Search for a common baryon source in high-multiplicity pp collisions at the LHC

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Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Search for a common baryon source in high-multiplicity pp collisions at the LHC

.ALICE Collaboration

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

Articlehistory:

Received21April2020

Receivedinrevisedform16September 2020

Accepted5October2020 Availableonline8October2020 Editor: M.Doser

Wereportonthemeasurementofthesizeoftheparticle-emittingsourcefromtwo-baryoncorrelations with ALICE inhigh-multiplicity ppcollisions at√

s=^{13 TeV.} ^The ^source ^radius^is ^studied ^with ^low relative momentum p–p, p–p, p–, and p– pairs as a function of the pair transverse mass mT consideringfortheﬁrsttimeinaquantitativewaytheeffectofstrongresonancedecays.Aftercorrecting forthiseffect,theradiiextractedforpairsofdifferentparticlespeciesagree.Thisindicatesthatprotons, antiprotons,s,andsoriginatefromthesamesource.WithinthemeasuredmTrange(1.1–2.2) GeV/c² the invariant radius of this common source varies between 1.3 and 0.85 fm. These results provide aprecise reference for studies of the strong hadron–hadron interactions and for the investigation of collectivepropertiesinsmallcollidingsystems.

©²⁰²⁰^CERN^for^the^benefitôf^theÂLICECollaboration.PublishedbyElsevierB.V.Thisisanopen accessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Correlationtechniqueshavebeenusedinparticlephysicssince the 1960s [1]. Signiﬁcant theoretical progress has been made to relate two-particle correlationsat small relative momenta to the study ofthespace-timepropertiesoftheparticle-emittingsource and the ﬁnal state interactions between the two particles [2,3].

Eventually,thesemethodswereusedtostudythesourcesize,also referred to as Hanbury Brown and Twiss (HBT) radius, created in heavy-ion collisions [4–14]. Collective effects such as hydrodynamic ﬂow introduce position-momentum correlations to the particleemission,andhencemodifythesourceradiiinheavy-ion collisions at LHC energies [5]. In these systems, the decrease of themeasuredsourceradiiwithincreasingpairtransversemomen- tumkT=| ^pT,1+ ^pT,2|/2,wherepTisthetransversemomentum ofeach oftheparticles, andthe transversemassmT=

k²_T+^m²^, where m is the average mass of the particle pair, is attributed to the collective expansion of the system created in the collision [5,15].Inthiscontext,therearepredictionsofacommonmT scalingoftheradiusfordifferentparticlepairs,whicharebasedon the assumption ofthe same ﬂow velocities andfreeze-out times forallparticlespecies [16,17].Therealsoisexperimentalevidence thatacommonmT scalingofthesourceradiusispresentforpro- tons and kaons in heavy-ion collisions [18]. On the other hand, forpionsthescalingseemstobeonlyapproximate [18,19],which could be explained by the larger effect of the Lorentz boost for lighter particles [16,18] but could also be inﬂuenced by the ef-

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

fect of feed-down from short-lived resonance decays. The radii obtainedforPb–Pb collisionsatthe LHCcan becompared tothe freeze-out volume obtained from statistical hadronization models [20] and are also essential ingredients for coalescence models [21–23].

Recent studies of high-multiplicity pp collisions reveal unex- pected similarities to heavy-ionreactions whenconsidering vari- ablesnormallylinkedtocollectiveeffects,angularcorrelations,and strangenessproduction[24–27].Thehadronizationinppcollisions isexpectedto occur ona similar time scaleforall particles, and ifacommonradialvelocityforallparticlesshouldbepresent,this wouldleadtoasimilarmT scalingofthesourcesizeasmeasured forheavy-ion collisions. Unfortunately, the informationregarding themT dependenceof the source size measured inpp collisions islimitedto low valuesofmT,asthe existingdata are basedon analysescarriedout withπ^–π ^and^{K–K pairs.}^These^studies^point toavariationoftheradiusasafunctionoftheeventmultiplicity andof thepair m_T [28–32]. However, aside a qualitative consideration ofa βT scaling [33], no quantitative description could be determinedsofar.

Itisknownthatstronglydecayingresonancesmayleadtosig- niﬁcantexponentialtailsofthesourcedistribution,whichcanin- ﬂuence inparticular the measured π^–π correlations inheavy-ion collisions [34–37]. This effect is even more pronounced insmall collision systemssuch aspp andp–Pb [38,39], andcan substan- tiallymodifythemeasured sourceradii,not onlyformesons,but forbaryonsaswell.Sofarasolidmodelingofthestrongresonance contributiontothesourcefunctionisstillmissing.

Inthiswork, wepresenttheﬁrststudy ofthesourcefunction with a quantitative evaluation of the effect of strong resonance

https://doi.org/10.1016/j.physletb.2020.135849

0370-2693/©²⁰²⁰^CERN^for^the^benefitôf^theÂLICECollaboration.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

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decays.The searchforacommonparticle-emitting sourceiscon- ductedemployingdatameasuredinhigh-multiplicityppcollisions at √

s=13 TeV. The emission sources of protons andbaryons are studied using p–p andp– correlationsasa function of the pairmT.After correctingfortheeffectofstrongresonancedecays, the overall source size decreases signiﬁcantly by up to 20% and the values extracted from the different pair combinations are in agreement.Thecommonparticle-emittingsourcedescribedinthis work willallow fordirectcomparisonsof thesourcesizes to the ones resulting from theoretical models and the presence of collective phenomena in smallcolliding systems to be studied ina complementary wayto analyses carried out so far [28–32,38,39].

