Investigation of the p–Σ0 interaction via femtoscopy in pp collisions

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Physics Letters B

www.elsevier.com/locate/physletb

Investigation of the p– ⁰ interaction via femtoscopy in pp collisions

.ALICE Collaboration

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

Articlehistory:

Received16November2019

Receivedinrevisedform27March2020 Accepted6April2020

Availableonline9April2020 Editor: B.Blank

ThisLetterpresentsthefirstdirectinvestigationofthep–⁰interaction,usingthefemtoscopytechnique inhigh-multiplicityppcollisionsat√

s=^{13 TeVmeasuredbytheALICEdetector.The0}isreconstructed viathedecaychanneltoγ,andthe subsequentdecayoftopπ⁻.Thephotonisdetectedviathe conversioninmaterialtoe⁺e⁻pairsexploitingthecapabilityoftheALICEdetectortomeasureelectrons atlowtransversemomenta.Themeasuredp–⁰correlationindicatesashallowstronginteraction.The comparison of the data to several theoretical predictions obtained employingthe CorrelationAnalysis ToolusingtheSchrödingerEquation(CATS)andtheLednický–Lyuboshitsapproachshowsthatthecurrent experimental precisiondoes not yetallow todiscriminate betweendifferentmodels,as it isthe case forthe availablescattering andhypernucleidata.Nevertheless, thep–⁰correlation functionisfound tobe sensitivetothe stronginteraction,and drivenby theinterplayofthedifferentspinand isospin channels.Thispioneeringstudydemonstratesthefeasibilityofafemtoscopicmeasurementinthep–⁰ channelandwiththeexpectedlargerdatasamplesinLHCRun3andRun4,thep–⁰interactionwill beconstrainedwithhighprecision.

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

1. Introduction

Aquantitative understanding of thehyperon–nucleon interac- tioninthestrangeness S= −^{1 sectoris}fundamentaltopindown the role of strangeness within low energy quantum chromody- namics and to study the properties of baryonic matter at finite densities.Thepossiblepresenceoftheisoscalarandtheisovec- tor(⁺,⁰,⁻)hyperonstatesintheinnercoreofneutronstars (NS) is currently under debate due to the limited knowledge of theinteraction of such hyperons with nuclear matter. The inclu- sion ofhyperons in the description ofthe nuclear matter inside NS typically contains only states, and the on-average attrac- tive nucleon– (N–) interaction leads to rather soft Equations ofState(EoS)forNS.Thesearethenunabletoprovidestabilityfor starsofabouttwosolarmasses [1,2].Thehyperonsarerarelyin- cludedintheEoSforNS becauseofthe limitedknowledge about theN–stronginteraction.

Indeed,whiletheattractiveN–interactionisreasonablywell constrained from the available scattering and light hypernuclei data [3–5], the nature of the N– interaction lacks conclusive experimental measurements. One of the major complications for experimentalstudies isthefactthat thedecayofall statesin- volves neutral decay products [6], thus requiring high-resolution calorimeters.

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

The mainsource ofexperimental constraintsonthe N– sys- tem comes from scattering measurements [7–9], analysis of ⁻ atoms [10–12],andhypernucleiproductiondata [13–16],although the latter are mainly dominated by large statistical uncertain- tiesandlarge kaondecaybackground.Latest hypernuclearresults obtained from different nuclear targets point towards an attrac- tive interaction in the isospin I=¹/2 channel of the N– sys- tem [13,14],andrepulsioninthe I=³/2 channel [15,16].Hyper- nuclearmeasurements,however,areperformedatnuclear satura- tiondensityandhenceinthepresenceofmorethanonenucleon, resultingin asubstantial modeldependenceintheinterpretation oftheexperimentaldata [17].

Additionally, the hyperon–nucleon dynamics are strongly af- fected by the conversion process N– ↔ ^N–,occurring in the I=¹/2 channel due to the close kinematic threshold between the two systems (about 80 MeV) [18–22]. This coupling is ex- pectedtoprovideanadditionalattractivecontributioninthetwo- body N– interaction in vacuum [21,22]. Indeed, depending on thestrength oftheN–↔^N– couplingatthetwo-bodylevel, the correspondingin-medium hyperonpropertiesare very differ- ent.Forastrongcoupling,thisleads toarepulsivesingle-particle potential U at large densities [21,22]. For the hyperon, the in-mediumpropertiesaremostlydeterminedbytheoverallrepul- sioninthe I=³/2 component [21,22]. Arepulsivecomponentin thehyperon–nucleoninteractionscouldshifttheonsetforhyperon productiontolargerdensities,above2–3timesthenormalsatura-

https://doi.org/10.1016/j.physletb.2020.135419

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

tiondensity,thusleadingtostifferEoSwhichareabletodescribe theexperimentalconstraintofNS.

