Multiplicity dependence of K*(892)0 and ϕ(1020) production in pp collisions at √s=13 TeV

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Multiplicity dependence of K*(892) ⁰ and φ ^{(1020) production in pp} collisions at √

s = ^{13 TeV}

.ALICE Collaboration

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

Articlehistory:

Received13December2019

Receivedinrevisedform25March2020 Accepted18May2020

Availableonline28May2020 Editor:L.Rolandi

Thestrikingsimilaritiesthathavebeenobservedbetweenhigh-multiplicityproton-proton(pp)collisions and heavy-ion collisions can be exploredthrough multiplicity-differentialmeasurements of identified hadronsinppcollisions.Withthesemeasurements,itispossibletostudymechanismssuchascollective flow that determine the shapesofhadron transverse momentum(pT) spectra, to searchfor possible modificationsoftheyieldsofshort-livedhadronicresonancesduetoscatteringeffectsinanextended hadron-gasphase, and to investigatedifferentexplanations providedby phenomenologicalmodels for enhancement of strangeness production with increasing multiplicity. In this paper, these topics are addressedthroughmeasurements oftheK^∗(892)⁰and φ(1020)mesonsatmidrapidityinppcollisions at√_s

= ^{13 TeVas afunctionofthe} charged-particlemultiplicity. Theresults includethe pTspectra, pT-integratedyields,meantransversemomenta,andtheratiosoftheyieldsoftheseresonancestothose oflonger-livedhadrons.Comparisonswithresultsfromothercollisionsystemsandenergies,aswellas predictionsfromphenomenologicalmodels,arealsodiscussed.

©^2020EuropeanOrganizationforNuclearResearch.PublishedbyElsevierB.V.Thisisanopenaccess articleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Recent studies of proton-proton (pp) and proton-lead (p–Pb) collisionsattheLHCwithhighcharged-particlemultiplicitieshave shown patterns of behavior that are reminiscent of phenomena observedinheavy nucleus-nucleus(A–A)collisionssuchasPb–Pb andXe–Xe.Thesystems createdinthesecollisions are compared by classifyingevents accordingto the final-statecharged-particle multiplicity,which is used asa measure of the “activity” of the event.In smallcollision systemssuch aspp andp–Pb,multiplic- ities range from a few to a few tens of charged particles per unit of rapidity, whereas in large systems (A–A collisions), mul- tiplicities of a few thousand chargedparticles per unit ofrapid- ity can be produced. As discussed below, measurements of az- imuthal anisotropies in particle emission [1–7] (quantified using theFouriercoefficientsofazimuthaldistributionsofproducedpar- ticles),themultiplicityevolutionofhadron pTspectra [8–11],and p_T-differential baryon-to-meson ratios suggest the possibility of collectiveflow even in smallsystems. Furthermore,the observed enhancementofstrangehadron production [8,9,12] couldindicate the productionof a quark–gluon plasma (QGP), while the possi- blesuppressionoftheyieldsofshort-livedresonances [8,11] may suggestthe presenceof an extendedhadronic phase.However, it remainsanopenquestionwhethertheunderlyingcausesofthese behaviorsaretrulythesameinsmallandlargecollisionsystems.

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

In order to investigatethis, the ALICE Collaborationhas mea- sured the p_T spectra and total yields of identified hadrons asa function ofthe charged-particle multiplicity inp–Pb collisions at

√sNN= 5.02 TeV [10,11,13–15] andpp collisions at √

s= ^{7 TeV} [8,12,16] for many species, including π^±, K^±, K⁰_S, K^∗(892)⁰, p, φ(1020), ,⁻, ⁻,deuterons, andtheir antiparticles.Thispa- per reportson an extension of these studies: a measurement of themultiplicityevolutionoftheproductionofK^∗(892)⁰,K^∗(892)⁰, and φ(1020) mesons inpp collisions at√

s= ^{13 TeV,the high-} estenergyreachedbytheLHCinruns1and2.Thepresentstudy takesadvantageofappdatasetrecordedduringRun2oftheLHC in2015withan integratedluminosity of0.88 nb⁻¹ andcomple- mentsotherrecentALICEpapersonlight-flavorhadronproduction inthe samecollision system, bothin inelasticcollisions [17] and asafunction ofcharged-particlemultiplicity [9,18,19].Forthere- mainder ofthispaper,the averageofK^∗(892)⁰ andK^∗(892)⁰ will bedenotedasK^∗0,whiletheφ(1020)willbedenotedasφ.

The ratios of the yields ofstrange hadronsto pion yields are observed to be enhanced in A–A collisions relative to minimum biasppcollisions [20–22],withtheyieldsincentralA–Acollisions beingwelldescribedbystatisticalthermalmodels [23–26].Incen- tral A–A collisions, strangeness is produced from the hadroniza- tion of a strangeness-saturated QGP andthe relative abundances of hadrons reflect the degree of equilibration of the system. At theLHC,hadron-to-pionyieldratiosareobservedtoincreasewith thecharged-particlemultiplicityinppandp–Pbcollisions [8–13];

the magnitude of the change from low to high multiplicity in-

https://doi.org/10.1016/j.physletb.2020.135501

0370-2693/©^2020EuropeanOrganizationforNuclearResearch.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

creases with the strangeness content of the hadron. The ratios in high-multiplicity pp andp–Pb collisions reach the values ob- served inperipheralPb–Pb collisionsandgenerallyfollowsimilar trends as the multiplicity increases frompp to p–A to A–A col- lisions.Furthermore,the yields ofstrange particlesare consistent between √

s= ^{7 and 13 TeV for similar} charged-particle multi- plicities. These results suggest that the yields of these hadrons dependprimarily on thecharged-particle multiplicity andare in- dependent of the collision system and energy. This is perhaps a surprising result: pp, p–Pb, and A–A collisions involve different physicalprocesses(e.g.differentcontributions fromjetsandmul- tiplepartonic interactions)andproduce pT spectrawithdifferent shapes. Nevertheless, the total abundances of hadrons, even rare particles like ⁻ and light nuclei, are consistent across the dif- ferent collision systems for a given charged-particle multiplicity, suggestingthattheremaybesomeunderlyingsimilaritiesbetween thedifferentcollisionsystems.Comparisonsofthesedifferentcol- lision systems atsimilar multiplicities may, forexample, help to addressthequestion ofwhetheraQGPmightbe presenteven in high-multiplicityppandp–Pbcollisions,oralternatively, whether non-QGPeffectsmightexplainbehaviorseeninA–Acollisions.

