.In Pb–Pb, twoevents are mixedifthey belong to the same centralityclass andthe differ- encebetween the collision vertex position is |^Vz| < 1 cm. In ppcollisions, two eventsare mixedwitha condition of|Vz| <

1cm and a difference in charged-particle densityat midrapidity (|^y|<0.5) of less than 5. To minimize the statistical fluctua- tionsinthebackgrounddistribution,eacheventismixedwithfive otherones. Theinvariant massdistributionfromthemixed-event isnormalizedtothesame-eventoppositely-chargedpairdistribu- tion in the mass region 1.1–1.3 (resp. 1.04–1.06) GeV/c² for K^∗0 (resp.φ), whichisaway fromthemasspeak (6forK^∗0 and7 forφ, is the width ofthe resonance). Afterthe combinatorial background subtraction, the signal peak is observed on top of a residualbackground.ThelatterisduetothecorrelatedK

π

orKK

pairsthatoriginatefromjetsandfromthemisidentificationofpar- ticles.It isshowninRef. [42] that theresidualbackgroundhasa smooth dependenceonmassandthe shapeofthebackground is well described by a second order polynomial [14,42]. The invari- ant mass distributions after mixed-event background subtraction arefittedwithaBreit-Wigner(resp.Voigtian)functionforthesig- nal peakof K^∗0 (resp. φ) plus asecond order polynomial forthe residual background [42]. The Voigtian function is a convolution of a Breit-Wigner distribution and a Gaussian, where the width

σ

of theGaussian accountsforthe massresolution. Thelatter is p_T-dependentandvariesbetween1and2MeV/c².Therawyields are measured as a functionof pT for K^∗0 andφ in pp collisions andinvariouscentralityclassesinPb–Pbcollisions.Adetailedde- scriptionoftheyieldextractionprocedureisgiveninRef. [42].

The measured yields are affected by the detector acceptance andreconstructionefficiency(A×

ε

rec).Thisisestimatedbymeans ofdedicatedMonteCarlosimulationsusingthePYTHIA(PYTHIA6 Perugia 2011tune andPYTHIA8Monash2013tune) [52,53] and HIJING [54] eventgenerators forpp andPb–Pbcollisions, respec- tively. The generated particles are then propagated through the detectormaterialusingGEANT3 [55].The A×

ε

rec iscalculatedas a function of p_T andis definedasthe ratioof thereconstructed K^∗0(φ) to the generated K^∗0(φ), both within |^y|< 0.5. For the reconstructionofresonances,thesametrackandPIDselectioncri- teriaare appliedtothesimulationsasusedintheanalysisofthe measured data. The A×

ε

rec is calculated for K^∗0(φ) that decay throughthehadronicchannelK^±

π

^∓(K⁺K⁻),henceitdoesnotin- cludethecorrectionforBR.InPb–Pbcollisions,the A×

ε

rechasa weakcentralitydependenceandtherawyieldsarecorrectedusing the A×

ε

recoftherespectivecentralityclass.

Theproceduretocorrecttherawyieldsisgivenby

1 N_event

d²N dydp_T

=

¹

N^acc_event d²N^raw dydp_T

ε

trig

. ε

vert

. ε

sig

(

A

× ε

rec

) .

BR

.

(1) The rawyields are normalizedto thenumberof acceptedevents (N_event^acc ) andcorrectedfor A×

ε

rec,triggerefficiency(

ε

trig),vertex reconstructionefficiency(

ε

vert),signalloss(

ε

sig)andtheBRofthe decaychannel.The yieldsinpp arenormalizedto thenumberof inelasticcollisionswithatriggerefficiencycorrection,

ε

trig=0.757

± 0.019 [56]. Thevertexreconstructionefficiencyinppcollisions isfound to be

ε

vert = 0.958.The signal losscorrection factor

ε

sig is determined based on MC simulations as a function of p_T and accountsfortheresonancesignallostduetotriggerinefficiencies.