Tothisend,differenttheoreticalapproachesincludingchiralef- fectivefieldtheories(

χ

EFT) [20] andmeson-exchangemodelswith hadronic [23] and quark [24] degrees offreedom providea simi- lardescriptionoftheavailabledatabyassumingastrongrepulsion inthe spinsinglet S=^{0, I}=¹/2 andspin triplet S=^{1, I}=³/2 andanoverallattractionintheremainingchannels.Recentabini- tio lattice calculations at quark physical masses show a similar dependenceon spin-isospin configurations for the central poten- tialterm [25]. The strength ofthe coupled-channel N–↔^N–

is strongly model dependent as well. Calculations based on chi- ral models [20,21] and meson-exchange models [18,26] predict a rather strong or much weaker coupling, respectively. A self- consistentdescriptionofthiscoupled-channeldemandsadetailed knowledgeofthestronginteractionintheN–system.

Recently, the study of two-particle correlations in momen- tum space measured in ultra-relativistic proton–proton (pp) and proton–nucleus collisions has proven to provide direct access to the interaction between particle pairs in vacuum [27–29]. The small size of the colliding systems of about 1 fm results in a pronouncedcorrelation signal fromstrong finalstate interactions, whichpermits thelatter to beprecisely constrained. These mea- surementsprovidedadditionaldatainthehyperonsectorwithan unprecedentedprecisioninthelowmomentumregime.InthisLet- ter,thesestudiesareextendedtothesector.Theelectromagnetic decayofthe⁰isexploitedforthefirstdirectmeasurementofthe p–⁰ interactioninppcollisions.Thisstudypavesthewayforex- tendingtheseinvestigationstothe charged states,inparticular inlightofthelargerdatasamplesexpectedfromtheLHCRuns3 and4.

2. Dataanalysis

ThisLetterpresentsresultsobtainedfromadatasampleofpp collisionsat√

s=^{13 TeVrecordedwiththeALICE}detector [30,31]

duringtheLHCRun2(2015–2018).Thesamplewascollectedem- ploying a high-multiplicity trigger with the V0 detectors, which consistoftwosmall-angleplasticscintillatorarrayslocatedonei- therside ofthecollision vertexatpseudorapidities2.8<

η

<5.1 and−³.7<

η

<−¹.7 [32].Thehigh-multiplicitytriggerisdefined bycoincidenthitsinbothV0detectorssynchronouswiththeLHC bunchcrossingandbyadditionallyrequiringthesumofthemea- sured signal amplitudes in the V0 to exceed a multiple of the averagevalueinminimumbiascollisions.Thiscorresponds,atthe analysis level, to the highest multiplicity interval containing the top0.17% ofallinelasticcollisions withatleastonechargedpar- ticlein |

η

_|<1 (referred to asINEL > 0). This data set presents asuitable environmenttostudycorrelationsduetotheenhanced production of strange particles in such collisions [33]. Addition- ally, the larger charged-particle multiplicity density withrespect tothe minimumbias sample significantly increasestheprobabil- ityto detect particle pairs. The V0 is alsoemployed to suppress backgroundevents,suchastheinteractionofbeamparticleswith mechanicalstructures ofthebeamline,orbeam-gas interactions.

In-bunch pile-upevents withmore than one collision per bunch crossingarerejectedbyevaluatingthepresenceofadditionalevent vertices [31].Theremaining contaminationfrompile-upeventsis onthepercentlevelanddoesnotinfluencethefinalresults.

Charged-particletrackingwithintheALICEcentralbarreliscon- ducted with the Inner Tracking System (ITS) [30] and the Time Projection Chamber (TPC) [34]. The detectors are immersed in a homogeneous 0.5 Tsolenoidal magneticfield along thebeam di- rection.TheITSconsistsofsixcylindricallayers ofhighposition- resolutionsilicondetectorsplacedradiallybetween3.9 and43 cm aroundthebeampipe.Thetwoinnermostlayers areSiliconPixel

Detectors (SPD)andcoverthepseudorapidityrange|

η

|<2.0 and

|

η

_|<1.4,respectively. Thetwo intermediatelayers are composed ofSiliconDriftDetectors,andthetwooutermostlayers aremade ofdouble-sidedSiliconmicro-StripDetectors(SSD),covering|