Several theoretical explanations of the multiplicity evolution of strange-hadron production have been put forward, including canonicalsuppression,ropehadronization,andcore-coronaeffects.

Instatisticalthermalmodelsoflargecollisionsystems,strangeness productionisdescribed throughthe useofagrandcanonical en- semble, where strangeness conservation is realized on average acrossthevolumeofthesystem.Inthecanonicalsuppressionpic- ture,strangenessproductioninsmallsystemsisinsteaddescribed using a canonical ensemble, requiring the exact local conserva- tionofstrangenesswithinthesmallvolume [8,27,28].Asthesize of the system decreases, it makes a transition from the grand- canonical to the canonical description, leading to a decrease in strange-hadron yields with decreasing multiplicity. In the rope- hadronizationpicture,thelargeranddensercollisionsystemsform colorropes [29–31],groups ofoverlapping stringsthat hadronize witha largereffectivestring tension.Thiseffect,implementedin modelssuchasDIPSY [32–34],alsoleadstoanincreaseinthepro- duction ofstrange hadronswithincreasing charged-particle mul- tiplicity. Core-corona separation is implemented in a variety of models, including EPOS [35–38] and those described in [39,40].

In these models, the collision is divided into “core” and “coron- a” regions, with the division determined by the string or parton density. Regions with a density greater than the threshold den- sitybecomethecore,whichmayevolveasaquark–gluonplasma.

This is surroundedby a more dilute corona, for whichfragmen- tationoccursas inthe vacuum. Strangeness productionis higher inthecoreregion, whichmakes upa greaterfractionofthe vol- umeofthelargercollisionsystems.Thisalsoresultsinstrangeness enhancementwithincreasingmultiplicity.

The φ meson is a useful probe for the study of strangeness enhancement. The φ contains two strange valence (anti)quarks, buthasnonetstrangeness.Its productionshouldthereforenotbe canonicallysuppressed,whiletheproductionofhadronswithopen strangeness(e.g. kaons or) maybe canonically suppressed [8].

It has, in fact, been rather difficult to describe enhancement of φ-mesonproductioninaframework that involvescanonical sup- pression [8].Incontrast,intherope-hadronizationorcore-corona interpretations, the yields of φ mesons evolve with multiplicity similarlytoparticleswithopenstrangeness,leadingtoanexpected increase in the pT-integrated φ/π ratio withincreasing charged- particle multiplicity. Measurements of φ-meson production as a function ofthe multiplicity mayhelp to distinguish betweenthe variousexplanationsofstrangenessenhancementinsmallsystems.

One ofthe mainmotivations forstudying resonances likeK^∗0 and φ in heavy-ion collisions is to learn more about the prop-

erties (temperature and lifetime) of the hadronic phase of the collision. Whenshort-lived resonances(suchasρ(770)⁰,K^∗0,and (1520)) decay, their daughters may re-scatter in the hadronic phase,leading toareductioninthemeasurableresonanceyields;

conversely, resonances may also be regenerated due to quasi- elastic scattering of hadrons through a resonance state [41–46].

Centrality-dependent suppression of ρ(770)⁰, K^∗0, and (1520) production was observed in Pb–Pb collisions [47–50], anda hint of K^∗0 suppression was reported forp–Pb collisions [11]. Obser- vations ofa similar suppressionin high-multiplicitypp collisions (e.g.,theK^∗0/K ratioinppcollisions at√

s= ^{7 TeV [8])mightbe} anindication forahadronicphasewithnon-zerolifetimeinhigh- multiplicityppcollisions.

Measurementsofidentifiedhadronscanalsobe usedtostudy collective motion in A–A collisions and to search for similar ef- fectsinsmallcollision systems.Innon-centralA–Acollisions, the initialspatial anisotropyintheoverlapregion ofthecollidingnu- clei results in azimuthally anisotropic pressure gradients in the produced medium, leading to azimuthal anisotropies in particle emission.Thisanisotropicflowisamanifestationofhydrodynamic behavior in theQGPproduced in theA–Acollision system. Mea- surements of azimuthal correlations and anisotropies in particle emission [1–7] alsosuggest thepossibilityofcollectivemotionin smallcollisionsystems.Itwasobservedthattheslopes ofhadron pT spectra increase with increasing multiplicity in pp and p–Pb collisions [8–11],whileanenhancementin pT-differentialbaryon- to-mesonratios(e.g.p/πand/K⁰_S)isobservedatintermediate p_T (2^pT^{7 GeV}/c).Thisisatleastqualitativelysimilartothebe- haviorobservedinPb–Pbcollisions [51–54],wheretheeffectscan be attributedto a collective expansion of thesystem. In thisin- terpretation, hadronsreceive amomentum boost inthedirection transverse to the beamaxis, which increases in magnitudewith increasing multiplicity andislargerformoremassiveparticles. It shouldbenoted,however,thatothereffects,includingrecombina- tion [55–57], may be able to account forthe observed behavior.

TheincreaseintheslopesofthepT spectraisalsomirroredinthe trendofthemeasuredmeantransversemomenta^pT^.Incontrast to theyields, whichevolve along a continuous trendwithmulti- plicityacross differentcollision systems,the ^pT^{valuesof light-} flavorhadronsfollowdifferenttrendsinpp,p–Pb,andPb–Pbcol- lisions [10–12,51],witha fasterincrease forthe smallersystems.