Theseanalysesconcentratedonπ^–π^andK–K correlationstudiesin ppcollisions,probingthekT andmT rangesofupto1–1.5 GeV/c² andobservinga decreaseofthesourceradius athighermT,with themeasuredradiireachingvaluesevenbelow1 fminthecaseof minimumbiasevents.ThehighermT rangeisonlyaccessiblewith baryonfemtoscopy.

Additionally, recentALICEstudies revealedthat smallcollision systems, such aspp, area suitable environment to study the interaction potential between more exotic pairs, like p–K⁻, p–, –,p–⁰,andp–⁻[40–44].Thedataofhigh-multiplicitytrig- gered pp collisions at √

s=^{13 TeV} ^provides ^a signiﬁcantly im- proved precision compared to the previously analyzed minimum bias data.Detailed studies ofthe interactions will be enabledby a precise knowledge of the size of the common source for particleemission, once correctedforthe broadeningdueto the resonance decays, which depends on the pair type. Moreover, the effectivesourcesizeisanimportantinputforthemodelingofco- alescence and hasconsequences forthe prediction of antimatter formation [21–23,45,46].

2. Dataanalysis

Thispaper presentsmeasurements ofthe p–p, p–p,p–,and p– correlation functions in high-multiplicity pp collisions at

√s=^{13 TeV}^performed^withALICE [47,48].The high-multiplicity trigger selected events based on the measured amplitude in the V0 detector system [49], comprisingtwo arraysof plasticscintil- lators at 2.8<

η

<5.1 and −³.7<

η

<−¹.7. The thresholdwas adjusted such that the selectedevents correspond tothe highest 0.17%fractionofthemultiplicity distributionofall INEL>0 collisions.Insuchevents,anaverageof30charged-particletracksare foundintherange|

η

_|<0.5 [50],whichconstitutesanincreaseby afactorofaboutfourwithrespecttotheminimumbiasdatasam- ple[42].The V0 timinginformationwasevaluatedwithrespectto theLHCclocktodistinguishcollisionswiththebeampipematerial orbeam–gasinteractions.

TheInnerTrackingSystem(ITS) [48] andTimeProjectionCham- ber (TPC) [51] arethemaintrackingdevicesinALICE.Theycover thefullazimuthalangleandthepseudorapidityrangeof|

η

_|<0.9.

The solenoidsurrounding thesedetectorscreates ahomogeneous magnetic field of B=⁰.5 T directed along the beam axis which defines the z direction. The spatial coordinates of the primary eventvertex(PV)arereconstructedonceusingglobaltracksrecon- structedwiththe TPC and ITS andonceusing ITS tracklets [47].If both methods yielda vertex, the longitudinaldifference between thetwo, z,isrequiredtobe lessthan 5 mm.The z component of the vertex, preferably determined by global tracks, hasto lay within |^Vz|<10 cmofthenominalinteraction pointtoensure a uniform detectorcoverage. Multiple reactions per bunch crossing areidentified bythepresenceofsecondary collisionvertices [47].

Approximately 10⁹ events fulﬁll the above requirements andare available forthe analysis. The identiﬁcation ofprotons andtheir respectiveantiparticlesfollowsthecompletesetofcriterialistedin Refs. [41,42].Primaryprotons areselectedin thetransverse- mo-

mentum rangebetween0.5 GeV/c and 4.05 GeV/c within |

η

|<

0.8. Particle identiﬁcation (PID) isperformed by using the infor- mationprovidedbythe TPC andtheTime-Of-Flight(TOF) [52] de- tectors.Theenergylossinthe TPC gasismeasuredforeachtrack, while the timing information of TOF is required for tracks with p>0.75 GeV/c.Particlesareidentiﬁedbyaselectiononthedevia- tionsfromthesignalhypothesesinunitsoftherespectivedetector resolution

σ

TPCand

σ

TOF,accordingtonσ=

n²σ,TPC+n²σ,TOF<3.

Thedistance ofclosest approach (DCA)to the PVisrestricted to a maximum of 0.1 cm in the transverse plane and 0.2 cm in the z direction, in order to suppress weak decay products or particles created in interactions with the detector material. The compositionofthesample isobtainedfollowingthe methodsde- scribed in [41]. For this purpose, events were generated with Pythia8.2 [53] (Monashtune [54]),processedbyGEANT3 [55],ﬁl- teredthroughtheALICEdetectorresponseandsubsequentlyhan- dledbythereconstructionalgorithm [48].Thesesimulationswere usedtoestimate thattheselectedprotonsandantiprotonshavea momentum-averaged purity of 99%. The fraction of primary and secondary contributions was estimated by a ﬁt of templates of their individual DCA distributions from MC to the p_T-integrated measureddistributions.Thiswaythesample wasfoundtoconsist of82% primaryparticles.Theremainder isduetoweak decaysof (⁺)baryonscontributingwith13%(5%).