η

|<

0.9 and |

η

_|<1.0, respectively. The TPC consists of a 5 m long, cylindrical gaseous detector with full azimuthal coverage in the pseudorapidityrange|

η

|<0.9.Particleidentification(PID)iscon- ductedviathemeasurementofthespecificionizationenergyloss (dE/dx)withup to159reconstructedspacepoints alongthepar- ticle trajectory. The Time-Of-Flight (TOF) [35] detector system is locatedataradialdistanceof3.7 mfromthenominalinteraction point andconsists ofMultigapResistive Plate Chambers covering thefullazimuthalanglein|

η

|<0.9.PIDisaccomplishedbymea- suringtheparticle’svelocityβviathetimeofflightoftheparticles inconjunctionwiththeirtrajectory.Theeventcollisiontimeispro- videdasa combinationofthe measurementsin theTOF andthe T0 detector,two Cherenkovcounter arrays placed atforward ra- pidity [36].

The primary eventvertex(PV)is reconstructedwiththecom- binedtrackinformationoftheITSandtheTPC,andindependently withSPDtracklets.Whenbothvertexreconstructionmethods are available, thedifference ofthecorresponding z coordinates isre- quired to be smallerthan 5 mm. Auniform detectorcoverage is assured byrestrictingthemaximaldeviationbetweenthe z coor- dinateof thereconstructedPV andthe nominalinteractionpoint to ±^{10 cm.Atotalof1}.0×¹⁰⁹ high-multiplicityeventsareused fortheanalysisaftereventselection.

The protoncandidates arereconstructedfollowingtheanalysis methods usedforminimumbiasppcollisions at√

s=^{7 TeV [27]}

and 13 TeV [28,29], and are selected from the charged-particle tracks reconstructed with the TPC in the kinematic range 0.5<

pT<4.05 GeV/c and|

η

_|<0.8. The TPCandTOF PIDcapabilities are employedtoselectprotoncandidatesby thedeviationnσ be- tween the signal hypothesis for a proton and the experimental measurement, normalized by the detector resolution

σ

.For can- didateswith p<0.75 GeV/c,PIDisperformedwiththeTPConly, requiring|ⁿσ|<3.Forlargermomenta,thePIDinformationofTPC andTOF are combined.Secondary particles stemming fromweak decays or the interaction of primary particles with the detector materialcontaminatethesignal.Thecorrespondingfractionofpri- maryandsecondaryprotonsareextractedusingMonteCarlo(MC) templatefitstothemeasureddistributionoftheDistanceofClos- est Approach (DCA) of the track to theprimary vertex [27]. The MC templates are generated using PYTHIA 8.2 [37] and filtered throughtheALICEdetector [38] andreconstructionalgorithm [30].

Theresultingpurityofprotonsisfoundtobe99%,withaprimary fractionof82%.

The ⁰ isreconstructedviathedecaychannel⁰→

γ

with a branching ratioof almost 100% [6]. The decay is characterized by a short life time rendering the decay products indistinguish- able fromprimary particles produced in theinitial collision. Due tothe smallmassdifference betweentheandthe⁰ ofabout 77 MeV/c², the

γ

has typically energies of only few hundreds of MeV. Therefore, it is reconstructed relying on conversions to e⁺e⁻ pairs inthe detectormaterial ofthe centralbarrel exploit- ing the unique capability of the ALICE detector to identify elec- trons downto transverse momentaof 0.05 GeV/c. Fortransverse radii R<180 cmand|

η

|<0.9 thematerial budget corresponds to (11.4±⁰.5)% of a radiation length X0, and accordingly to a conversion probability of (8.6±⁰.4)% [39]. Details ofthe photon conversionanalysisandthecorrespondingselectioncriteriaarede- scribed in [39,40]. The reconstruction relieson the identification of secondary vertices by forming so-called V⁰ decay candidates from two oppositely-charged tracks using a procedure described in detail in [41]. The products of the potential

γ

conversion are reconstructed with the TPC and the ITS in the kinematic range

Fig. 1.Invariantmassdistributionoftheγ andγ candidates,intwopTintervalsof1.5−2.0 GeV/cand6.5−7.0 GeV/c.ThesignalisdescribedbyasingleGaussian, andthebackgroundbyapolynomialofthirdorder.Thenumberof⁰candidatesisevaluatedwithinM⁰(pT)±3 MeV/c².Onlystatisticaluncertaintiesareshown.

pT>0.05 GeV/c and|

η

_|<0.9. Thecandidates forthe e⁺e⁻ pair are identified by a broad PID selection in the TPC −⁶<nσ<7.