The pTvaluesinthe highestmultiplicitypp collisions reach,or in some casesexceed, the ^pT ^{values observedin central Pb–Pb} collisions. The increase in^pT ^{inpp collisions isdueto changes} inthe shapesofthe p_T spectra atlow p_T; for p_T^{4 GeV}/c,the shapes ofhadron p_T spectra are essentially independent ofmul- tiplicity [9,58]. The color reconnection (CR) mechanism [59–63]

describes the interconnections and interactions between strings that originate from different multi-parton interactions. It is im- plementedinvariousforms,sometimesincludingtheformationof colorropes, inseveraleventgenerators basedon stringfragmen- tation. Color reconnection can also modify the yields of hadron species(e.g.increasingtherateofbaryonformation)andcanlead to collectiveflow-like effects,eveninsmallcollision systemsand ineventgeneratorslikePYTHIAthatdonotincludeQGPformation.

The results reported here will allow the study of K^∗0 and φ productionasfunctionsofbothenergyandmultiplicityinppcol- lisions. The presented results reach higher values of multiplicity than previously measured in pp collisions and therefore provide importantadditionalinformationontheproductionoflight-flavor hadrons atLHC energies. This paperis organized asfollows. The ALICEdetectorandthecriteriaadoptedfordataselectionare de- scribedinSection2.Asummaryofthedataanalysisprocedureis giveninSection3.TheresultsarepresentedanddiscussedinSec- tion4,followedbyasummaryandconclusionsinSection5.

Table 1

Charged-particle multiplicity densities at midrapidity dNch/dη|η|<0.5 for the INEL>0 class and the various V0M multiplicityclasses [9].

Class dNch/dη|η|<0.5 INEL>0 6.89±^0.11

I 25.75±^0.40

II 19.83±^0.30

III 16.12±^0.24

IV 13.76±0.21

V 12.06±0.18

VI 10.11±0.15

VII 8.07±^0.12

VIII 6.48±^0.10

IX 4.64±^0.07

X 2.52±^0.04

2. Eventandtrackselection

The ALICEdetector is described in detail in [64,65]. The sub- detectorsthatare relevanttotheanalysisdescribed inthispaper aretheTimeProjectionChamber(TPC),theTime-of-Flightdetector (TOF),the Inner TrackingSystem(ITS), the V0detectors, andthe T0detectors.TheTPCandITSareusedfortrackingandfindingthe primaryvertex,whiletheTPCandTOFareusedforparticleidenti- fication.TheV0detectors(scintillatorarrays)andtheT0detectors (arrays ofCherenkov counters) sit on eitherside ofthe nominal centerofthe detectoratsmall angleswith respectto thebeam- line. The V0 detectors are used for triggering and to define the multiplicityestimatoratforwardrapidities(pseudorapidityranges

−³.7<

η

<−¹.7 and2.8<

η

<5.1).TheT0detectorsprovidetim- inginformation,includingastartsignalfortheTOF.

The K^∗0 and φ mesons are reconstructed from a sample of 5×^{107 ppcollisionsat}√

s= ^{13 TeVrecordedin2015.Themini-} mumbiastriggerrequiredhitsinbothV0detectorsincoincidence withprotonbunchesarrivingfrombothdirections.Beam-induced backgroundandpile-upeventsare removedoffline; see [9,65] for details.Selected eventsmustalsohavea primary collisionvertex reconstructed with the two innermost layers of the ITS and lo- catedwithin±^{10 cmalongthebeamaxisofthenominalcenterof} theALICEdetector.Resultsinthispaperarepresentedfordifferent eventclassescorrespondingtosubdivisionsofthe“INEL>0”event class,whichisdefinedasthesetofinelasticcollisionswithatleast onechargedparticleintherange|

η

|<1 [66]. TheINEL>0 sam- ple isdivided intomultiplicity classes based on the total charge depositedinbothV0detectors(calledthe“V0Mamplitude”).Thus, theeventclassesaredeterminedbythenumberofchargedparti- clesatforwardrapidities,whiletheK^∗0andφyieldsaremeasured at midrapidity (|^y|<0.5); this is to avoid correlations between theK^∗0andφyieldsandthemultiplicityestimator.Particleyields, yieldratios,andmeantransversemomentaareplottedfordifferent multiplicity classes(whichcorrespond todifferent centralitiesfor A–Acollisions)asfunctionsofthecorrectedmeancharged-particle multiplicitydensityatmidrapidity^dNch/d

η

_|η_|<0.5,where

η

isthe pseudorapidityinthelabframe.Asin [9],thevariousmultiplicity classesare denoted usingRoman numerals, with classI (X)hav- ingthehighest(lowest)multiplicity.SeeTable1forthevaluesof ^dNch/d

η

_|η_|<0.5 measuredforeachV0Mmultiplicityclass.

SincetheK^∗0andφmesonsareshort-lived(i.e.,theirlifetimes areofthe orderof ∼^{10−23 sandtheir decay verticescannot be} distinguished from the primary collision vertex), they cannot be measureddirectlybythedetector.Instead,they arereconstructed viatheirhadronicdecaystochargedpionsandkaons:K^∗0→π^±K^∓ (branchingratio66.503±⁰.014%) andφ→^{K+K− (branchingra-} tio 49.2±⁰.5%) [67]. Charged tracks are selected using a set of standard track-quality criteria, described in detail in [11]. Pions

andkaons are identified usingthe specificionization energy loss dE/dx measured in theTPC andthe flight time measured inthe TOF.WherethedE/dxresolutionoftheTPCisdenotedas

σ

TPC,pi- ons andkaonsare requiredtohavedE/dxvalueswithin 2

σ

TPC of theexpectedvaluefor p>0.4 GeV/c,within4

σ

TPC for0.3<p<

0.4 GeV/c,andwithin 6

σ

TPCfor p<0.3 GeV/c (typically,

σ

TPC∼ 5% of the measured dE/dx value). When a pion orkaon track is matchedtoahitintheTOF,thetime-of-flightvalueisrequiredto be within3

σ

TOF oftheexpectedvalue (

σ

TOF∼80 ps) [68]. These event- andtrack-selectioncriteriaarevariedfromtheirdefaultval- uesandthe resultingchanges inthe yields areincorporated into thesystematicuncertainties,whicharesummarizedinTable2.