The

ε

sig(pT) correctionisonlysignificantfor pT <2.5GeV/c and has a value of lessthan 5% both forK^∗0 and φ in pp collisions.

In Pb–Pb collisions, theyields of K^∗0 andφ in a givencentrality class are normalized by the number of events in the respective V0M(sum ofV0AandV0Camplitude)eventcentralityclass.The correctionfactors

ε

trig,

ε

vertand

ε

sig(pT)arecompatiblewithunity inthereportedcentralityclassesinPb–Pbcollisionsandhenceare notused.

3.2. Systematicuncertainties

The systematic uncertainties in the measurement of K^∗0 and φ yields in pp and Pb–Pb collisions are summarized in Table 1.

Thesourcesofsystematicuncertaintiesarerelatedtotheyieldex- traction method, PID and track selection criteria, global tracking efficiency,theknowledgeoftheALICEmaterialbudgetandofthe interaction crosssection of hadronsinthe detectormaterial.The uncertaintiesare reportedforthreetransversemomentumvalues, low,midandhighpT.ForPb–Pbcollisions allthesystematicun- certaintiesexcepttheonerelatedtotheyieldextractionarecom- mon inthevarious centralityclassesandthe valuesgiveninthe

Table 1

SystematicuncertaintiesinthemeasurementofK^∗0andφyieldsinppandPb–Pbcollisionsat√

sNN=^{5.02TeV.Theseun-} certaintiesareshownfor threetransversemomentumvalues,low,midandhighpT.ForPb–Pbcollisionsallthesystematic uncertaintiesexceptyieldextractionarecommoninvariouscentralityclassesandthevaluesgiveninthetableareaveraged overallcentralityclasses.

Systematicvariation Pb–Pb pp

K^∗0 φ K^∗0 φ

pT(GeV/c) pT(GeV/c) pT(GeV/c) pT(GeV/c)

0.6 4.5 18 0.5 4.25 18 0.1 4.25 18 0.5 4.25 18

Yield extraction (%) 7.3 7.5 10.1 4.4 1.9 4.9 11.8 7.9 8.2 2.4 3.5 3.5

Track selection (%) 2.7 1.4 3.0 3.0 1.3 1.0 1.4 1.0 1.9 4.0 2.0 5.5

Particle identification (%) 5.4 3.0 5.0 1.0 1.5 2.4 2.1 3.2 6.9 0.3 1.7 6.5

Global tracking efficiency (%) 4.7 7.4 4.0 4.7 8.2 3.1 2.0 3.1 3.4 2.0 3.2 2.4

Material budget (%) 1.4 0 0 5.7 0 0 3.4 0 0 5.7 0 0

Hadronic Interaction (%) 2.4 0 0 1.3 0 0 2.8 0 0 1.3 0 0

Total (%) 10.9 11.0 12.3 9.2 8.6 6.4 13.0 9.1 11.4 7.7 5.4 9.5

Fig. 1.ThepTdistributionsof(a)K^∗0and(b)φmesonsinppcollisionsandvariouscentralityclassesinPb–Pbcollisionsat√_s

NN=^{5.02TeV.Thevaluesareplottedatthe} centerofeachbin.Thestatisticalandsystematicuncertaintiesareshownasbarsandboxes,respectively.

tableareaveragedoverallcentralities.Theyieldextractionmethod includes the uncertainties due to variations of the fitting range, thechoiceofcombinatorialbackgroundestimationtechnique,nor- malization range and residual background shape. The uncertain- tiesduetoyield extractionareestimatedto be7.9–11.8% forK^∗0 (resp.2.4–3.5% forthe φ)in ppand7.3–10.1% (resp. 1.9–4.9%) in Pb–Pbcollisions. The PIDsystematicuncertainties variesbetween 2.1–6.9% (0.3–6.5%) for K^∗0 (φ) in pp and Pb–Pb collisions. The contributiontotheuncertaintyfromtheglobaltrackingefficiency iscalculatedfromthecorrespondingvaluesforsinglechargedpar- ticles [51] andresultsina2.0–8.2%uncertaintybycombiningthe two charged tracks used in the invariant mass reconstruction of K^∗0 and φ. The contribution from variation of the track selec- tion criteria is 1.0–5.5%. The systematic uncertainties due to the hadronic interaction cross section are estimated to be less than 2.8%andcontributeonlyatlow pT (<2GeV/c).Theuncertainties in the description of the material budget of ALICEdetector sub- systems inGEANT3 (see Ref. [57] fordetails)give a contribution lowerthan5.7% ontheyields ofK^∗0 andφinpp andPb–Pb col- lisions. The material budget uncertainty is significant only at pT

