Measurement of strange baryon–antibaryon interactions with femtoscopic correlations

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Physics Letters B

www.elsevier.com/locate/physletb

Measurement of strange baryon–antibaryon interactions with femtoscopic correlations

.ALICE Collaboration

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

Articlehistory:

Received25September2019

Receivedinrevisedform10January2020 Accepted13January2020

Availableonline16January2020 Editor: L.Rolandi

Two-particlecorrelationfunctionsweremeasuredforpp,p,p,andpairsinPb–Pbcollisionsat

√_s

NN=².76 TeVand √_s

NN=⁵.02 TeVrecordedbytheALICEdetector.Fromasimultaneousfittoall obtainedcorrelationfunctions,realandimaginarycomponentsofthescatteringlengths,as wellasthe effective ranges,wereextracted forcombined pand ppairs and,for thefirsttime, for pairs.

Effectiveaveragedscatteringparametersforheavierbaryon–antibaryonpairs,notmeasureddirectly,are alsoprovided.Theresultsrevealsimilarlystronginteractionbetweenmeasuredbaryon–antibaryonpairs, suggestingthattheyallannihilateinthesamemanneratthesamepairrelativemomentumk^∗.Moreover, thereportedsignificantnon-zeroimaginarypartandnegativerealpartofthescatteringlengthprovide motivationforfuturebaryon–antibaryonboundstatesearches.

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

1. Introduction

The interaction of baryons is a fundamental aspect of many sub-fields of nuclear physics. It is investigated extensively with numerousmethods,amongwhichare includedthedetailedanal- ysisofthepropertiesofatomicnuclei,thededicatedexperiments wherebeams ofone baryon type are scatteredon other baryons bound inatomic nuclei [1–6], andthe femtoscopytechnique [7].

Thelatterinvolvestheanalysisofmomentumcorrelationsoftwo particlesproducedinnuclearorelementarycollisions [8–12].Itis especiallyinterestingtoprobetheinteractionintheregionofthe lowrelative momentumofthepair,asitisthe mostrelevantfor a precise extraction of the strong interaction scattering parame- ters.Inparticular,thepossiblecreationofboundstatesforagiven baryon–baryonpairwasinvestigatedextensively [13–18].

Nuclearcollisions at relativisticenergies are abundant sources of various particle species. In particular, the number of baryons and antibaryons created in each central Pb–Pb collision at the LargeHadron Collider (LHC) [19] isof the orderof one hundred each atmid-rapidity (|^y|<0.5) [20–22], whichmakes it feasible tostudydetailsoftheirinteractions.Theseparticlesinclude,, ,andandanapproximatelyequalamountoftheircorrespond- ingantiparticles.

The interactions of baryons are well known for pp pairs and pn pairs. Measurements were also performed for p pairs [23–25]. Recently, a comparative study of the baryon–baryon and antibaryon–antibaryon interaction using Au–Au collisions at

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

√sNN=^{200 GeVhasbeenperformedby theSTARexperimentat} theRelativistic HeavyIonColliderandfound thatthe pp interac- tiondoesnotdifferfromtheppsystem [26].Also,correlationmea- surementsof baryon–baryonpairsin ppcollisions at√

s=^{7 TeV} andp–Pb collisions at √

sNN=⁵.02 TeV performedby the ALICE detector [27] attheLHCprovidemoreconstraintsonthe interac- tion of p and [28,29] as well asp⁻ [30] at low relative pairmomentum.

Concerningproton–antiprotonpairs,thestronginteractionwas studied in detail [31–35]. Of particular interest is protonium (or antiprotonichydrogen)–aproton–antiprotonCoulombboundstate, wherethestronginteractionalsoplaysasignificantrole.Thepro- toniumatomsarecreatedbystoppingantiprotonsinhydrogenand the stronginteraction is studiedvia shifts inthe X-rayspectrum fromthe expectedQED transitionsfrom excited states.In partic- ular, thereis evidenceof a contributionfromthe strong force to the 1Sand2P states.However, thenature ofprotoniumin these states, whetherit can be considered a nuclear bound state or a resultof theCoulomb interaction, remains an open question. For moredetailswereferthereadertothereviewpaper [35].

For baryon–antibaryon pairs with non-zero strangeness there ismuch lessexperimental dataavailable. However, low massen- hancements in the invariant mass distributions of pp, p, and pairs havebeen observed in charmonium and B meson de- cays [36–39]. Those enhancements, except for the pp pair, are slightly above the mass threshold of the baryon–antibaryon sys- tems and have widths which are below 200 MeV/c². Theoreti- cal interpretations of these results predict the existence of vari- ous baryon–antibaryon bound statesandpropose their classifica- https://doi.org/10.1016/j.physletb.2020.135223

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

tion [36].Resultspresentedinthislettermightshednewlighton thisdomain.

Thebaryon–antibaryonscatteringparameters,whenmeasured, could be implemented in the well-established model of heavy- ion collisions, UrQMD [40], which has the important feature of includingrescatteringin thehadronic phase.In particular, recent comparisonsoftheoretical calculationswiththeALICEdatashow thataproperdescriptionofthisphaseiscriticalforthecorrectre- productionof a large number ofobservables, like particle yields, transverse-momentum spectra,femtoscopy ofidentified particles, aswell as ellipticflow [41–44].The baryon–antibaryon annihila- tionisacriticalcomponentoftherescatteringprocess.Yet,atthe moment,forallbutnucleon-antinucleonpairs,onehastorelyon assumptionsabouttheinteractioncrosssection.Currentlyitisas- sumedthatallbaryon–antibaryonpairsannihilateinthesameway aspp pairsatthesametotalenergyofthepair,√

s,inthepairrest frame [40].