The resulting

γ

candidate isobtained asthe combinationof the daughtertracks.OnlycandidateswithpT>0.02 GeV/c andwithin

|

η

_|<0.9 are accepted. Combinatorial background from primary e⁺e⁻ pairs,orDalitzdecaysofthe

π

⁰ and

η

mesonsis removed byrequiringthat theradialdistanceoftheconversionpoint,with respecttothedetectorcentre,rangesfrom5 cmto180 cm.Resid- ual contaminations from K⁰_S and are removed by a selection in the Armenteros-Podolandski space [40,42]. Random combina- tionsofelectrons andpositrons are furthersuppressedbya two- dimensionalselectiononthe anglebetweentheplane definedby thee⁺e⁻pair,andthemagneticfield [43] incombinationwiththe reduced

χ

² ofa refitof thereconstructed V⁰ assuming that the particleoriginatesfromtheprimaryvertexandhasM_V0=^{0 [40].}

The Cosine of the Pointing Angle (CPA) between the

γ

momen- tumand the vector pointingfrom the PVto the decay vertexis requiredtobeCPA>0.999.InadditiontothetightCPAselection, thecontributionofparticlesstemming fromout-of-bunchpile-up issuppressedbyrestrictingtheDCAofthephotontobealongthe beamdirection(DCA_z<0.5 cm).Afterapplicationoftheselection criteria,about946×¹⁰⁶

γ

candidateswithapurityofabout95.4%

areavailableforfurtherprocessing.

Theparticlecandidatesarereconstructedviathesubsequent decay→^p

π

⁻withabranchingratioof63.9% [6],followingthe procedures described in [27,28]. For the the charge conjugate decayisexploited,andthesameselectioncriteriaareapplied.The decayproductsarereconstructedwiththeTPCandtheITSwithin

|

η

_|<0.9.ThedaughtercandidatesareidentifiedbyabroadPIDse- lectionintheTPC|ⁿσ|<5.Theresultingcandidateisobtained asthecombinationofthedaughtertracks.Thecontributionoffake candidatesis reduced by requesting a minimum pT>0.3 GeV/c.

ThecoarsePIDselectionofthedaughtertracksintroducesaresid- ualK⁰_Scontaminationinthesampleofthecandidates.Thiscon- taminationisremovedbya 1.5

σ

rejectiononthe invariantmass assumingadecayinto

π

⁺

π

⁻,where

σ

correspondsto thewidth ofaGaussianfittedtotheK⁰_S signal.Topologicalselectionsfurther enhancethepurityofthesample.Theradialdistanceofthede- cayvertexwithrespecttothedetectorcentrerangesfrom0.2 cm to100 cmandCPA>0.999.InadditiontothetightCPAselection, particles stemming from out-of-bunch pile-up are rejectedusing thetiming informationoftheSPDandSSD,andtheTOFdetector.

One ofthe two daughter tracks isrequired to have a hit in one ofthesedetectors.Afterapplicationoftheselectioncriteria,about

188×^{106 (178}×¹⁰⁶⁾ () candidates with a purity of 94.6%

(95.3%)areavailableforfurtherprocessing.

The ⁰ (⁰) candidatesare obtainedby combiningall () and

γ

candidatesfromthesameevent,wherethenominalparticle masses [6] are assumedforthe daughters. Inparticular the tim- ingselectiononthedaughtertracksoftheassuresthatthe⁰ candidatesstemfromtherightbunchcrossing.Incaseadaughter trackisusedtoconstructtwo

γ

,,andcandidates,oracombi- nationthereof,theone withthesmallerCPAisremovedfromthe sample.Inordertofurtheroptimizetheyieldandthepurityofthe sample,only⁰candidateswithpT>1 GeV/c areused.