The () candidates are selected following the procedures discussed in[41,42] by reconstructing the weak decay→^pπ⁻ (→^pπ⁺^),^which^hasâ^branching^ratioôf63.9% [56].Thecombi- natorialbackgroundisreducedbyrequiringthedistanceofclosest approachbetweenthedaughtertracksatthesecondaryvertexto be smallerthan 1.5 cm.A straight lineconnectingthe secondary vertexwiththePVdefinesthetrajectoryofthecandidate.Pri- marybaryons areselectedbyrequiringacosineofthepointing angle (CPA) between the momentum vector of the candidate anditstrajectorytobelargerthan0.99.Thereconstructeddaugh- terparticletracksare requiredtohaveanassociatedhit eitherin theSiliconPixelDetector(SPD) ortheSiliconStripDetector(SSD) layersofthe ITS or the TOF detectorinorder tousetheir timing information to reduce the remaining contributions from out-of- bunchpile-up.Theproton-pioninvariantmassdistributionisfitted using the sum of a double Gaussian to describe the signal and a second order polynomial for the combinatorial background. In the p_T rangebetween0.3to4.3 GeV/c,the andcandidates arereconstructedwithamassresolutionbetween1.5 MeV/c² and 1.8 MeV/c². Choosing a mass window of 4 MeV/c² around the nominal mass [56] results in a pT-averaged purity of 96%. Sim- ilarly to the case of protons, CPA templates of the primary and secondarycontributionsaregeneratedusingMCsimulations.These andaproductionratiobetweenand⁰ of1/3 [57–60],areused to decompose the sample ofselected and candidates. It is found to consist of 59% baryons directly produced in the collision, while19% originate from electromagneticdecays of a ⁰. Additionalcontributionsfromweakdecaysof⁻ and⁰ amount to11%each.

3. Correlationfunction

The observable in femtoscopic measurements is the correlationfunction C(k^∗),wherek^∗=¹₂ · |^p^∗2−^p^∗1| ^denotes ^the^relative momentum of particle pairs and p^∗₁ andp^∗₂ are the particlemo- menta inthe pair rest frame (PRF, p^∗₁= −^p^∗₂^). Ît îs ^computed âs C(k^∗)=N Â_B⁽₍_k^k∗^∗⁾),where A(k^∗)istherelativemomentumdistribu- tion of correlated particle pairs, obtained from the same event, and B(k^∗) the corresponding distribution of uncorrelated pairs.

Thelatter isobtainedby pairingidentiﬁed particles ofone event withparticlesfroma different(“mixed”)event. In ordertoavoid

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Table 1

Weightparametersoftheindividualcomponentsofthep–p andp–correlationfunction.Misidentiﬁcations ofparticlespeciesXaredenotedasX and˜ feed-downcontributionshavethemotherparticlelistedasasub- index.Forthecontributionsinboldtext,thecorrelationfunctionsaremodeledaccordingtotheinteraction potential,whiletheothersareassumedtobeﬂat.

p–p p–

Pair λparameter(%) Pair λparameter(%) Pair λparameter(%)

pp 67.0 p 46.1 p+⁰ 0.5

pp 20.3 p− 8.5 p+0 1.0

pp 1.5 p0 8.5 p˜ 0.3

p⁺p 8.5 p⁰ 15.4 p˜⁻ 0.1

p⁺p⁺ 0.3 p 7.0 p˜0 0.1

pp⁺ 1.3 p⁻ 1.3 p˜⁰ 0.1

˜

pp 0.9 p⁰ 1.3 p˜ 3.3

˜

pp 0.1 p0 2.3 p˜ 0.5

˜

pp⁺ 0.1 p⁺ 2.9 p⁺˜ 0.2

˜

pp˜ 0 p+− 0.5 p˜˜ 0

anybias duetoacceptanceandreconstruction effects,only those eventsare mixed,forwhich thedifferencebetweenthepositions ofthevertexin z directionislessthan2 cmandthenumbersof globaltrackswithin|

η

|<0.8 differbylessthanfour.Thenormal- izationfactorN ^is^calculatedⁱⁿ^the^region^k^∗∈ [²⁴⁰,340]^MeV/c, where no femtoscopic signal is present and C(k^∗) theoretically approachesunity. In thelaboratory frame,the single-particletra- jectoriesofp–p and p–p pairsatlowk^∗ arealmostcollinearand hencehavea

η

and

ϕ

^∗∼^0.^Here,

η

referstothepseudorapid- ityofthetrackand

ϕ

^∗istheazimuthaltrackcoordinatemeasured at9radii inthe TPC,rangingfrom85 cm to245 cm,takinginto accounttrackbendingbecauseofthemagneticfield.Duetodetec- toreffectsliketracksplittingandmerging [18] thereconstruction efficiency for pairs in same and mixed events differs. In order to avoid a bias in the correlation function, a close-pair-rejection (CPR) criterion is applied by removing p–p and p–p pairs fulfill- ing

η

²+

ϕ

^∗²<0.01.Forp–andp–pairsnorejectionis considered.

A totalnumberof 1.7×¹⁰⁶ ⁽¹.3×¹⁰⁶⁾ ^{p–p (p–p)} ^and⁰.6× 10⁶ (0.5×¹⁰⁶⁾ ^p– (p–) pairs are found in the region k^∗<

200 MeV/c.Thecorrelationfunctionsofbaryon–baryonpairsagree within statistical uncertainties with their antibaryon–antibaryon pairs [18,61]. Therefore inthe following p–p denotes the combi- nation of p–p⊕^{p–p and} accordinglyforp–. The p–p and p–

correlation functionswere obtainedseparately in7 and6mT in- tervals,respectively,chosensuchthat thetotalamountofparticle pairsisevenlydistributed.