Femtoscopyallows oneto accessthebaryon–antibaryon inter- action at low pair relative momentum in a way which is com- plementary to dedicated scattering experiments.Only the strong interaction is present for p (p) and pairs, while for pp pairs, where also the Coulomb interaction is present, it is the dominantcontribution [7,45].Therefore,theparametersofthisin- teraction,together withthesourcefunction, determinetheshape ofthecorrelationfunction.Inaddition,theso-called“residualcor- relation”effect(presenceofanadmixtureofweakdecayproducts inthe sample ofa givenbaryon–antibaryon pair) results innon- trivial interconnections between measured correlation functions.

Thefemtoscopictechniquehasbeenemployedalreadytomeasure p and p scatteringparameters by the STARexperiment [46].

However, the mostimportant limitation of that studyis the fact thatnocorrectionsforresidualcorrelationswereapplied.

In this letter the scatteringparameters are extracted for p, p, and for the first time for pairs from femtoscopic cor- relations measured in Pb–Pb collisions at √

sNN=².76 TeV and

√sNN=⁵.02 TeVregistered bythe ALICEexperimentatLHC.The residualcorrelationsareaccountedforintheformalism proposed in Ref. [47] which does not attempt to “correct” for this effect (asproposedinan alternativeprocedureinRef. [48]),butinstead usesit toextract informationaboutthestronginteraction poten- tialparameters forthe parent particles.Therefore, itallows fora single andsimultaneous fitto allmeasured correlation functions.

This provides maximum statistical accuracy forthe obtained pa- rameters,minimisesthenumberoffitparameters andprovidesa non-trivialinternalconsistencyverification.

Recently, the pand pcorrelations measured by STAR [46]

havebeenreanalysedtakingintoaccounttheresidualcorrelations effect [47]. Thatstudy suggests that all baryon–antibaryon pairs mightannihilateinasimilarwayasafunctionoftherelativemo- mentumofthe pairk^∗,insteadofthepaircentre-of-mass energy

√s.Thiswork aims toprovide moreexperimental constraintson thesescenarios.

2. Experimentanddataanalysis

The data sample used in this work was collected in LHC Run 1 (2011) and Run 2 (2015), where two beams of Pb nuclei were brought to collideat thecentre-of-mass energyof √

s_NN= 2.76 TeVand√

sNN=⁵.02 TeV,respectively.Productsofthecolli- sionsweremeasuredbytheALICEdetector [27].Theperformance ofALICEisdescribedinRef. [49].

Inthisanalysistheminimum-bias(MB)triggerwas used.Itis basedonthe V0detectorconsistingoftwoarraysof32scintilla- tor counters, which are installed on each side of the interaction

Table 1

Centralityrangesandcorrespondingaveragecharged-particlemultiplicityden- sitiesatmid-rapiditydNch/dηforPb–Pbcollisionsat√

sNN=2.76 TeV [50]

and√

sNN=5.02 TeV [52].

Centrality dNch/dη√

sNN=2.76 TeV dNch/dη√

sNN=5.02 TeV

0–5% 1601±60 1943±53

5–10% 1294±^{49 1586}±⁴⁶

10–20% 966±^{37 1180}±³¹

20–30% 649±^{23 786}±²⁰

30–40% 426±^{15 512}±¹⁵

40–50% 261±9 318±12

point and cover pseudorapidity¹ ranges 2.8<

η

<5.1 (V0A)and

−³.7<

η

<−¹.7 (V0C).The MB triggerrequireda signalin both V0 detectors within a time window that is consistent with the collision occurringatthe centreof theALICEdetector. Theevent centrality wasdetermined by analysingthe amplitude ofthesig- nal fromtheV0detectorwiththe proceduredescribed indetails inRef. [50].

The position of the collision vertex was reconstructed using the signal from the Inner Tracking System (ITS) [27]. The ITS is composed of sixcylindricallayers ofsilicon detectorsand covers

|

η

_|<0.9. Its information can be used for tracking and primary vertex determination. However, in this analysisit was used only forthelatter.Theprimaryvertexforan eventwas requiredto be within±^{8 cmfromthecentreofthedetector.}

The analysis was performed in six centrality [51] ranges for both collision energies. They are listed in Table 1 together with their correspondingaveragecharged-particlemultiplicity densities atmid-rapidity^dNch/d

η

[50,52].

Charged-particletrajectory(track)reconstructionforbothcolli- sion energies was performed usingthe TimeProjection Chamber (TPC) detector [53]. The TPC is divided by the central electrode into two halves.Eachhalf iscapped withareadout plane which is composed of 18 sectors(covering the full azimuthal angle

ϕ

) with159padrowsplacedradiallyineachsector. Atracksignal in the TPC consistsof space points (clusters), and each of them is reconstructed in one ofthe padrows.A trackwas required tobe composedofatleast80clusterstominimisethepossibilitythata signal left bya singleparticle isreconstructedastwotracks. The parameters ofthe trackare determined by performing a Kalman fittoasetofclusters.Thequality ofthefitisdeterminedbycal- culating the

χ

² whichwasrequiredtobe lowerthan 4forevery cluster (each cluster has two d.o.f.), in order to select only well fittedtracks.