3. Dataanalysis

The K^∗0 and φ signals are extracted using the same invari- antmassreconstructionmethoddescribed in [11,17,48].Invariant mass distributions of unlike-charge πK or KK pairs in the same event are reconstructed after particle identification. The combi- natorial background is estimated usingmultiple methods. In the

“like-charge” method, tracks of identical charge from the same eventarecombinedtoformpairs.Thisbackgroundis2√

n₋₋n₊₊, where n₋₋ and n₊₊ are the number of negative-negative and positive-positive pairs in each invariant mass bin, respectively.

In the “mixed-event” method, tracks from one event are com- bined with oppositely charged tracks fromup to 5 other events withsimilarprimaryvertexpositionsandmultiplicitypercentiles.

Specifically, it is required that the longitudinal positions of the primaryverticesdifferbylessthan1 cmandthemultiplicityper- centiles computed using the V0M amplitude differ by less than 5%. The mixed-event πK (KK) background is normalized so that it has the same integral as the unlike-charge same-event dis- tribution in the invariant mass range 1.1<m_πK<1.15 GeV/c² (1.05<mKK<1.08 GeV/c²). In evaluating the systematicuncer- tainties,theboundariesofthenormalizationregionforthemixed- eventbackgroundarevariedby∼^{100 MeV}/c² fortheK^∗0analysis and∼^{10 MeV}/c² forφ.

After subtraction ofthe combinatorial background,the invari- ant mass distribution consists of a resonance peak sitting on top of a residual background of correlated pairs. This correlated backgroundcontains contributions fromjets, resonancedecays in which a daughter is misidentified, and decays with more than two daughters. In the analysis of the φ meson in pp collisions, thesignal-to-background ratioislarge andthe backgroundisob- servedtovaryslowly intheregionofthepeak.Forthesereasons, athirdapproachisalsousedtodescribethebackgroundintheφ analysis;thecombinatorialbackgroundisnotsubtracted,butisin- stead parameterizedtogether withthe residualbackground using afunctionasdescribedbelow.Thishastheadvantageofproviding smallerstatisticaluncertaintiesthantheothermethods.

For pT<4 GeV/c,all threemethodsprovidegooddescriptions ofthe KK backgroundandgive φyields within a fewpercent of each other.The final φ yields for pT<4 GeV/c are theaverages ofthoseextractedusingthethreemethodsofdescribingthecom- binatorialbackground,whilethespreadamongtheresultsforthe differentmethodsisincorporatedintothesystematicuncertainties.

As pT increases, the yields of hadrons decrease, along with the magnitudes of all of the combinatorialbackgrounds studied. The mixed-event background,which lacks anycontribution fromcor- relatedpairs,isobservedtobecome smallerthanthesame-event (like- orunlike-charge)combinatorialbackgroundsaspTincreases, eventuallytending to0forp_T valueshigherthantherangescon- sidered here. While the mixed-event background could still be usedfortheφanalysisfor4≤^pT≤^{8 GeV}/c,thetwoothertech- niques havesmaller statisticalfluctuationsinthis p_T range. Con- sequently,themixed-event techniqueis notused forthe analysis

Table 2

Sources ofsystematic uncertaintiesfor the pT spectraof K^∗0 and φ reported for low,intermediate,and high pT. Whenonlyone valueis givenforone par- ticle,the uncertaintydoesnotdependon pT. “Signalextraction”includesvaria- tionsofthecombinatorial background,mixed-eventnormalizationregion, fitting region,peakshape,andresidualbackgroundfunction.The“signal-loss”uncertainty ismultiplicity-dependent,hencevaluesarequotedforthehighestandlowestmul- tiplicityclasses(IandX,respectively).Thetext“negl.”indicatesanegligibleuncer- taintyand“had.int.crosssec.”isshortfor“hadronicinteractioncrosssection.”

Particle pT(GeV/c)

K^∗0 φ

0.2 2.2 6.5 0.7 2 6

event/track selection 4.3% 1.6% 2.9% 2.7% 2.9% 3.2%

signal extraction 10.3% 6.7% 7.7% 2.7% 3.1% 3.1%

ITS-TPC matching 2.0% 2.0%

branching ratio negl. 1.0%

material budget 2.0% 0.5% negl. 5.3% 1.0% negl.

had. int. cross sec. 2.6% 1.2% negl. 2.1% 2.6% negl.

signal loss, class I negl. negl.

signal loss, class X 3.9% 2.4% 0.9% 2.3% 4.8% 2.2%

ofφfor pT>4 GeV/c.Themixed-eventtechniqueistheprimary methodusedfortheextractionoftheK^∗0 yields;variationsofthe yieldduetotheuseofalike-chargebackgroundarecoveredbythe systematicuncertainties.However,forpT<0.8 GeV/cinmultiplic- ityclassI, thelike-chargemethodispreferred,sinceitprovidesa betterdescriptionofthebackground.Athigh pT,themixed-event backgroundfortheK^∗0 analysisexhibitsthesamebehaviorasfor theφ,buttheproblemsappearathigherpTvaluesthanforφ.The mixed-eventtechniquethereforeremainsthebestavailableoption forthisK^∗0 analysis,evenatthehighendofthep_T rangethatwas studied.