< 2 GeV/c and negligible at higher p_T. The total p_T-dependent systematicuncertainties ontheK^∗0(φ)yields are estimatedtobe 9.1–13.0% (5.4–9.5%) in pp collisions and 10.9–12.3% (6.4–9.2%) inPb–Pb collisions.Thecommonsystematicuncertainties fordif- ferent particles (global tracking efficiency, material budget and

hadronicinteraction)are canceled outincalculatingparticleyield ratioslikeK^∗0/Kandφ/K.

4. Resultsanddiscussion

4.1. TransversemomentumspectrainppandPb–Pbcollisions

The pT distributions of the K^∗0 and φ mesons for |^y|<0.5, normalized to thenumber ofevents andcorrected forefficiency, acceptanceandbranchingratioofthedecaychannel,areshownin Fig.1.TheresultsforPb–Pb collisionsarepresentedforeightdif- ferentcentralityclasses(0–10%upto70–80%in10%widecentral- ityintervals)togetherwiththeresultsfrominelasticppcollisions atthesameenergy.

The p_T-integratedparticleyieldshavebeenextractedusingthe proceduredescribedinRefs. [14,42].ThepTdistributionsarefitted witha Lévy-Tsallisfunction [58,59] inpp anda Boltzmann-Gibbs blast-wavefunction[60] inPb–Pbcollisions.Theyieldshavebeen extracted from the data in the measured p_T region and the fit functionshavebeenusedtoextrapolateintotheunmeasured(low and high pT) region. The low-pT extrapolation covers pT < 0.4 GeV/c forK^∗0(φ)andaccountsfor8.6% (7.2%)and12.5%(12.7%)of thetotalyieldinthe0–10%and70–80%centralityclassesinPb–Pb collisions,respectively.Inppcollisions,theK^∗0ismeasuredinthe range 0< pT < 20GeV/c.Forthe φ meson, thelow-pT extrap- olation covers p_T < 0.4GeV/c,accounting for15.7% ofthe total

Fig. 2. pT-integrated particle yield ratios K^∗0/K⁻ and φ/K⁻ as a function of dNch/dη^1/3 measuredatmidrapidityinpp,p–PbandPb–Pbcollisionsat √

sNN

=^{5.02TeV.ForPb–Pbcollisionsat}√_s

NN=^2.76TeV,theφ/K⁻ valuesaretaken fromRef. [14] andtheK^∗0/K⁻valuesaretakenfromRef. [42].Theratiosforp–

Pbcollisionsare taken fromRef. [17].Statisticaluncertainties (bars)areshown togetherwith total(hollowboxes) andcharged-particle multiplicity-uncorrelated (shadedboxes) systematicuncertainties.Thermalmodelcalculationswithchemi- calfreeze-outtemperatureTch=156MeVforthemostcentralPb–Pbcollisions [34,64] arealsoshown.EPOS3modelpredictions [32] ofK^∗0/K andφ/K ratiosin Pb–Pbcollisionsarealsoshownasvioletlines.

yield.Theextrapolatedfractionoftheyieldisnegligiblefor pT >

20GeV/c.