The identification of primary protons (antiprotons) was per- formed using the combined information fromboth the TPC and the Time-OF-Flight (TOF) detectors (a signal from both detectors was required), while the identification of () decay products (charged secondarypions and(anti)protons)requiredinformation onlyfromtheTPC.TOFisacylindricaldetectorcomposedofMulti- gapResistiveProportionalChambers(MRPC)locatedatr∼=^{380 cm} fromthebeamaxis.TracksarepropagatedfromtheTPCtotheTOF andmatchedto hitsinthisdetector.InthecaseofbothTPCand TOF, thesignals (energy loss dE/dx forthe TPC andthe time of flightfortheTOF)werecomparedtotheexpectedonesforagiven particle. The measured–expected signal deviationwas divided by the appropriate detectorresolution

σ

.The trackwas acceptedas a proton(pion)ifit fellwithin 3

σ

ofcombinedTPCandTOFex- pectedsignalsforaproton(pion)inagivendetector.

Trackswere acceptedforanalysisiftheir pseudorapidityrange was within the range |

η

_|<0.8 to avoid regions of the detector

1 Pseudorapidityisdefinedasη= −^ln(tan(θ/2)),whereθisthepolarangle.

Fig. 1.Rawinvariantmassdistributionofpπ⁻(pπ⁺)pairsusedtoobtainthe() candidatesfor Pb–Pbcollisionsat √

sNN=5.02 TeVinthe0–5% centralityrange.

Thedashedlinesrepresenttheselectionwidthusedintheanalysis.Notethatthe meanvalueofthedistributionisslightlyshiftedfromtherestmassof()by

∼^{1 MeV/c2dueto}imperfectionsintheenergylosscorrectionsthatareappliedin thetrackreconstruction.

withlimitedacceptance.Theparticleidentificationqualitydepends on the transverse momentum pT, thus a pT∈^[0.7, 4.0] GeV/c rangewasusedforprimary(anti)protonstoassuregoodpurityof thesample.Tomakesurethatthesampleisnotsignificantlycon- taminated by secondary particles coming from weak decaysand particle–detectorinteractions,aselectioncriterionontheDistance ofClosestApproach(DCA)totheprimaryvertexwasalsoapplied, separatelyinthetransverseplane(DCAxy<2.4 cm)andalongthe beamaxis(DCAz<3.2 cm).Thesecriteriawereoptimisedinorder toselectahighpuritysample of(anti)protons. The pT-integrated purity,basedonMonteCarlosimulations,ofthep(p)samplewas 95.4%(95.2%).

Theselectionof()isbasedontheirdistinctivedecaytopol- ogy in the decay channel ()→^pπ⁻ (pπ⁺), with a branch- ing ratio of 63.9% [31]. The reconstruction process, described in Ref. [54], is based onfinding candidates made of two secondary tracks having opposite charge and large impact parameter with respectto the interaction point. The purityof and samples is larger than 95% within the selected invariant mass range of

|^Mpπ−^MPDG|≤⁰.0038 GeV/c².The p_T-integratedinvariantmass distributionof()candidatesisshowninFig.1.

Thefemtoscopiccorrelationismeasuredasafunctionofthere- ducedmomentumdifferenceofthepairk^∗=¹₂

p1∗− ^p2∗ ,where

p₁^∗and ^p2∗ denotemomentaofthetwoparticlesinthepairrest frame.Itisdefinedas

C

(

_k

^∗

) =

N^A

(

_k

^∗

)

B

(

k^∗

) .

(1)

ThedistributionA,calledthe“signal”,isconstructedfrompairs ofparticlesfromthesameevent.Thebackgrounddistribution Bis constructedfrom uncorrelatedparticles measured withthe same single-particle acceptance. In this analysisit was built using the eventmixingmethodwiththetwoparticlescomingfromtwodif- ferenteventsforwhichthevertexpositionsinthebeamdirection agreewithin 2 cmandthe multiplicities differby nomore than 1/4 ofthe widthofthe givencentrality class forwhich thecor- relation function is calculated. Each particle was correlated with particlesfrom10 other events.Theparameter N ^{is anormalisa-} tionfactor.

In thiswork, the analysis is further simplified by performing all measurements as a function of the magnitudeof the relative momentumk^∗= |^k∗|^only.TheN ^{parameterwascalculatedduring}

thebackgroundsubtractionproceduredescribedinSec.3,inaway that thecorrelation functionapproaches unityink^∗∈ [⁰.13, 1.5] GeV/c forpp pairsandink^∗∈ [⁰.23, 1.5] ^{GeV/c forp},p,and pairs.

3. Fittingprocedure

Theextractionofthescatteringparametersfromthemeasured correlationfunctionsrequiresadedicatedfittingprocedure,which takesintoaccountthestrongandCoulombinteraction,depending onagivenpair.Thefittingformulaischosenappropriatelyforeach baryon–antibaryonpair.Afterwards,asimultaneousfittoallmea- suredpairs,takingintoaccountresidualcorrelations,isperformed.