The invariant mass distributions are fitted with a peak func- tionaddedtoasmoothresidualbackgroundfunction.ForK^∗0,the peak is described using a Breit-Wigner function. The mass reso- lutionof thedetectorfor theφ→^{K−K+ channel isof thesame} orderofmagnitudeastheφ width.Therefore, theφpeak isde- scribed using a Voigt function: a convolution of a Breit-Wigner functionandaGaussianwhichaccountsforthemassresolutionof thedetector.TheK^∗0 andφwidthparametersarebydefaultfixed to their vacuumvalues;to calculatethe systematicuncertainties, theseparametersare allowed tovaryfreely andtheφresolution parameteris fixedto thevalues(approximately 1–2 MeV/c²) ex- tracted from the Monte Carlo simulations described below. The residual backgroundis parameterized usinga second-order poly- nomial.ToevaluatethesystematicuncertaintiesintheK^∗0 yields, athird-orderpolynomialisusedinstead.Fortheφsystematicun- certainties, a first-order polynomial and a function of the form A+^BmKK+^C

mKK−^2M(K^±) are used. Here, A, B, and C are free parameters, mKK is the kaon-kaon pair invariant mass, and M(K^±)isthemassoftheK^±.Thefitsareperformedintheinvari- antmassintervals0.75<mπK<1.07 GeV/c² fortheK^∗0 analysis and0.995<mKK<1.09 GeV/c² forthe φ. Theranges ofthefits are variedby ∼^{20 MeV}/c² forK^∗0 and ∼^{10 MeV}/c² forφ;the resultingchangesintheyieldsare includedinthesystematicun- certainties.Finally,particleyields areextractedby integratingthe invariant mass distribution in the peak region (0.798≤^mπK≤ 0.994 GeV/c² forK^∗0 and1.01≤^mKK≤¹.03 GeV/c² forφ),sub- tractingtheintegraloftheresidualbackgroundfunctionunderthe peak,andaddingtheyieldsinthetailsofthepeakfitfunctionout- sidetheintegrationregion.Thesystematicuncertaintyarisingfrom

“signal-extraction”, as quoted in Table 2, covers the aforemen- tioned variations in the combinatorial background, mixed-event normalizationregion,residualbackgroundfunction,peakfunction, andfitrange.Anadditionaluncertaintyoriginatesfromtheproce- dure usedto matchtracksegments in theITSwithtracks inthe TPC.Thebranchingratiocorrectionfortheφyieldintroducesa1%

uncertainty,whilethecorrespondinguncertaintyforK^∗0isnegligi-

ble.Uncertaintiesintheyieldsduetouncertaintiesinthematerial budgetofthedetectorandthecrosssectionsforhadronicinterac- tionsinthatmaterialaretakenfromapreviousstudy [11].

The raw particle yields are corrected for the branching ra- tios, aswell as the acceptance and efficiency of the reconstruc- tion procedure. The correction for acceptanceand efficiency(de- noted as A×

ε

) is calculated using several different event gen- erators (PYTHIA6Perugia 2011 tune [69],PYTHIA8 Monash2013 tune [70],andEPOS-LHC [38]),withparticlespropagated through a simulation ofthe detector using GEANT3 [71]. No dependence on thegeneratorisobservedandtheaverage A×

ε

forthethree generators is usedin orderto reduce statisticalfluctuations. This correction isofthesameorderasreportedin [11].Adependence on multiplicity is observed; for pT<3 GeV/c, A×

ε

increases by ∼^{10% from} multiplicity class I to class X. In the calculation of A×

ε

, a weighting procedure is used to account forthe fact that (1) A×

ε

may varysignificantly overthe widthof a pT bin inthe measuredspectrum and(2)thesimulated pT distributions usedinthecalculationdonotnecessarilyhavethesameshapesas themeasuredp_T distributions.IntheMonteCarlosimulations,the generatedandreconstructed pT spectra(thedenominatorandnu- merator inthe A×

ε

calculation, respectively) areconstructed in narrow p_T binsandthenweightedusingafitofthemeasured p_T spectra.Thesimulated pT spectraafterthisweightingareusedto recalculate A×

ε

in thewider pT binsusedforthemeasured pT spectra.Thisprocedure (alsoused in [8,9,47,48,50] andothers) is repeateduntilthe changesinthe correctionfactorbecome negli- giblebetweeniterations;nomorethanthreeiterationsareneeded fortheprocesstoconverge.

A “signal-loss” correction is also applied, which accounts for K^∗0 andφmesonsinnon-triggeredevents.Thisisevaluatedusing the same simulations as the acceptanceand efficiency. Tocalcu- late this correction factor, the simulated resonance p_T spectrum beforetriggeringandeventselectionisdividedbythecorrespond- ing pT spectrumafterthose selectionsforeach multiplicity class.

The signal-loss correction typically deviates from unity by <1%, but can deviate by ∼^{10% at low p}T forthe lowest multiplicity class. Different event generators provide different descriptions of the non-triggered component of the various multiplicity classes.

Following [9], thePYTHIA6simulation isused toobtain the cen- tral values for this correction, while an uncertainty is evaluated by comparing the central values to those givenby PYTHIA8and EPOS-LHC. Finally, the pT spectraare normalizedby the number ofacceptedeventsandcorrectedasin [9] toaccountforINEL>0 events that do not pass the event-selection criteria. This correc- tion, which is calculated using the PYTHIA6 simulation, is most important (24%) forthelowest multiplicity class andis <1%for high-multiplicitycollisions(classesI-VIII).

4. Results

The p_TspectraforK^∗0andφinthevariousmultiplicityclasses, aswellastheratiosofthesespectratotheinclusiveINEL>0 spec- trum, are shownin Fig.1. For pT^{4 GeV}/c the increase in the slopes of the p_T spectra from low to high multiplicity is clearly visible.Forhigher pT,thespectra indifferentmultiplicity classes allhavethesameshape,indicatingthattheprocessesthatchange the shape of the pT spectra in different multiplicity classes are dominantprimarilyatlow pT.A similarbehaviorwasreportedfor unidentifiedchargedhadrons,K⁰_S,,,andforthesamecolli- sionsystem [9,58].

The p_T-integratedyieldsdN/dy andmeantransversemomenta ^pT^{areextractedfromthe p}Tspectrainthedifferentmultiplicity classes.For eachmultiplicity class, theφ yieldis extrapolatedto the unmeasuredregion (p_T<0.5 GeV/c) by fitting a Lévy-Tsallis function [72–74] tothemeasured pTspectra.Formultiplicityclass

Fig. 1.pTspectraofK^∗0andφinppcollisionsat√

s=13 TeVfordifferentmultiplicityclasses,scaledbyfactorsasindicated.Thelowerpanelsshowtheratiosofthe multiplicity-dependentpTspectratothemultiplicity-integratedINEL>0 spectra(withbothlinearandlogarithmicverticalscales).