The theoretical correlation function is related to the two- particle emittingsource S(r^∗) andwave function ψ(r^∗,k^∗) [5]. It canbewrittenas

C

(

k^∗

) =

d³r^∗S

(

r^∗

)|ψ (

r

^∗

,

_k

∗

)|

²

,

(1)

wherer^∗ istherelativedistancebetweentheparticlepairdeﬁned inthePRF. Whenﬁttingthisfunction tothedatainthisanalysis, the freeparameters aresolely relatedto S(r^∗).The ψ(r^∗,_k∗)and theresultingC(k^∗)canbedeterminedwiththehelpofthecorre- lationanalysistoolusingtheSchrödingerequation(CATS) [62].The frameworkwas developedinordertomodelthecorrelationfunc- tioninsmallsystems,wherethestronginteractioncangiveriseto aparticularlypronouncedcorrelationsignal.Therefore,ψ(r^∗,k^∗)is preciselycalculatedasthenumericalsolutionofthesingle-channel Schrödinger equation,such thatadditionallytoquantumstatistics and Coulomb interactions the strong interaction can be included viaalocalpotential V(r^∗).

Residual correlationsfrom impurities and feed-down of long- lived resonances decayingweakly or electromagnetically [34] are taken into account by calculating the model correlation function C_model(k^∗)as

C_model

(

k^∗

) =

¹

+

i

λ

i

(

C_i

(

k^∗

) −

¹

),

(2)

wherethe sumruns overall contributions andwith themethod discussedinRef. [41].Inparticulartheweightsλi,whicharelisted separatelyforp–p andp–inTable1,arecalculatedfrompurity andfeed-downfractionsreportedinSec.2.

Tomodelthe p–p (p–)correlation function,residualcorrela- tionsduetothefeed-downfromp–(p–⁰ andp–⁻)pairsare explicitlyconsidered,whileallothercontributionsareassumedto be ﬂat. The residual correlations are modeled with CATSassum- ing the same source radius as the initial particle pair and use theoreticaldescriptions oftheir interactions followingRef. [63,64]

forp–⁻ and Ref. [65–67] for p–⁰. The models describing the p–interactionwillbediscussedlaterinthissection.Thecontri- butions of thesepairs to the p–p and p–correlation functions have to be scaled by λi and their signal smeared via a decay matrix [41,68] whichisbuiltaccordingtothekinematicsofthede- cay.Therefore,theresidualsignaloftheinitialpairistransformed to the momentum basis ofthe measured pair. Additionally, each contribution C_i is smearedto take into account effects ofthe fi- nite momentum resolution of the ALICE detector. Exceptfor the genuinecorrelations,thesestepsresultinaC_i(k^∗)∼^{1 for}âll^combinations, in particular due to the rather small λ parameters of mostresidualcontributionsasshowninTable1.Eitheraconstant oralinearbaselineC_non₋_femto(k^∗)isincludedinthetotalfitfunc- tion Cfit(k^∗)=^Cnon−^femto(k^∗)·^Cmodel(k^∗). Theconstant factorcan, ifnecessary,introduceaslightcorrectionofthenormalizationN^. The linear baseline function extrapolates any remaining slope of C(k^∗)inthenormalizationregion,whichmayariseduetoenergy and momentum conservation [41,69], to the femtoscopic region.

Thedefaultassumptionisaconstant,withCnon−^femto(k^∗)=^a.

ThesourcefunctionS(r^∗)isassumedtohaveaGaussianproﬁle

S

(

r^∗

) =

¹

(

4

π

r₀²

)

³^/²^exp

−

^r^∗² 4r²₀

,

(3)

where r₀ represents the source radius. The best ﬁt to the p–p correlationfunction withC_ﬁt(k^∗) isperformedinthe regionk^∗∈ [⁰,375] ^MeV/c and determines simultaneously all free parameters,namely r0 and the onesrelated to C_non₋_femto(k^∗).The gen- uine p–p correlation function is calculated by using CATS [62]

andthestrongArgonne v₁₈ potential [70] in S, P,and D waves.

Thesystematicuncertaintiesonr0 associatedwiththefittingpro- cedure are estimated by i) modifying the upper limit of the fit regionto350 MeV/c and400 MeV/c,ii)replacingthenormaliza- tionCnon−^femto(k^∗)=â^byâ^linear^function,ⁱⁱⁱ⁾êmploying^different modelsdescribingthe residualp–interaction asdiscussedlater in the text, and iv) modifying the λ parameters by varying the composition of secondary contributions by ±^20%, ^while ^keeping thesumofprimaryandsecondaryfractionsconstant.

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Fig. 1.Thecorrelationfunctionofp–p (left)andp–(right)asafunctionofk^∗inoneexemplarymTinterval.Statistical(bars)andsystematic(boxes)uncertaintiesare shownseparately.Thefilledbandsdepict1σ uncertaintiesofthefitswithCfit(k^∗)andareobtainedbyusingtheArgonnev18[70] (blue),χEFTLO [71] (green)andχEFT NLO [74] (red)potentials.Seetextfordetails.

In comparison to p–p, the theoretical models describing the p– interaction are much less constrained since data from hy- pernuclei and scattering experiments are scarce [41,71–74]. The femtoscopicfitisperformedintherangek^∗∈ [⁰,224]^MeV/c.The limitedamountofexperimentaldataleavesroomfordifferentthe- oretical descriptions of the p–interaction. In the measurement this is accounted for by performing the fits twice, where the S wave function of the p– pair is obtained once from chiral effective field theorycalculations(

χ

EFT)atleading order(LO) [71]

and once from the one at next-to-leading order (NLO) [74]. The systematic uncertainties on r0 associated with the fit procedure are estimated by i) changingthe upper limit ofthe fit region to 204 MeV/c and244 MeV/c,ii) replacing the normalizationcon- stantC_non₋_femto(k^∗)=â^byâ^linear^function,ândⁱⁱⁱ⁾^modifying^the λparametersbyvaryingR0/by±^20%.