Thedetailsoftheprocedurearedescribedbelow.

The two-particle correlation function inthe pairrest frame is definedas [55,56]

C

(

_k^∗

) =

S

(

r^∗

) (

_k^∗

,

r^∗

)

^2d3r∗

,

(2)

where S(r^∗) isthesourceemission function,(_k^∗,r^∗)is thepair wavefunction,and^{r∗ istherelative separationvector. Thesource} isassumedto havea spherically-symmetricGaussiandistribution according to measurements [12,57]. The pair wave function de- pendsontheinteractionsbetweenbaryonsandantibaryons.When only the strong interaction is present, the correlation function can be expressed analyticallyasa function of thescatteringam- plitude f(k^∗)=

1

f0+¹₂^d0k^∗2−^ik∗₋1

, and the one-dimensional source size R. This description is calledthe Lednický–Lyuboshitz analyticalmodel [7] (seeAppendixAfordetails).Inthiswork,the spin-averagedscatteringparametersareobtained,i.e.^f0thereal and ^f0 imaginary parts of the spin-averaged scatteringlength, andd0fortherealpartofthespin-averagedeffectiverangeofthe interaction.Theusual femtoscopicsignconvention isused,where apositive^f0 correspondstoattractivestronginteraction.

Accounting for residual correlations is an important ingredi- ent of every correlation function analysis involving baryons. A fraction of observed (anti)baryons comes from decays of heavier (anti)baryons.This isillustratedin Fig.2,wherethe maincontri- butions tothe pp correlationfunction aremarked inblue,to the pinyellowandtotheinred.Insuchacase,thecorrelation function is built forthe daughter particles, while theinteraction hastakenplacefortheparent baryons.Toaccount forthiseffect, thefittingformulausedinthisworkcontainsasumofcorrelation functionsforeachpossiblecombinationof(anti)baryons,weighted by thefraction λ ofgivenresidual pairs.One needsto transform the theoreticalcorrelation function ofapair intothemomentum frameoftheparticlesregisteredinthedetector [47].

Theprocedure forthecorrelation functionanalysistakinginto accountresidualcorrelationshasbeenperformedbeforeandisde- scribedindetailinRef. [58].Thesameprocedurewascarriedout inthisanalysis.

The fractionsofresidualpairs λ were calculatedbasedon the AMPTmodel [59] (aswellasHIJING [60] forevaluationofsystem- atic uncertainties) after full detector simulation, estimating how manyreconstructed pairs come fromprimary particles andwhat isthepercentageofthosecomingfromthegivendecay.Theyalso takeintoaccountother impuritiesresultingfrommisidentification ordetectoreffects;therefore,their sumisnotequaltounity.The obtainedvaluesoffractionsarelisted inTable2.Themomentum transformation matrices [47] were generated using the THERMI- NATOR 2 model [61] for all residual components of all analysed systems.Thefinalcorrelationfunctionforaxy pairisdefinedas

Fig. 2.Illustrationofthelinksbetweendifferentbaryon–antibaryonpairsthrough the residual correlation. Main contributions to the pp correlation function are markedinblue,tothepinyellowandtotheinred.Solidlinesshowcon- nectionsbetweenstudiedpairs,whiledashedlinespresentothermajorresidual contributionsthatareuniqueforagivensystem.

C_xy

(

k^∗

) =

¹

+

i

λ

i C_i

(

k^∗

) −

¹

,

(3)

wherethesumisoverallresidualcomponentsofthexypairand λi andC_i(k^∗)arethefractionandthecorrelationfunction ofi-th pair,respectively [47].

Correlationfunctionswereobtainedforfourbaryon–antibaryon pairsystemspp, p,p,and.Sincethecorrelationfunctions pand p were found tobe consistent with each other within theuncertainties,theywere alwayscombinedandarefurtherde- notedasp⊕^p.A simultaneousfitis desirablebecauseofthe presenceofresidual correlationswhichlink differentpairs.Three setsofunknownscatteringparameters,componentsoftheanalyt- ical formula(A.2) used in the fit, were introduced for p⊕^p, aswell asheavier,not measureddirectly, baryon–antibaryon pairs, further referred to asBB, consisting ofpairs containing and baryons.The pp systemwasusedasareference.However, duetothepresenceoftheCoulombinteractionandcoupledchan- nels,theanalyticaldescription isnolongervalidinthiscase(see AppendixAfordetails).Nevertheless,coupled-channeleffectsbe- come negligible for large sources asthe ones obtained in Pb-Pb collisionsystems.Thetheoreticalpp correlationfunctionswereob-

tained by generating pp pairs with the THERMINATOR 2 model and by applying weights accounting for the final state interac- tions with an approximatetreatment of the nn coupled channel, usinga numericalmodelby R.Lednický [7,11] with experimental constraints on strong interaction parameters from previous mea- surements [32,62,63].