4.2.Particleratios

Fig. 2 shows the K^∗0/K and φ/K ratios as a function of ^dNch/d

η

^1/3 [46,47,51] forPb–Pb collisions at√

sNN = ^2.76[14, 42] and5.02TeV,p–Pb collisionsat√

sNN =^5.02TeV [17] andpp collisions at √

s=^{5.02 TeV. The kaon yields in Pb–Pb at} √ s_NN

= ^{5.02 TeV are from Ref. [51]. The dN}ch/d

η

^1/3 measured at midrapidity, is used here asa proxy for the systemsize. This is supported by the observation of the linear increase in the HBT radiiwith^dNch/d

η

^1/3 [61,62].TheK^∗0/K ratiodecreasesforris- ing ^dNch/d

η

^{1/3 while the} φ/K ratio is almost independent of ^dNch/d

η

^1/3.Theratiosexhibit asmooth trendacrossthediffer- entcollisionsystemsandcollisionenergiesstudied.TheK^∗0/K and φ/K ratiosinPb–Pb collisionsat√

sNN =^{2.76and5.02TeVarein} agreementwithinuncertainties.

Theresonanceyieldsaremodifiedduringthehadronicphaseby rescattering(whichwouldreducethemeasuredyields)andregen- eration(whichwouldincreasethemeasuredyields).Theobserved dependenceoftheK^∗0/K ratioonthecharged-particlemultiplicity isconsistentwiththebehaviorthatwouldbeexpectedifrescatter- ingisthecauseofthesuppression.Thefactthattheφ/K ratiodoes notexhibitsuppressionwithcharged-particlemultiplicitysuggests that the φ, which has a lifetime an order of magnitude larger than that ofthe K^∗0, decays predominantlyoutside thehadronic medium. Theoretical estimates suggest that about 55% of the of K^∗0 mesonswith momentum p=^{1 GeV}/c, decaywithin 5 fm/c ofproduction (a typical estimate for the time between chemical and kinetic freeze-out in heavy-ion collisions [22,32,63]), while only7% of φ mesons with p=^{1 GeV}/c decaywithin that time.

This supports the hypothesis that the experimentally observed decrease of the K^∗0/K ratio with charged-particle multiplicity is caused by rescattering. A similar suppression has also been ob- served for

ρ

⁰/

π

[15] and ^∗/[13] in central Pb–Pb collisions relativetoperipheralPb–Pbandppcollisionsat√

sNN=^2.76TeV.

Inaddition,theK^∗0/K ratiofromthermalmodelcalculationswith- outrescatteringeffectsandwithchemicalfreeze-outtemperature

Fig. 3.Lowerlimitonthehadronicphaselifetimebetweenchemical andkinetic freeze-outasafunctionof^dNch/dη^1/3inp–Pb [17] andPb–Pbcollisionsat√

sNN

=5.02TeV.Thebarsandbandsrepresentthestatisticalandsystematicuncertain- ties,respectively,propagatedtothelifetimefromtheuncertaintiesassociatedwith themeasuredK^∗0/KratiosinPb–Pb (p–Pb)andppcollisionsat√

sNN=5.02TeV.

Tch = ^{156 MeV for the most central Pb–Pb collisions [34,64] is} found to be higher than thecorresponding measurements, while the measured φ/K ratio agrees with the thermal model predic- tions.The K^∗0/K andφ/K ratiosinPb–Pbcollisionsarealsocom- pared to EPOS3 model calculationswithand without a hadronic cascadephasemodeled byUrQMD [32].TheEPOS3modelpredic- tionsshowninthefigureareforPb–Pbcollisions at√

s_NN =^2.76 TeVbutnosignificantqualitativedifferencesareexpectedbetween the two energies. The EPOS3 generator withUrQMD reproduces theobservedtrendoftheK^∗0/K andφ/K ratioswhichfurthersup- portstheexperimentaldata.