Thesystematicuncertainties oftheexperimentalp–p andp–

correlation function take into consideration all single-particle se- lectioncriteria introduced inthe previous section,as well asthe CPRcriteriaonthep–p pairs.Allcriteriaarevariedsimultaneously up to 20%around thenominalvalues.To limitthe biasofstatis- ticalfluctuations, only variations witha maximumchangeof the pairyieldof20%areconsidered.Toobtainthefinalsystematicun- certainty on the source size,the fit procedureis repeatedfor all variationsoftheexperimentalcorrelationfunction,usingallpossi- bleconfigurationsofthefitfunction.Thestandarddeviationofthe resulting distribution for r0 is considered as the final systematic uncertainty.

In Fig. 1 the p–p and p– correlation functions of one rep- resentative mT interval are shown. The grey boxes represent the systematicuncertaintiesofthedataandcorrespondtothe1

σ

interval extractedfrom the variations of the selection criteria. The resulting relative uncertaintyof the p–p (p–) correlation func- tionreachesamaximumof2.4%(6.3%)inthelowestmeasuredk^∗ interval.Unlikeformeson–mesonorbaryon–antibaryonpairs,the broadbackgroundrelatedtomini-jetsisabsentforbaryon–baryon pairs [41,75]. The width ofthe ﬁt curves corresponds to the 1

σ

intervalextractedfromthevariationsofalltheﬁts.Incaseofthe p–p correlationfunction,thisresultsina

χ

²/ndf=¹.9.Theﬁtof thep–correlationfunctionusing

χ

EFTcalculationsatLOyieldsa

χ

²/ndf=0.91 whiletheﬁtusing

χ

EFTcalculationsatNLOyields a

χ

²/ndf=⁰.67.

Eachcorrelationfunctionineverym_T intervalisﬁttedandthe resultingradii are showninFig.2.The central valuecorresponds to themean estimatedfromthedistribution ofr0 obtainedfrom

Fig. 2.Sourceradiusr0asafunctionof mT^for^theâssumptionôfâ^purely^Gaus- siansource.Thebluecrossesresultfromfittingthep–p correlationfunctionwith thestrong Argonne v18 [70] potential.Thegreensquared crosses(red diagonal crosses)resultfrom fittingthe p– correlation functionswith thestrong χEFT LO [71] (NLO [74])potential.Statistical(lines)andsystematic(boxes)uncertainties areshownseparately.

thesystematicvariations. The statisticaluncertaintiesare marked withsolidlines,whiletheboxescorrespondtothesystematicun- certainties.Therelativevalue ofthelatterisatmost2.4%forthe radiiextractedfromp–p correlationsand8.3% and5.7%forthose extracted from p– correlations using the NLO and LO calcula- tions,respectively.Thedecreaseofthesourcesizewithincreasing m_T is consistent with a hydrodynamic picture, however, the ex- pectedcommonscaling [16] ofthedifferentparticlespeciesisnot observedforthetwoconsideredpairtypes.Thetwomeasurements show a similar trend that is shifted by an offset, indicating that therearedifferencesintheemissionofparticles.

4. Modelingtheshort-livedresonances

Theeffectofshort-lived resonances(c

τ

^{10 fm)}^feeding^into protons and baryons could be a possible explanation for the difference between the source sizes determined from p–p and p–correlations,whichwasobservedinFig.2.Inthepast,Bose- Einsteincorrelationsbetweenidenticalpions,measured inheavy- ion collisions, were interpreted in terms of a two-component source.It constitutes a core, which is the originof primary par-

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Fig. 3.Asketchrepresentingthemodiﬁcationofr_core^∗ intor^∗(dash-dottedlines),duetothepresenceofresonances(graydisks),decayingintotheparticlesofinterest(blue disks).ThecoordinatesystemisdeterminedbytherestframeofthetwodaughtersandconsistentwithEq. (1),wherek^∗representstheirmomenta(solidbluelines).The bluedottedlinesrepresenttheremainingdecayproducts,whichareassumedtobesinglepions.Incaseofaprimordialparticleintheinitialstateinsteadofaresonance, thelatterisnotconsidered(s^∗_res_,_i=0).

ticles, and a halo, which is the origin of pions produced by the decay of resonances [76]. In a detailedinvestigation of MC sim- ulations of heavy-ion collisions the source sizes were extracted from π^–π ^pairs ^for ^systems ^both ^with^and ^without ^the ^presence ofthesecontributions,andindeeddifferencesofabout1 fmwere found [35,77]. Similar effects are expected to arise for baryons, sinceshort-livedresonancessuchasandN^∗ decaymainlyintoa baryonandapion.Theexponentialnatureofthedecayisreﬂected in the appearance of exponential tails in the source distribution andan effective increaseof thesource size.Inspired by thispic- ture, a source distribution forbaryons is builtstarting fromtwo components:aGaussiancoreandanon-Gaussianhalo.