Thesourcesizesforprimarypp,p⊕^p,andpairswere taken from previous measurements of other baryon–baryon and meson–meson pairs [58]. We assume that the one-dimensional source size R, for each pair, dependson the transverse mass of thepair,mT=

m²+^p2T,andonthecharged-particlemultiplicity N_ch[64] followingtherelations

R

(

m_T

;

^Nch

) =

^a

(

N_ch

)

m^γ_T

,

(4) and

R

(

N_ch

;

^mT

) = α (

m_T

)

³

N_ch

+ β(

m_T

),

(5)

where the

γ

exponent and the a(Nch),

α

(mT) and β(mT) func- tions are empirical and include the constraint of the minimum possible source size (N_ch=^{1) being equal to the proton radius,} Rp≈⁰.88 fm [31].Therelations (4) and (5) are usedforallpairs, includingthosecontributingviaweakdecays.

The experimental correlation function isalso affectedby phe- nomena other than the strong and Coulomb interactions, such as jets and elliptic flow [65–67]. Those effects are treated as a background.Foreach experimentalfunction,abackgroundfitwas performedinak^∗regionwherefemtoscopiceffectsarenotpromi- nent. It was found, using the THERMINATOR 2 model, that the resultsarenotdependentonthek^∗fitrangewhenthebackground is fitted by a third order polynomial. Next, the estimated back- groundwassubtractedfromtheexperimentalcorrelationfunction.

Theprocedure flattensthefunctionforhigherk^∗ andtheslopeis larger for lesscentral collisions, which isconsistent withelliptic flow, as it should be more prominent for semi-central collisions andlessforcentralcollisions [65].

As anexample,the correlationfunctionsforpp, p⊕^pand pairsforthe10–20%centralityintervalandtwocollisionen- ergiesarerepresentedtogetherwiththesimultaneousfitinFig.3.

The momentumresolutioneffectwas investigatedwithMonte Carlosimulations bycreatinga two-dimensionalmatrix ofgener- atedandreconstructedk^∗.Eachsliceofthedistributionwas then fitted with a Gaussian function. Withinthe k^∗ region of interest the widthoftheGaussian functionisconstant; therefore,thefit- tingfunctionwassmearedwithaGaussianwithawidthconstant ink^∗.

Table 2

Fractionsofresidualcomponents ofpp,p⊕^p,and correlationfunctionsfrom Monte CarloeventssimulatedwithAMPTmodelafterfulldetectorsimulation.Thevaluesinparentheses representfractionsobtainedwiththeHIJINGmodelusedforevaluationofsystematicuncertain- ties.Fractionsarethesameforcorrespondingantipairs.

pp p⊕^p

Pair λ Pair λ Pair λ

pp 0.25 (0.32) p 0.29 (0.28) 0.37 (0.24)

p 0.12 (0.19) 0.08 (0.09) ⁺ 0.04 (0.06)

p⁻ 0.04 (0.04) ⁻ 0.03 (0.02) ⁰ 0.03 (0.05)

0.02 (0.03) p^0/+ 0.02 (0.03) ⁰ <0.01 (0.20)

⁻ 0.01 (0.01) p⁰ <0.01 (0.12) ⁰⁰ <0.01 (0.05) ⁺⁻ <0.01 (<0.01) ⁰ <0.01 (0.04) ^0/−0 <0.01 (0.02) ^0/+ <0.01 (0.01) ^0/−0/+ <0.01 (<0.01) ⁺⁰ <0.01 (<0.01)

^0/−+ <0.01 (<0.01)

Fig. 3.Correlationfunctionsofpp,p⊕p,andpairsforPb–Pbcollisionsat√

sNN=5.02 TeV(left)and√

sNN=2.76 TeV(right)togetherwiththesimultaneous femtoscopicfitforthe10–20%centralityclass.

Table 3

Valuesofthe spin-averagedscatteringparametersf0, f0,and d0 for p⊕p and pairs, as wellas effective parameters accounting for heavierbaryon–antibaryon(BB)pairsnotmeasureddirectly,extractedfrom thesimultaneousfit.

Parameter p⊕p BB

f0(fm) −1.15^±_±⁰₀^._.²³₀₅⁽₍^syst_stat^.)_.) −0.90^±_±⁰₀^._.¹⁶₀₄⁽₍^syst_stat.)^.) −1.08^±_±⁰₀^._.¹¹₂₀⁽₍^syst_stat.)^{.) f}0(fm) 0.53^±_±⁰₀^._.¹⁵₀₄⁽₍^syst_stat.)^.) 0.40^±_±⁰₀^._.¹⁸₀₆⁽₍^syst_stat^.)_.) 0.57^±_±⁰₀^._.²⁵₁₉⁽₍^syst_stat)^.)

d0(fm) 3.06^±_±⁰₀^._.⁹⁸₁₄⁽₍^syst_stat^.)_.) 2.76^±_±⁰₀^._.⁷³₂₉⁽₍^syst_stat^.)_.) 2.69^±_±⁰₀^._.⁴⁶₇₄⁽₍^syst_stat.)^.)

4. Results

Thestrong-interaction scatteringparameters ^f0, ^f0,andd0 for pp, p⊕^p, , and BB pairs resulting from the simulta- neous fit are summarised in Table 3 and plotted in Fig. 4 to- gether with statistical (bars) and systematic (ellipses) uncertain- ties.² Fig. 4alsoshowsscatteringparametersforvarious baryon–

baryon and baryon–antibaryon pairs extracted in previous stud- ies [68–71].