The fact that K^∗0/K⁻ decreases with increasing ^dNch/d

η

^1/3

implies that rescattering of the decay products of K^∗0 in the hadronic phase is dominantover K^∗0 regeneration. This suggests that K^∗0↔^K

π

is not in balance. Hence in Pb–Pb the K^∗0/K⁻ ratiocan be used toget an estimate ofthetime between chem- icalandkineticfreeze-out,

τ

,as,[^K∗0/K⁻]kinetic = [^K∗0/K⁻]chemical

× ^{e−τ/τK∗0, where}

τ

_K∗0 is the K^∗0 lifetime. Here,

τ

_K∗0 is taken as 4.16 fm/c ignoring any medium modification of the width of the invariant mass distribution of K^∗0. Furthermore, it is as- sumed that [^K∗0/K⁻]chemical is given by the values measured in ppcollisionsandthePb–Pb collisiondataprovidesanestimatefor [^K∗0/K⁻]kinetic. This is equivalent to assuming that all K^∗0’s that decaybeforekineticfreeze-outarelostduetorescatteringeffects and there is no regeneration effect between kinetic and chemi- cal freeze-out which issupported by AMPT simulations [31]. All theassumptions listedabove leadto anestimate of

τ

asalower limitforthetime spanbetweenchemical andkinetic freeze-outs.

AdecreaseintheK^∗0/Kratiowithincreasingmultiplicityhaspre- viously alsobeenobserved in p–Pbcollisionsat√

sNN =5.02TeV [17].Thismightindicatethepresenceofrescatteringeffectinhigh multiplicity p–Pb collisions and is suggestive of a finite lifetime ofthehadronicphase.Forcomparisonwehavealsoestimatedthe hadronicphaselifetimeinp–Pbdata.Fig.3showstheresultsfor

τ

boostedbyaLorentzfactor(∼^1.65forp–Pb collisionsand1.75for Pb–Pb collision) asa function of^dNch/d

η

^{1/3.Neglecting higher} order terms, theLorentz factor isestimated as

1+(^pT/mc)². Here m is the rest mass of the resonance and ^pT ^{is used as} anapproximation forp forthemeasurementsatmidrapidity.The time interval between chemical and kinetic freeze-out increases withthe systemsize asexpected. Forcentral Pb–Pb collisionsat

√s_NN = ^{5.02TeV, thelower limitof timebetweenchemical and}

Fig. 4.Particleyieldratios(K^∗0+K^∗0)/(K⁺+K⁻)inpanel(a)and(2φ)/(K⁺+K⁻)inpanel(b),bothasafunctionofpTforcentralityclasses0–10%and70–80%inPb–Pb collisionsat√

sNN=5.02TeV.Forcomparison,thecorrespondingratiosarealsoshownforinelasticppcollisionsat√

s=5.02TeV.Thestatisticaluncertaintiesareshown asbarsandsystematicuncertaintiesareshownasboxes.Inthetext(K^∗0+K^∗0),(K⁺+K⁻)aredenotedbyK^∗0andK,respectively.

Fig. 5.Particleyieldratios(K^∗0+K^∗0)/(π⁺+π⁻)inpanel(a)and(2φ)/(π⁺+π⁻)inpanel(b),bothasafunctionofpTforcentralityclasses0–10%and70–80%inPb–Pb collisionsat√

sNN=5.02TeV.Forcomparison,thecorrespondingratiosarealsoshownforinelasticppcollisionsat√

s=5.02TeV.Thestatisticaluncertaintiesareshown asbarsandsystematicuncertaintiesareshownasboxes.Inthetext(K^∗0+K^∗0),(π⁺+π⁻)aredenotedbyK^∗0andπ,respectively.

kinetic freeze-out is about 4–7 fm/c. This is of the same order of magnitude asthe K^∗0 lifetime, but aboutan order of magni- tude shorter than the φ lifetime. A smooth increase of

τ

with systemsizefromp–Pb toPb–Pb collisionsisobserved.TheEPOS3 generatorwithUrQMDreproduces theincreasingtrendof

τ

with multiplicity qualitatively [32]. If a constant chemical freeze-out temperatureisassumed, then the increase of

τ

withmultiplicity inPb–Pb collisionscorrespondstoadecreaseofthekineticfreeze- outtemperature.Thisisinqualitativeagreementwithresultsfrom blast-wave fits to identified particle p_T distributions [51], which are interpreted asdecrease inthe kinetic freeze-out temperature fromperipheraltocentralcollisions.