Inthiswork,theresonanceyieldsaretakenfromthestatistical hadronizationmodel(SHM) [78].Since thisstudyaims atquanti- fyingtheeffectofstronglydecayingresonancesonthesourcedis- tribution,inthefollowingonlyprimordialparticlesandsecondary decay products of short-lived resonances will be considered. Ac- cordingtotheSHM,theamountofprimordialprotons(baryons) areonly Pp=³⁵.8% (P=³⁵.6%) [79],implyingthattheeffectof thesecondariesissubstantial.Forprotons,57differentresonances withlifetimes0.5fm<c

τ

<13fm areconsidered.Relativetothe total numberofprotons, 22% originatefrom thedecayof a⁺⁺

resonance,15%fromthedecayofa ⁺ resonance,and7.2%from a ⁰ resonance.The remaining secondary protonsoriginate from heavier N^∗, and resonances, which contribute individually with less than 2%. Similarly, secondary baryons stem from 32 considered resonanceswithlifetimes 0.5 fm<c

τ

<8.5 fm. Most prominently^∗+,^∗⁰,and^∗− are eachtheoriginof12% ofall baryons,whiledecaysofheavierN^∗,,andresonancesindi- viduallycontributewithlessthan1%.Theweightedaverageofthe lifetimes(c

τ

res)oftheresonancesfeedingintoprotons(baryons) is 1.65 fm (4.69 fm),while the weighted average of the masses is1.36 GeV/c² (1.46 GeV/c²).Althoughtheamountofsecondaries is similarfor protonsandbaryons,there isa signiﬁcant differ- enceinthemeanlifetimeofthecorrespondingresonances,which ismuchlongerforthe.Qualitativelythiswillimplyalargeref- fectivesourcesizeforp–,asobservedinFig.2.

Inthefollowingthesourcefunction S(r^∗)isconstructedinclud- ingtheeffectofshort-livedresonances,assumingthatallprimor- dialparticlesandresonancesareemittedfromacommonGaussian sourceofwidthrcore.Consequently,theparticlesstudiedintheﬁ- nalstatecaneitherbeprimordialsordecayproductsofshort-lived resonances.Forapairofparticlestherearefourdifferentscenarios regardingtheirorigin,thefrequencyofeachgivenby P1P2, P1P˜2,

P˜1P2 and P˜1P˜2.Here P1,2 are the fractions of primordial parti- clesand P˜1,2=¹−^P1,2 thefractionsofparticlesoriginatingfrom short-livedresonances.Thetotalsourceis

S

(

r^∗

) =

^P1P2

×

^SP₁P₂

(

r^∗

) +

^P1P

˜

2

×

^S_P₁P˜₂

(

r^∗

)

+ ˜

^P1P₂

×

^S_P_˜₁_P₂

(

r^∗

) + ˜

^P1P

˜

₂

×

^S_P_˜₁_P_˜₂

(

r^∗

).

(4) To evaluate S(r^∗), the required ingredients are the fractions of primordial and secondary particles, and the individual source functionscorresponding tothepossiblecombinationsforthepar- ticleemission.Dependingontheaveragemassandlifetimeofthe resonances feeding to the particle pair of interest,each of these scenarios willresultin slightlydifferentsource sizes andshapes.

These composite source functions are diﬃcult to compute ana- lytically,however, a simplenumerical evaluation, outlined in the following, allows to iteratively build the full source distribution S(r^∗)for a givenrcore. The primordialemission of particles with arelativedistancer^∗_coreisrandomlysampledfromaGaussianwith widthequaltorcore.Theresultingparticlesarethen,basedonthe probabilities P1,2 andP˜1,2,assignedtobeeitherprimordialparti- clesorresonances.Theresonancesarepropagatedandtheirdecays are simulated. Forsimplicity it is assumed that each decay pro- ducesoneproton()andonepion.Itwascheckedthatincluding three-bodydecaysatthisstage wouldhavea negligibleeffecton theextractedradii.

Fig.3isaschematicrepresentationofthesourcemodiﬁcation, whichinvectorformisgivenas:

^r^∗

=

^r^∗_core

−

^s^∗_res_,₁

+

^s^∗_res_,₂

,

(5) where^s^∗_res_,₁₍₂₎ îs^the ^distance^traveled^by ^the ^first^(second) ^resonance.Thisislinkedtotheflighttimetres,whichissampledfrom anexponentialdistributionbasedonthelifetimeoftheresonance

τ

res:

s^∗_res

= β

_res^∗

γ

_res^∗tres

=

p^∗_res Mres

tres

,

(6)

where ^p^∗res is the momentum and Mres the mass of the corre- spondingresonance.Fortheone-dimensionalsourcefunctionS(r^∗) theabsolutevaluer^∗= |^r^∗|^needs^to^be^evaluated.^Given^the^deﬁ- nitionsinEq. (5) andEq. (6),therequiredingredientsarer^∗_core,the momenta,massesandlifetimes oftheresonances, aswell asthe anglesformedbythethreevectorsr^∗_core,s^∗_res_,₁ ands^∗_res_,₂.

(6)

Fig. 4.Thesourcefunctionsforp–p (bluecircles)andp–(redopencircles),gener- atedbyfoldingtheexponentialexpansionduetothedecayoftherespectiveparent resonanceswithacommonGaussiancorewithrcore=1.2 fm(dashedblackline).

AdditionallyshownareﬁtswithGaussiandistributions(dottedlines)toextractthe effectiveGaussiansourcesizes.