Fig. 2.Mean transversemomentapTofK^∗0andφasfunctionsofdNch/dη|η|<0.5.Resultsareshownforppcollisionsat√

s=13and7 TeV [8],aswellasforp–Pb collisionsat √_s

NN=5.02 TeV [11].Themeasurementsinppcollisionsat √

s=^{13 TeVarealsocomparedtovaluesfromcommonevent}generators [33,38,69,70].Bars representstatisticaluncertainties,openboxesrepresenttotalsystematicuncertainties,andshadedboxesshowthesystematicuncertaintiesthatareuncorrelatedbetween multiplicityclasses(negligibleforp–Pb).

I(X)the extrapolatedφyield is12%(34%)ofthe totalyield.The K^∗0 is measured down to pT=^{0 and no low-p}T extrapolationis neededtocalculatedN/dy forthatparticle.Theextrapolatedyield athighpTisnegligibleforbothparticles.The^pT^{isevaluatedus-} ingthemeanvalueofthefitfunctionwithineachpTbin,weighted bythemeasuredyieldineach bin.Forφ,thefitfunctionisused to calculate the yield and mean pT in the low-pT extrapolation region,but thisisnot needed forK^∗0. The sources of systematic uncertaintyforthepTspectraalsocontributetothesystematicun- certaintiesofdN/dyand^pT^{,exceptfortheITS-TPCmatchingand} branching ratio uncertainties, which are p_T-independent and do not contribute to theuncertainties ofthe ^pT^{values. Additional} uncertaintiesindN/dy and^pT^ofφareevaluatedbyvaryingthe fitrangeandtheformoftheextrapolationfunction:Bose-Einstein, Boltzmann,andBoltzmann-Gibbsblast-wave [75] distributions,as wellasanexponentialinm_T(wherem_T≡

M²+^p2_T/c²andMis themassoftheparticle).Theuncertaintyinthetotalφyielddue totheextrapolationinclassI(X)is1% (4.4%).Thereisnoextrap-

olationuncertaintyforthedN/dy ofK^∗0. Varyingthefitfunction produces a negligible changein ^pT ^{forK∗0 andsuch variations} are not included in the systematic uncertainties. The systematic uncertainties on the yield and ^pT ^{are obtained by varying the} parametersusedinthedefaultanalysis.Toinvestigatewhetherthe changesintheyielddN/dyand^pT^{arecorrelatedbetweendiffer-} entmultiplicity bins,the effectofchangingeach parameteris si- multaneouslyevaluatedforboththeminimumbiaseventclassand each individual multiplicity class. The multiplicity-correlated and uncorrelatedcomponentsofthesystematicuncertaintiesaresepa- rated,withthelatterbeingplottedasshadedboxesinFigs.2-5.

The meantransversemomenta ^pT^{forK∗0 and}φare shown inFig.2asfunctionsof^dNch/d

η

_|η_|<0.5andcomparedwithother ALICEmeasurementsandresultsfrommodelcalculations.The^pT valuesin pp collisions at √

s= 7 TeV [8] and 13 TeVfollowap- proximately the same trend. The ^pT ^{values of K∗0 and} φ rise slightly faster as a function of ^dNch/d

η

_|η|<0.5 in pp collisions than in p–Pb collisions for ^dNch/d

η

|η|<0.5^{5; the p}T ^values in pp and p–Pb collisions both rise faster than those in Pb–Pb

Fig. 3.Mean transversemomentaforK^∗0 andφarecomparedwiththoseforK⁰_S, (anti)protons,+,⁻+⁺,and⁻+⁺inppcollisionsat√

s=^{13 TeVasa} functionof^dNch/dη|η|<0.5[9,18].Thevaluesfor+inthelowestmultiplicity classandfor⁻+⁺ areshiftedhorizontallyforvisibility.Barsrepresentstatis- ticaluncertainties,openboxesrepresenttotalsystematicuncertainties,andshaded boxesshowthesystematicuncertaintiesthatareuncorrelatedbetweenmultiplicity classes.

collisions as discussed in [8,11]. The measured ^pT ^{values are} compared withfive differentmodel calculations:PYTHIA6 (Peru- gia 2011tune) [69],PYTHIA8(Monash 2013tune,both withand withoutcolor reconnection) [70], EPOS-LHC [38],andDIPSY [33].

PYTHIA8withoutcolor reconnectionprovides an almost constant ^pT^{as dN}ch/d

η

_|η|<0.5 increases; thisisa very different behav- ior with respect to the trends measured by ALICEand given by the other model calculations. Turning color reconnection on in PYTHIA8 gives better qualitative agreement with the measure- ments,althoughthecalculationstillsomewhatunderestimatesthe ^pT^{valuesforhadronscontaining strange quarks(K0}S,K^∗0,φ,, ,and ) [9]. Color reconnectionin PYTHIA8introduces aflow- likeeffect,resultinginan increase in^pT^{valueswithincreasing} multiplicity without assuming the formation of a medium that couldflow [62].PYTHIA6provides agooddescriptionofthe^pT valuesforφ,butunderestimates^pT^{forK∗0.Thep}T^valuespre- dicted by EPOS-LHC are consistent withthe measured values for φ,butslightlybelowthevaluesforK^∗0.Amongthemodelresults obtainedforthepresentwork,EPOS-LHCgivesthebestagreement withthemeasureddata.DIPSYgivesalargerincreasein^pT^from low to high ^dNch/d

η

_|η|<0.5 than is actually observed; this dis- crepancyisgreaterfortheφandisalsoobservedforotherstrange hadrons [9].