Asthesimultaneousfityieldssimilar values,withinuncertain- ties, of parameters forp⊕^p and , as well as heavier BB pairs,one can perform a fit assuming a single set of parameters forall those systems. By doing so there is practically no change intheresults;inparticular,thereduced

χ

²≈¹.83 (p<0.00001) of the first fit becomes

χ

²≈¹.87 and other scattering parame- terschangeveryslightly,withinsystematicuncertainties.Thistest confirmsthatthedatapointscanbecorrectlydescribedwhenone assumesthatallbaryon–antibaryonpairshavesimilarvaluesofthe scatteringlengthandtheeffectiverangeofthestronginteraction.

5. Discussion

Femtoscopic correlation functions for pp, p⊕^p and have been measured in Pb–Pb collisions at energies of √

sNN= 2.76 TeVand√

sNN=⁵.02 TeVregisteredbytheALICEexperiment.

Theanalysiswas performedinsixcentralityintervals, yielding36 correlationfunctionsintotal.

2 DetailsofthesystematicuncertaintyestimationarediscussedinAppendixB.

For the first time parameters of the strong interaction, the scattering length and the effective range, were extracted for p⊕^pandpairs.Moreover,parametersforheavierbaryon–

antibaryon pairs, which were not measured directly, were esti- mated.

Severalconclusions can be drawnfromthe extractedparame- ters.Therealandimaginarypartsofthescatteringlength,^f0and ^f0,andtheeffectiveinteractionrange,d0,havesimilarvaluesfor all baryon–antibaryon pairsatlow k^∗.Therefore,thedata canbe described usingthe sameparameters for allstudied pairs, which providesavaluableinputfortheoreticalheavy-ioncollisionsmod- els.Note thatthe assumptionusedin theUrQMDmodel,namely that ^f0 is the same for different baryon–antibaryon pairs as a functionofthecentre-of-mass energyofthepair,meansthat the inelasticcrosssectionwouldbedifferentatthesamerelativepair momentumk^∗.

A significant non-zeroimaginary part ofthe scatteringlength ^f0 indicates thepresenceoftheinelasticchanneloftheinterac- tion,whichinthecaseofbaryon–antibaryon includestheannihi- lationprocess.

Thenegativevalueoftherealpartofthescatteringlength,^f0, obtained forall baryon–antibaryon pairs may haveone ofa two meanings: either the strong interaction is repulsive, or a bound state can be formed.The significant magnitudeof the imaginary part ofthe scatteringlength, ^f0, showsthat baryon–antibaryon scatteringmayoccur throughinelasticprocesses(annihilation).In the UrQMDmodel, three scenarios can be considered [47]: i) all baryon–antibaryon pairs annihilate similarly atthe same relative momentumk^∗;ii)^f0 isthesameforallbaryon–antibaryonpairs, but expressed as a function of the pair centre-of-mass energy, meaningthat^f0 issmallerforbaryon–antibaryonpairsofhigher totalpairmass; iii)theinelasticcrosssection isincreasedforev- erymatching quark–antiquarkpairin thebaryon–antibaryon sys- tem. In this scenario, in the specific case of this work, ^f0 for p⊕^pshouldbe lowerthan forpp and ,whichisnot ob- served. UrQMDby defaultusesscenarioii)to modelthebaryon–

antibaryon annihilation, which in our case would lead to a de- creaseof^f0 whilegoingfrompp topairs; however,similar valuesof^f0forallbaryon–antibaryonpairsreportedinthiswork favourscenarioi).

Fig. 4.(Top)Comparisonofextractedspin-averagedscatteringparameters^f0and ^f0forp⊕^p,pairsandforeffectiveBB pairs,withpreviousanalysesofpp pairs(singlet) [32,33,35,72].(Bottom)Comparisonofextractedspin-averagedscat- teringparametersf0andd0forp⊕p,pairsaswellaseffectiveBB,with selectedpreviousanalysesofotherpairs:pp (singlet) [73],pp (singlet) [72],pn (singlet) [74],nn (singlet) [74],p (singlet) [69],and (spin-averaged) [70].

(Notethat the measurementofthe scatteringparametersbythe STARex- periment [70] didnotaccountforresidualcorrelations.Therecentanalysisof correlationsbytheALICECollaboration [28],properlytakingintoaccountthosecor- relations,disfavourstheSTARresults.)

Inelasticscatteringiscompatiblewithaboundstate,wherethe baryonandantibaryoncreateashort-livedresonancewhichdecays stronglyintothreemesons.Evidenceforaprocessinwhichapar- ticleinthemass rangeof2150–2260 MeV/c² decaysintoa kaon andtwo pions has beenreported by various experiments in the pastandlistedbytheParticleDataGroup(PDG)asK₂(2250)[31].

Thereportedmassisslightlyabovethepthreshold,thewidthof theresonanceiscompatiblewithastrongly decayingsystemand the decay products match the valencequark content of the p pair.A nucleon–antihyperonsystemhasalsobeenlistedbyPDGas K₃(2320),withprotonandinthefinalstate,whichcorresponds toaboundstateundergoinganelasticscattering.Theresultspre- sented inthis paper support the existence of baryon–antibaryon boundstatessuch asK2(2250)andK3(2320).Furtherstudiescan providemoreevidenceontheexistenceofthosestates.