The masses and lifetimes of the resonances are ﬁxed to the average values reportedabove. The remaining unknown parameters,themomentaoftheresonancesandtheirrelativeorientation withrespecttor^∗_core,arerelatedtothekinematicsoftheemission.

In this work, the EPOS transport model [80] is used to quantify these parameters, by generating high-multiplicity pp events at √

s=^{13 TeV} ^and ^selecting ^the ^produced ^primordial ^protons, baryons andresonancesthatfeedintotheseparticles.Sincethe yields oftheheavierresonances areover-predictedbyEPOS,they are weighted such that their average mass Mres reproduces the expectation fromthe SHM. The source function S(r^∗) is builtby selecting a random r^∗_core and a random emission scenario based on theweights P1,2,which areknown fromtheSHM. A random EPOSeventwiththesameemissionscenarioisusedtodetermine

p^∗_res_,₁₍₂₎ andtheir relative directionto^rcore^∗ .To obtainr^∗ the res- onancesarepropagated,usingEq.(5) and(6), andthek^∗ oftheir daughtersisevaluated.Onlyeventswithsmallk^∗ arerelevantfor femtoscopy, thus, if the resulting k^∗>200 MeV/c, a new EPOS eventispicked.Theaboveprocedureisrepeateduntiltheresulting S(r^∗)achievesthedesiredstatisticalsigniﬁcance.

With thismethod, the modification ofthe source size due to the decay of resonances is fixed based on the SHM and EPOS, while the onlyfree fitparameter is thesize r_core of theprimor- dial (core) source. This procedure is used to refit the p–p and p– correlation functions. Theuncertainties are evaluated in the same wayasinthe caseofthe pure Gaussian source.Additional uncertainties duetoshort-lived resonances decayingintoprotons (baryons)areaccountedforbyrepeatingthefitandalteringthe massby0.2%(0.6%)andthelifetimesby2%(13%) [56].Whencom- paring the individual fits of the correlation functions in one mT intervalwiththeonesassumingapureGaussiansourcetheresult- ing

χ

² is found tobe similar. This impliesthat each systemcan still be described by an effective Gaussian source, albeit loosing thedirectphysicalinterpretationofthesourcesize.Thisproperty becomesevident fromFig. 4,in whichthe differentsource functions, used to describe the m_T bin plotted in Fig. 1, are shown.

As expected, aftertheinclusion oftheresonances, thesamecore functionresultsindifferenteffectivesourcesforp–p andp–.The Gaussian parametrizationyields an almost equivalent description of the source function up to about r^∗∼^{6 fm,} ^while ^for ^larger values thenew parametrizationwithinclusion of the resonances shows an exponential tail. Since most of the particles are emit- tedatlowerr^∗ values,thecorrespondingcorrelationfunctionsare similar. However, one major differencewiththe newapproach is the resulting source size, as the Gaussian coreis more compact than the effective sources. The resultingm_T dependence of r_core measuredwithp–p andp–pairsisshowninFig.5.Therelative

Fig. 5.Sourceradiusrcore asafunctionof mTfortheassumptionofaGaussian sourcewithaddedresonances.Thebluecrossesresultfromﬁttingthep–p correla- tionfunctionwiththestrongArgonnev18[70] potential.Thegreensquaredcrosses (reddiagonalcrosses)resultfromﬁttingthe p– correlationfunctionswiththe strongχEFTLO [71] (NLO [74])potential.Statistical(lines)andsystematic(boxes) uncertaintiesareshownseparately.

systematicuncertaintyisatmost2.6%forthecoreradiiextracted fromp–p correlationsand8.4%and6.2%forthoseextractedfrom p–correlationsusingthe NLO andLOcalculations, respectively.

Incontrast toa Gaussian source, thenew parametrizationofthe source function provides a common m_T scaling of r_core for both p–p andp–.Thisresultiscompatiblewiththepictureofacom- monemissionsourceforallbaryonsandtheirparentresonances.

5. Summary

The results forp–p and p– correlationsin high-multiplicity ppcollisionsat√

s=^{13 TeV}demonstrateacleardifferenceinthe effective proton and source sizes if a simple Gaussian source is assumed. A newprocedure was developed to quantify forthe ﬁrst time the modiﬁcation of thesource function dueto the effect of short-lived resonances. The required input is provided by thestatisticalhadronizationmodelandtheEPOStransportmodel.

Theansatz is thatthe sourcefunction isdetermined by thecon- volution of a universal Gaussian core source of size r_core and a non-Gaussianhalo.Theformerrepresentsauniversalemissionre- gionforallprimordialparticlesandresonances,whilethelatteris formedbythedecaypointsoftheshort-livedresonances.Thispic- tureisconﬁrmed by theobservationof a commonmT scaling of rcore forthe p–p andp–pairsinhigh-multiplicity ppcollisions, withrcore∈ [⁰.85,1.3] ^fm^for^mT∈ [¹.1,2.2]^GeV/c².Comparedto thevaluesobtainedwhenaneffectiveGaussianparametrizationis used,theoverallvaluesaresigniﬁcantlydecreasedbyupto20%.

The measurement of the core size of a common particle- emittingsource,correctedfortheeffectofstrongresonances,will allow for direct comparisons with theoretical models. Addition- ally,detailedstudiesofthemT dependenceofthecoreradiuswill enable complementary investigations of collective phenomena in smallcollisionsystems.