Further,to quantify the pT-dependenceofthe rescatteringef- fect observed in Pb–Pb collisions, a set of pT-differential yield ratios was studied: K^∗0/K, φ/K,K^∗0/

π

, φ/

π

, p/K^∗0 and p/φ as showninFigs.4,5and6.Thechoiceoftheratiosismotivatedby thefollowingreasons:(a)theratioofresonanceyieldsrelativeto theonesofkaonsandpionscanshedlightontheshapesofthepT distributionsofmesonswithdifferentmassandquarkcontent,and (b)theratiosoftheprotonyieldwithrespecttotheyields ofthe

resonancesallowcomparisonsamonghadronsofsimilarmass,but differentbaryon numberandquark contentto bemade. Forcase (a), ratiosin0–10%, 70–80%Pb–Pb collisions andpp collisions at

√sNN = ^{5.02TeVarecompared.Forcase(b),ratiosin0–10%Pb–}

Pbcollisions andpp collisions at√

s_NN =^{5.02TeVare compared} with0–5%inPb–Pb collisionsat√

sNN =^{2.76TeV.Theratiosfor} 70–80%inPb–Pbcollisionsareclosertothecorrespondingresults inpp collisions.Noticeably,therearedistinct differencesbetween centralandperipheral(pp)collisionsintheratiosforpT below∼ 2 GeV/c and intermediate p_T (between 2 and 6 GeV/c) but the ratiosareconsistentathigher pT[42].

Atlow pT,theK^∗0/KandK^∗0/

π

forcentralcollisionsarelower than in peripheral (pp) collisions, while the corresponding yield ratios forφ meson arecomparable within theuncertainties. This observation is consistent with the suppression of K^∗0 yields due torescatteringinthehadronicphase.Itdemonstratesthatrescat- tering affects low momentum particles. At intermediate pT, both ratios show an enhancement forcentral Pb–Pb collisions relative toperipheralandppcollisions,whichismoreprominentforφ/K, φ/

π

andK^∗0/

π

. Thisis consistent withthe presenceof a larger

Fig. 6.Particleyieldratios(p+^p)/(K^∗0+^{K∗0)inpanel(a)and(p}+ ¯^p)/(2φ)inpanel(b),bothasafunctionofpT for0–10%centralPb–Pb collisionsandinelasticpp collisionsat√

sNN=^{5.02 TeV.For}comparison,similarratiosarealsoshownfor0–5%centralPb–Pb collisionsat√

sNN=2.76 TeV [42].Thestatisticaluncertaintiesare shownasbarsandsystematicuncertaintiesareshownasboxes.Inthetext(K^∗0+^K∗0)and(p+^{p)aredenotedbyK∗0andp,}respectively.

radialflowincentralcollisions relativetoperipheralandppcolli- sions [51].GiventhatthemassesofK^∗0 andφ mesonsarelarger thanthose ofthe chargedkaonandpion,the resonances experi- encea largerradialfloweffect.IncentralPb–Pb collisions,for pT below5 GeV/c, the p/φ ratiois observed to be independent of pTandthe p/K^∗0 ratioexhibitsaweak pT-dependencewithinthe uncertainties, in contrast to the decrease of both ratios with p_T observedinppcollisions. Inturn,thissuggeststhattheshapesof the pT distributionsaresimilarforK^∗0,φand pinthis pT range.

Although the quark contents are different, the masses of these hadrons are similar, indicating that this is the relevant quantity indeterminingspectrashapes.Thisisconsistentwithexpectations fromhydrodynamic-based models [65,66]. Within the uncertain- ties,the p/K^∗0 andp/φratiosforcentralPb–Pb collisionsat√

sNN

=5.02TeVand2.76TeV [42] areconstantatintermediate pT.This isconsistent with theobservation ofsimilar order radial flow at bothenergies, obtained fromthe analysisof pT spectra ofpions, kaonsandprotons [51].ForpT>6GeV/c,theK^∗0/K,φ/K,K^∗0/

π

, φ/

π

,p/K^∗0 andp/φyieldratiosincentralcollisionsaresimilarto peripheral andpp collisions, indicating that fragmentationis the dominanthadronproductionmechanisminthis p_T region.Thisis consistentwithpreviousmeasurementsat√

sNN =2.76TeV [42].