Finally,negativevaluesoftheextractedrealpartofthescatter- inglength ^f0 show eitherthatthe interactionbetweenbaryons and antibaryons is repulsive, or that baryon–antibaryon bound statescanbeformed.Combinedwiththenon-zeroimaginarypart ^f0 which, asmentioned earlier,is associated withthe inelastic processes,it favoursthe boundstates scenarioover therepulsive interaction. In that casea baryon–antibaryon pair would form a resonance decaying into a group of particles different from the original ones (for instance, p→^X→^K+π⁺π^{−, where X is the} hypotheticalbaryon–antibaryon boundstate).Further studieswill shed more light on existence of such particles. The scenario of

a repulsive interaction is not completely ruled out, butit would manifestinexperimentsasasystematicspatialseparationofmat- terandantimatter,neverobservedbefore.

In summary, the strong-interaction cross section parameters (the scatteringlengthandtheeffectiverange) ofstrangebaryon–

antibaryon pairs have been measured at low relative pair mo- mentum usingthefemtoscopictechnique.Theywere foundtobe the samewithinthesystematicuncertainties forallstudied pairs and compatible with the pp parameters measured in other ex- periments. Therefore, a global picture of the baryon–antibaryon annihilation proceeding in a very similar way, regardless of the strange-quarkcontent,issuggested. Finally,theresultsareconsis- tentwiththeformationofbaryon–antibaryonboundstates.Future searchesforsuchparticleswillthereforebeofcrucialimportance.

Acknowledgements

The ALICECollaboration 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 supportin buildingandrun- ningthe ALICEdetector:A.I. AlikhanyanNationalScience Labora- 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 NacionaldeDesenvolvimentoCientíficoeTecnológico(CNPq),Uni- versidade Federaldo RioGrandedo Sul(UFRGS),Financiadorade Estudos e Projetos (Finep) and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil; Ministry of Science &

Technology of China (MSTC), National Natural Science Founda- tion ofChina (NSFC) andMinistryofEducation ofChina (MOEC), China; Croatian Science Foundation and Ministry of Science and Education, Croatia; Centro de Aplicaciones Tecnológicas y De- sarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Edu- cation, Youth and Sports of the Czech Republic, Czech Repub- lic; The Danish Council for Independent Research – Natural Sci- ences,theandDanishNationalResearchFoundation(DNRF), Den- mark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Énergie Atomique (CEA), Institut National de Physique Nu- cléaire et de Physique des Particules (IN2P3) and Centre Na- tional de la Recherche Scientifique (CNRS) and Rlégion des Pays de laLoire, France;Bundesministerium fürBildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI Helmholtzzentrum fürSchwerionenforschungGmbH,Germany;GeneralSecretariatfor ResearchandTechnology,MinistryofEducation,ResearchandRe- ligions, Greece; National Research Development and Innovation Office,Hungary;DepartmentofAtomicEnergy,GovernmentofIn- dia (DAE), Department of Science and Technology, Government of India(DST), University Grants Commission, Government ofIn- dia(UGC)andCouncilofScientificandIndustrialResearch(CSIR), India; IndonesianInstitute of Science, Indonesia; Centro Fermi – MuseoStorico dellaFisica eCentroStudi e RicercheEnricoFermi andIstitutoNazionalediFisicaNucleare(INFN),Italy;Institutefor Innovative Science and Technology, Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion of Science (JSPS) KAKENHIandJapaneseMinistryofEducation,Culture, Sports,Sci- enceand Technology (MEXT),Japan; Consejo Nacionalde Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Interna-

cionalenCiencia yTecnología(FONCICYT)and DirecciónGeneral deAsuntosdelPersonalAcademico(DGAPA),Mexico;Nederlandse OrganisatievoorWetenschappelijkOnderzoek(NWO),Netherlands;

TheResearchCouncilofNorway,Norway;CommissiononScience andTechnology forSustainableDevelopment inthe South(COM- SATS),Pakistan;PontificiaUniversidadCatólicadelPerú,Peru;Min- istryof Science andHigher Education andNationalScience Cen- tre, Poland; Korea Institute of Science and Technology Informa- tion and National Research Foundation of Korea (NRF), Republic ofKorea; Ministry of Education andScientific Research, Institute of Atomic Physics and Ministry of Research and Innovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research(JINR),MinistryofEducation andScience oftheRussian Federation, National Research Centre Kurchatov Institute, Russian Science Foundation and Russian Foundation for Basic Research, Russia;Ministry ofEducation,Science, Researchand Sportofthe Slovak Republic, Slovakia; National ResearchFoundation ofSouth Africa,SouthAfrica;SwedishResearchCouncil(VR)andKnut&Al- iceWallenbergFoundation(KAW),Sweden;EuropeanOrganization forNuclear Research, Switzerland; NationalScience andTechnol- ogyDevelopment Agency (NSDTA), Suranaree University ofTech- nology(SUT)andOfficeoftheHigherEducationCommissionunder NRUprojectofThailand,Thailand;TurkishAtomic EnergyAgency (TAEK),Turkey;NationalAcademyofSciencesofUkraine,Ukraine;

ScienceandTechnologyFacilitiesCouncil(STFC),UnitedKingdom;

NationalScienceFoundationoftheUnitedStatesofAmerica(NSF) andUnitedStatesDepartmentofEnergy,OfficeofNuclearPhysics (DOENP),UnitedStatesofAmerica.