Thevaluesof^pT^{forK∗0 and}φarecomparedwiththosefor K⁰_S, (anti)protons, andstrange baryonsin the same collision sys- tem in Fig. 3. In central A–A collisions, a mass ordering of the ^pT ^{values is observed; particles with similar masses(e.g., K∗0,} p, and φ) have similar ^pT ^{[11,51]. This behavior has been in-} terpretedasevidencethat radialflowcould bea dominantfactor in determining the shapes of hadron pT spectra in central A–A collisions. However, this mass ordering breaks down for periph- eralPb–Pb collisions,aswell asp–Pbandppcollisions(see Fig.7 in [14] and measurementsreportedin [8,9,18]).Inppcollisionsat

√s= ^{13 TeV, the p}T^{values for K∗0 are greater than those for} themoremassiveprotonandforthesamemultiplicity classes.

The^pT^valuesforφexceedthoseforandevenapproachthose for,despite the approximately 30% largermass of the . This couldbeamanifestationofdifferencesbetweenthe pT spectraof mesonsandbaryonsordifferentbehavior forresonances incom- parison tothe longer livedparticles. In [8], the Boltzmann-Gibbs blast-wave model was used to predict the pT spectra of light- flavorhadronsbasedonacombinedfitofπ^±,K^±,and(anti)proton p_T spectra.Thisstudy suggested that strange hadrons(K⁰_S,,, and)andotherlight-flavorhadronsmightparticipateinacom-

mon radial flow, even in pp collisions, but that K^∗0 and φ do notfollowthiscommonradialexpansion(fordetailsofthisstudy, see [8]).The samebehavior could resultinthe violationofmass orderingfor^pT^seenat√

s=^{13 TeV.}A deviationofthe^pT^val- ues of short-lived resonances above the trend for other hadrons could inprinciplebeexplainedby re-scatteringoftheresonance- decaydaughtersduring thehadronicphaseofthecollision,which is expected to be most important at low pT [41]. However, the strongestre-scatteringphenomenaoccurincentralA–Acollisions, where no deviationfrom mass ordering isobserved. In addition, such effects wouldbe strongerfor theshorterlived K^∗0 thanfor the φ, which decays predominantly outside the hadronic phase (even incentralA–Acollisions)andshould beminimally affected byre-scattering.Ontheotherhand,theobservedviolationofmass ordering could be dueto differencesbetweenbaryon andmeson pT spectra.Baryon-to-mesonratiossuchasp/πand/K⁰_Sareob- served [8,10] tobeenhancedatintermediatep_T(∼^{3 GeV}/c),even in pp and p–Pbcollisions, while similar enhancement is not ob- served in meson-to-meson ratios like K/π. Differences between baryons and mesons have also beenobserved inthe m_T spectra ofhadronsmeasuredatRHICenergies [76,77].FormT^{1 GeV}/c, mesonmTspectrafollowonecommontrend,whilebaryonsfollow a different, more steeply falling trend as a function of m_T. Such differencesbetweentheshapesofbaryonandmesonspectramay resultinmesonshavinglarger^pT^{valuesthanbaryonswithcom-} parable masses.The breakdownofmassordering, with^pT(p)<

^pT(K^∗0)≈ ^pT()<^pT(φ)≈ ^pT()^{,isa commonfeatureof} the modelsshowninFig.2.Thisbehaviormaybe aconsequence ofhadron productionviafragmentationathigh pT ormT;meson formation requiresonlythe productionofa quark-antiquark pair, whilebaryonformationrequiresadiquark-antidiquarkpair [76].

The pT-integrated yields ofK^∗0 andφ are showninFig. 4as functionsof^dNch/d

η

_|η|<0.5.Forbothparticles,dN/dyexhibitsan approximatelylinearincreasewithincreasing^dNch/d

η

|η|<0.5.Re- sultsforppcollisionsat√

s=^{7and13 TeVandforp–Pbcollisions} at√

sNN=^{5.02 TeVfollow}approximatelythesametrends.Thisin- dicates that,for a givenmultiplicity, K^∗0 andφ productionrates do not depend on the collision system orenergy. Similar results are seenforstrangehadrons [9].ThedN/dy valuesarealsocom- paredwiththoseobtainedfromthesamemodels studiedforthe discussion of ^pT^{. Forthe K∗0, EPOS-LHC and PYTHIA8 without} color reconnection give the best descriptions, the other PYTHIA calculations exhibit fair agreement with the measured data, and DIPSYtendstooverestimatetheK^∗0yields.Theφyieldstendtobe slightlyoverestimatedbyEPOS-LHCandslightlyunderestimatedby DIPSY, while the PYTHIAcalculationsunderestimate the φyields by about40%. The selectedPYTHIA tunes alsounderestimate the yields of , , and by similar factors [9]. For thesebaryons, the EPOS-LHC description becomes less accurate withincreasing strangenesscontent;DIPSYdescribestheandyieldswell,but underestimatestheyieldsof[9].

The ratiosofthe pT-integratedparticleyieldsK^∗0/K,φ/π, φ/K, and/φareshowninFig.5asfunctionsof^dNch/d

η

|η|<0.5[9,18].

Within their uncertainties the ratios in pp collisions at √ s= ⁷ and 13 TeV andin p–Pbcollisions at √

sNN= ^{5.02 TeVare con-} sistent for similar valuesof ^dNch/d

η

|η|<0.5. There isa hintof a decreaseinK^∗0/K withincreasing^dNch/d

η

_|η|<0.5inallthreecol- lisionsystems;forppcollisionsat√

s= ^{13 TeVtheK∗0}/K ratioin thehighestmultiplicityclassisbelowthelow-multiplicityvalueat the2.3

σ

level(consideringonlythemultiplicity-uncorrelated un- certainties). ThedecreaseinK^∗0/K incentralPb–Pbcollisions [11, 48,49] hasbeenattributedtore-scatteringoftheK^∗0 decayprod- uctsinthehadronicphaseofthecollision [46].Itremainsanopen question whether a decreasein pp collisions could be caused by the same mechanism. EPOS-LHC provides the best description of theK^∗0/K ratioinppcollisionsat√

s=^{13 TeV.PYTHIAandDIPSY}

Fig. 4.pT-integrated yieldsdN/dyofK^∗0(averageoftheparticleandantiparticle)andφasfunctionsof^dNch/dη|η|<0.5.Resultsareshownforppcollisionsat√ s=^13and 7 TeV [8],aswellasforp–Pbcollisionsat√

sNN=5.02 TeV [11].Themeasurementsinppcollisionsat√

s=^{13 TeVarealsocomparedwithvaluesfromcommonevent} generators [33,38,69,70].Barsrepresentstatisticaluncertainties,openboxesrepresenttotalsystematicuncertainties,andshadedboxesshowthesystematicuncertaintiesthat areuncorrelatedbetweenmultiplicityclasses.