5. Summary

Thetransverse momentum distributionsof K^∗0 andφ mesons havebeenmeasuredatmidrapidity(|^y|<0.5)forvariouscollision centralities in Pb–Pb and inelastic pp collisions at √

s_NN = ^5.02 TeV using the ALICE detector. The K^∗0 yields relative to charged kaonsin Pb–Pb collisionsshow a suppression withrespectto pp collisions, which increases with the system size, quantified us- ing ^dNch/d

η

^1/3 measured at midrapidity. In contrast, no such suppression is observed for the φ mesons. The lack of suppres- sionfor the φ meson can be attributed to the fact that mostof themdecayoutsidethefireballbecauseofitslongerlifetime(

τ

φ = 46.3 ± ^{0.4 fm}/c). Because of a shorter lifetime (

τ

_K∗0 = 4.16 ± 0.05 fm/c), a significant number of produced K^∗0 decays in the hadronicmedium.Thedecayproduct(s)undergointeractionswith otherhadrons inthemedium resultingin asignificant changein their momentum, and no longer contributing to the K^∗0 signal reconstructed in the experiment. Althoughboth rescatteringand regenerationarepossible,theresultspresentedhererepresentan

experimental demonstration of the predominance of rescattering effects in the hadronic phase of the system produced in heavy- ioncollisions.Theeffectofrescatteringincreaseswiththesystem size.Furthermore,theK^∗0/K yieldratiosincentralPb–Pb collisions aresignificantlylowercomparedtothevaluesfromthermalmodel calculationswithoutrescatteringeffects,whilethemeasured φ/K yieldratioagreeswiththemodelcalculation.Thisfurthercorrob- orates the hypothesis that rescatteringaffects the measured K^∗0 yields in Pb–Pb collisions. A lower limit for the lifetime of the hadronicphaseisdetermined byusingtheK^∗0/KratiosinPb–Pb andpp collisions at √

sNN = 5.02 TeV.The lifetime, asexpected, increaseswithsystemsize.ForcentralPb–Pb collisions,itisabout 4–7fm/c.

The pT-differentialyieldratiosofK^∗0/

π

andK^∗0/Karestudied incentralPb–Pb,peripheralPb–Pb andppcollisionstounderstand the p_T-dependence of the rescattering effect. It is observed that rescatteringdominantly affectsthe hadronsat pT < 2 GeV/c. At intermediate pT (2–6 GeV/c), the φ/K, φ/

π

, K^∗0/

π

, p/K^∗0 and p/φyieldratiosareenhancedincentralPb–Pb collisionsrelativeto peripheralPb–Pb andppcollisions.Inaddition,thespectralshapes ofK^∗0,φandp,whichhavecomparablemasses,aresimilarwithin theuncertaintiesfor pT below5GeV/c inPb–Pb collisions. These measurementsdemonstratetheeffectofhigherradialflowincen- tralPb–Pb collisionsrelativetoperipheralPb–Pb andppcollisions.

Acomparisonofthe p/K^∗0 andp/φ ratiosforcentralPb–Pb col- lisions at√

s_NN = ^{5.02and2.76TeV showstheconstancyof the} ratios with pT.Thisis consistentwiththeobservation ofcompa- rable radial flow at √

sNN = ^{5.02 TeV and2.76 TeV. For higher} pT, above 6 GeV/c, all the ratios agree within the uncertainties forcentralandperipheralPb–Pb,andppcollisions,indicatingthat particleproductionviafragmentationathightransversemomenta isnotsignificantlymodifiedinthepresenceofamedium.

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- videdbyallGridcenters andtheWorldwideLHCComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the