Appendix A. Lednický–Lyuboshitzmodel

The wave function of the pair, (k^∗,^r∗), in Eq. (2), depends onthetwo-particleinteraction.Baryonsinteractwithanti-baryons via the strong and, if they carry a non-zero electric charge, the Coulomb force. In such a scenario, the interaction of two non- identicalparticlesisgivenbytheBethe–Salpeteramplitude,corre- spondingtothesolutionofthequantumscatteringproblemtaken withtheinversetimedirection:

⁽⁺⁾

−^k∗

(

r

^∗

,

_k^∗

) =

AC

( η ) √

¹

2

×

e^{−ik∗·r∗}F

( −

ⁱ

η ,

1

,

i

ζ

⁺

) +

^fC

(

_k

^∗

)

G

˜ ( ρ , η )

r^∗

,

(A.1)

whereA_CistheGamowfactor,ζ^±=^k∗r∗(1±^cosθ^∗),

η

=¹/(k^∗a_C), F istheconfluenthypergeometricfunction,andG˜ isthecombina- tionofthe regular andsingular S-waveCoulomb functions. θ^∗ is theanglebetweenthepairrelativemomentumandrelativeposi- tioninthepairrestframe,whileaC istheBohrradiusofthepair.

Thecomponent fC isthestrong-scatteringamplitude,modifiedby theCoulombinteraction.

When only the strong interaction is present, the correlation function can be expressed analytically asa function ofthe scat- tering amplitude f(k^∗)=

1

f0+¹₂^d0k^∗2−^ik∗₋1

, and the one- dimensionalsourcesize R.ThisdescriptioniscalledtheLednický–

Lyuboshitzanalyticalmodel [7]:

C

(

k^∗

) =

¹

+

σ

ρ

_σ

1

2

^f

(

k^∗

)

R

²

1

−

^dσ0 2

√

π

^R

+

²

^f

(

k^∗

)

√ π

^{R F1}

(

2k^∗R

) −

^f

(

k^∗

)

R F2

(

2k^∗R

)

,

(A.2)

wherethesumisoverallpair-spinconfigurations

σ

,withweights

ρ

σ (arealnumber)being1/4 and3/4 forsingletandtripletstates,

respectively,and F1(z)=_z

0(e^x2−z2/z)dxandF2(z)=(1−^e−z2)/z.

When the Coulomb interaction is also present, e.g., in the pp case, thesource emission functionis numericallyintegratedwith the pair wave function containing a modified scattering ampli- tude [45]:

fC

(

k^∗

) =

1

f0

+

¹

2d0k^∗2

−

^ik∗

−

² aC

h

( η ) −

^ik∗AC

( η )

₋1

,

(A.3)

whereh(

η

)=

η

^2∞

n=1

[ⁿ(n²+

η

²)]⁻¹−γ−^ln|

η

_|(γ=⁰.5772 is the Eulerconstant).

The description becomes more complicated when coupled channels(suchasnn→^{pp inthepp system) arepresent.Forde-} tailsseeRef. [45,75].

Appendix B. Systematicuncertainties

Theanalysiswasalsoperformedontracksreconstructed using theinformationfromboththeITSandtheTPC,asopposedtousing those having the information fromthe TPC only. The correlation functions obtained from the analysis of those tracks were fitted with the procedure described in Sec. 3. Differences on extracted scatteringparametersarebetween4%and17%,depending onthe studiedpairandthescatteringparameter.

Inaddition,severalcomponentsofthefitprocedure werevar- ied.Shiftingthecorrelationfunctionnormalisationrangeink^∗ by

±⁰.1 GeV/c yields almost no change on the extracted scattering parameters(maximum1%).Achangeofthebackgroundparametri- sation from the third to the fourth-order polynomial results in differencesofup to19%for^f0 andbelow10%forotherparam- eters.The second-orderpolynomial was alsotestedbutit failsto describethelowk^∗regionandthereforecannotbeusedtoextract reliable information.Moreover, the use of residual pair fractions

Table B.1

List ofcontributionsto thesystematicuncertainty ofthe scattering parameters.Valuesareaveragedovercollisionenergiesandcentrality ranges.

p⊕^p

Uncertainty source f0(%) f0(%) d0(%)

Normalisation range <1 <1 <1

Background parametrisation <1 2 3

Fit range dependence 3 8 14

Fractions of residual pairs 10 8 19

Momentum resolution correction 7 11 4

Track selection 11 14 4

Source size variation 9 18 20

Uncertainty source ^f0(%) ^f0(%) d0(%)

Normalisation range <1 <1 <1

Background parametrisation 6 19 2

Fit range dependence 2 4 5

Fractions of residual pairs 6 15 18

Momentum resolution correction 4 7 2

Track selection 7 17 4

Source size variation 12 35 19

BB

Uncertainty source ^f0(%) ^f0(%) d0(%)

Normalisation range <1 1 1

Background parametrisation 6 17 6

Fit range dependence 6 12 11

Fractions of residual pairs 7 19 8

Momentum resolution correction 3 3 1

Track selection 9 <1 12

Source size variation 13 36 9