Ontheother hand,the assumptionof acommoncoresource, modiﬁed by the resonances feeding to the particle pairof interest,allowsforaquantitativedeterminationoftheeffectivesource foranykindofparticlepair. Firstofall, itenableshigh-precision studiesoftheinteractionpotentialsofmoreexoticbaryon–baryon pairs [41,42,44] thatrelyontwo-particlecorrelationmeasurements in momentum space anduse the p–p correlation asa reference toﬁx the emission source.It is alsorelevant forcoalescence ap- proachesaddressingtheproductionof(anti)(hyper)nuclearclus- ters.A crucial next step is to investigatethe applicability ofthe

(7)

newmethodformeson–meson andbaryon–mesoncorrelations. If the samemT scaling isobserved asforbaryons,thiswill provide an even more precisequantitative understanding ofthe common particle-emitting source.In anycase, such a study will shed fur- therlightontheproductionmechanismofparticlesandwillbea valuableinputfortransportmodels.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompetingﬁnan- cialinterestsorpersonalrelationshipsthatcouldhaveappearedto inﬂuencetheworkreportedinthispaper.

Acknowledgements

The ALICE Collaboration would like to thank all its engineers andtechniciansfortheirinvaluablecontributionstotheconstruc- tion of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collab- oration gratefully acknowledges the resources and support pro- videdbyallGridcentresandtheWorldwideLHCComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the following fundingagenciesfortheir supportinbuildingandrun- ningtheALICEdetector:A.I.AlikhanyanNationalScienceLabora- tory(YerevanPhysicsInstitute)Foundation (ANSL),State Commit- teeofScienceandWorldFederationofScientists(WFS),Armenia;

Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung,Austria;MinistryofCommunicationsandHighTech- nologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de DesenvolvimentoCientíﬁco e Tecnológico (CNPq), Fi- nanciadora de Estudose Projetos(Finep), Fundação de Amparoà Pesquisa do Estado de SãoPaulo (FAPESP) andUniversidadeFed- eraldoRioGrandedoSul(UFRGS),Brazil;MinistryofEducationof China (MOEC), MinistryofScience& Technology ofChina (MSTC) and NationalNatural Science Foundation of China (NSFC), China;

Ministry of Science and Education and Croatian Science Founda- tion,Croatia;CentrodeAplicacionesTecnológicasyDesarrolloNu- clear (CEADEN),Cubaenergía, Cuba;Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the Villum Fonden and Danish National Research Foundation (DNRF), Den- mark;Helsinki Institute ofPhysics(HIP), Finland;Commissariatà l’Énergie Atomique (CEA) and Institut National de Physique Nu- cléaire etde Physique desParticules(IN2P3)andCentre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum fürSchwerionenforschungGmbH,Germany;GeneralSecretariatfor ResearchandTechnology,MinistryofEducation,ResearchandRe- ligions,Greece;NationalResearchDevelopmentandInnovationOf- fice,Hungary; DepartmentofAtomicEnergy, GovernmentofIndia (DAE),DepartmentofScienceandTechnology,GovernmentofIndia (DST), University Grants Commission,Government ofIndia (UGC) andCouncil ofScientific andIndustrialResearch,India (CSIR),In- dia; Indonesian Institute of Science, Indonesia; Centro Fermi - MuseoStorico dellaFisica eCentroStudi e RicercheEnricoFermi andIstitutoNazionalediFisica Nucleare(INFN),Italy;Institutefor Innovative Science and Technology, Nagasaki Institute of Applied Science(IIST),JapaneseMinistryofEducation,Culture,Sports,Sci- enceandTechnology (MEXT)andJapan SocietyforthePromotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Interna- cional enCienciay Tecnología(FONCICYT)andDirección General deAsuntosdelPersonalAcademico(DGAPA),Mexico;Nederlandse OrganisatievoorWetenschappelijkOnderzoek(NWO),Netherlands;

TheResearchCouncil ofNorway, Norway;CommissiononScience

andTechnology forSustainableDevelopment inthe South(COM- SATS),Pakistan;PontificiaUniversidadCatólicadelPerú,Peru;Min- istry of Science and Higher Education, National Science Centre andWUT ID-UB,Poland; Korea Institute ofScience and Technol- ogyInformationandNationalResearchFoundationofKorea(NRF), Republicof Korea;Ministry of Education andScientific Research, Institute ofAtomic Physics andMinistryof ResearchandInnova- tion andInstitute of Atomic Physics, Romania; Joint Institute for NuclearResearch(JINR), MinistryofEducationandScienceofthe Russian Federation, National Research Centre Kurchatov Institute, RussianScience Foundation andRussianFoundation forBasic Re- search,Russia;MinistryofEducation,Science,ResearchandSport oftheSlovak Republic, Slovakia; NationalResearchFoundation of South Africa, South Africa; Swedish Research Council (VR) and KnutandAliceWallenberg Foundation (KAW),Sweden;European OrganizationforNuclear Research,Switzerland;SuranareeUniver- sityofTechnology (SUT), NationalScienceandTechnology Devel- opmentAgency(NSDTA)andOfficeoftheHigherEducationCom- missionunderNRU project ofThailand,Thailand;Turkish Atomic Energy Agency (TAEK), Turkey; National Academy of Sciences of Ukraine,Ukraine;ScienceandTechnologyFacilitiesCouncil(STFC), UnitedKingdom;NationalScienceFoundationoftheUnitedStates ofAmerica(NSF) andUnited StatesDepartmentofEnergy, Office ofNuclearPhysics(DOENP),UnitedStatesofAmerica.

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