Fig. 5.Ratios of pT-integrated particle yieldsK^∗0/K,φ/π, φ/K,and /φ inpp collisionsat√

s=^{13 TeVasfunctionsofdN}ch/dη|η|<0.5[9,18].Thesemeasure- mentsarecomparedwithdatafromppcollisionsat√

s=^{7 TeV [8],p–Pbcollisions} at √

sNN=5.02 TeV [11,13],and Pb–Pb collisionsat √

sNN= 2.76 TeV [48,49].

Thewidths ofthe boxesfor pp collisions at √

s=13 TeV andp–Pb collisions donotrepresenttheuncertaintiesof^dNch/dη|η|<0.5. Themeasurementsfor pp collisionsat√

s=^{13 TeVarealsocomparedtoresultsfromcommoneventgener-} ators [33,38,69,70] andaCanonicalStatisticalModelcalculation [8].

tendto overestimate the ratioforlarge multiplicities anddo not reproducetheapparentdecreasewithincreasing^dNch/d

η

_|η|<0.5.

Theφ/π ratiogradually increases fromthelowest-multiplicity ppcollisions to mid-central Pb–Pbcollisions. This ratiocompares theyields oftwomesonswithzeronetstrangeness,oneofwhich hashiddenstrangeness.The canonicalstatisticalmodel(CSM) [8]

witha chemicalfreeze-outtemperatureof156 MeVpredicts that thisratio shouldhavelittledependenceon themultiplicity,since theφwouldnot besubjectto canonicalsuppression. Theresults ofthe CSMcalculation are inconsistent with the observed trend oftheφ/πratio.Forppcollisions at√

s=^{13 TeV, theincreasing} trendofthe φ/π ratiois reproduced fairly wellby the EPOS-LHC andDIPSY models, while the PYTHIA calculations underestimate the magnitude of the ratio. The φ/K ratio also follows a simi- lartrend in the threecollision systems.It is fairly constant as a

function of ^dNch/d

η

|η|<⁰.5,although there is an apparent small increase with ^dNch/d

η

_|η|<0.5 from the lowest multiplicities up to ^dNch/d

η

_|η_|<0.5≈^{400. EPOS-LHCsomewhat} overestimates the φ/K ratio,butisclosertothemeasuredvaluesthanPYTHIA,which significantlyunderestimatesφ/K.WhilePYTHIA6andDIPSYunder- estimate the φ/K ratio, both results exhibit small increases with increasing multiplicity, which isqualitatively similar to the mea- sured trend.The CSMcalculation does not describe thebehavior ofthemeasuredφ/K ratioforthe^dNch/d

η

_|η|<0.5 rangespanned bytheALICEppmeasurements.

In addition tocomparing the yields of φ topions and kaons, it may be instructive to compare and φ. These two particles contain thesame numberofstrange valence (anti)quarks: φ isa s¯^{s boundstateand} contains twostrange valence quarks.How- ever, would be subject to canonical suppression, unlike the strangeness-neutral φ. Fig. 5 also shows the /φ ratio in pp, p–Pb, and Pb–Pb collisions. The ratio increases with increasing ^dNch/d

η

|η|<0.5 for low-multiplicity collisions and is then fairly constantforawiderangeofmultiplicities:fromppandp–Pbcolli- sionsat^dNch/d

η

_|η|<0.5≈^{7 tocentralPb–Pb}collisions.Thereisa possiblesmallincreaseinthe/φratiofrom^dNch/d

η

|η|<0.5≈⁷ tothe highest-multiplicityp–Pbcollisions,aswell asadifference on the 1.5

σ

level between the p–Pb and Pb–Pb measurements at ^dNch/d

η

_|η|<0.5≈^50. Nevertheless, there is no clear increase in the ratio for ^dNch/d

η

|η|<0.5≥^{7. The decrease in} /φ with decreasing ^dNch/d

η

|η|<⁰.5 for low multiplicities could be inter- pretedasevidenceofcanonicalsuppressioninsmallsystems;the canonical statistical model predicts a decrease in the /φ ratio withdecreasing^dNch/d

η

|η|<⁰.5 thatisqualitativelysimilartothe measured data.However, canonicalsuppression wouldalsoresult in an increase inthe φ/K ratio withdecreasing ^dNch/d

η

_|η|<0.5, which is not observed. Given that and K havedifferent num- bersof strange valence (anti)quarks,it is expectedthat would bemoreaffectedby canonicalsuppression [8].Itwillbe interest- ing to extend the study of the φ/K ratio to lower multiplicities totest ifthereis anyincrease inthisratiodueto canonicalsup- pressionofkaonyields.Themeasuredmultiplicityevolutionofthe /φ and φ/K ratios suggests that the φ meson behaves as if it had between 1 and 2 units of strangeness: i.e., is enhanced morethanφ,whichis(possibly)enhancedmorethanK.Inaddi- tion,thereareindicationsofincreasesinthep/πand/K⁰_S ratios withincreasing^dNch/d

η

|η|<0.5[8,9] whicharequalitativelysimi- lartotheincreasein/φ,butsmallerinmagnitude.Thissuggests thatbaryon-mesondifferences(e.g.,baryonsuppressionormeson enhancement)mightbeacontributingfactor,butnottheonlyrea- son,forthelow-multiplicitybehaviorofthe/φratio.EPOS-LHC, which includes core-corona effects, gives an increasing trend in