The resulting invariant mass spectrum is shown in Fig. 1 for two p_T intervals. In order to obtain the raw yield, the signal is fitted with a single Gaussian, and the background with a third- orderpolynomial. Dueto thedeterioratingmomentum resolution for low p_T tracks, the meanvalue ofthe Gaussian M0 exhibits a slight pT dependence, which is well reproduced in MC simu- lations. The ⁰ (⁰) candidates for femtoscopy are selected as M0(p_T)±^{3 MeV/c2.Thewidthoftheintervalischosenasacom-} promisebetweenthe candidatecountsandpurity.In total,about 115×^{103 (110}×^{103) 0} (⁰) candidates arefound at a purity of about 34.6%. Due to the enhanced combinatorial background at low p_T, the purity increases from about20% at the lower p_T thresholdtoitssaturationvalueofabout60%above5 GeV/c.Only one candidateper eventisused,andisrandomly selectedinthe very rare casein which more than one is available. In lessthan one permille ofthecaseswhenthe trackofa primary protonis alsoemployed asthe daughtertrackofthe

γ

orthe ,thecor- responding⁰ candidateisrejected.Sinceonly stronglydecaying resonancesfeedtothe⁰ [6],allcandidatesareconsideredtobe primaryparticles.

3. Analysisofthecorrelationfunction

The experimental definition of the two-particle correlation function,forbothp–p andp–⁰pairs,isgivenby [44],

C

(

k^∗

) =

N

×

^Nsame

(

k^∗

)

N_mixed

(

k^∗

)

k^∗→∞

−−−−→

1

,

(1)

withthesame(N_same)andmixed(N_mixed)eventdistributionsofk^∗ anda normalizationconstant N^{.The relative momentumof the} pairk^∗ isdefinedask^∗=¹₂× |^p∗1−^p∗2|^,wherep∗1 andp^∗₂ are the momenta ofthe twoparticles in thepair restframe, denotedby the^∗.Thenormalizationisevaluatedink^∗∈ [²⁴⁰,340]^{MeV/c for}

p–p andink^∗∈ [²⁵⁰,400] ^{MeV/c forp–0} pairs,whereeffectsof finalstate interactionsare absentandhencethecorrelationfunc- tionapproachesunity.

The trajectories of the p–p and p–p pairs at low k^∗ are al- mostcollinear,andmightthereforebeaffectedbydetectoreffects liketracksplittingandmerging [45].Accordingly, thereconstruc- tionefficiencyforpairsinthesameandmixedeventmightdiffer.

To this end, a close-pair rejection criterion is employed remov- ingp–p andp–p pairsfulfilling

η

²₊

ϕ

^∗2<0.01,wherethe azimuthalcoordinate

ϕ

^∗considersthetrackcurvatureinthemag- neticfield.

A total number of 1.7×^{106 (1}.3×^{106) p–p (p–p ) and 587} (539)p–⁰ (p–⁰) pairs contribute to the respective correlation functionin theregionk^∗<200 MeV/c.Toenhancethe statistical significance of the results, the correlation functions of baryon–

baryon andantibaryon–antibaryonpairs are combined.Therefore, inthefollowingp–⁰denotesthecombinationp–⁰⊕^p–0,and correspondinglyforp–p.

The systematic uncertainties of the experimental correlation functionareevaluatedbysimultaneouslyvaryingallproton,,

γ

, and⁰ single-particleselection criteriaby up to20% aroundthe nominalvalues.Onlyvariations thatmodifythepairyieldby less than10%(20%)forp–⁰ (p–p)withrespectto thedefaultchoice areconsidered, andthe ⁰ purityby lessthan 5%.Theimpact of statisticalfluctuationsisreducedbyevaluatingthesystematicun- certainties in intervalsof 100 MeV/c (20 MeV/c) in k^∗ forp–⁰ (p–p). Theresulting systematicuncertainties are parametrizedby anexponentialfunctionandinterpolatedtoobtainthefinalpoint- by-pointuncertainties.Attherespectivelylowestk^∗,thetotalsys- tematic uncertainties are of the order of 2.5% for both p–p and p–⁰.

Using thefemtoscopy formalism [44], thecorrelation function can be relatedto the source function S(r^∗) andthe two-particle wavefunction(r^∗,k^∗)incorporatingtheinteraction,

C

(

k^∗

) =

d³r^∗S

(

r^∗

) | (

r^∗

,

k^∗

) |

²

,

(2)

where r^∗ refers to the relative distance between the two parti- cles. As demonstrated in [27–29,46] the correlation function be- comes particularly sensitive to the strong interaction for small emissionsourcesformedinppandp–Pb collisions.Forthisstudy, asphericallysymmetricemittingsourceisassumed, withaGaus- sianshapedcoredensityprofileparametrizedbyaradiusr₀,which isobtainedfromafittothep–p correlationfunction,similarlyas in [28,29].Followingthepremiseofacommonemissionsourcethe suchextractedradiusisthenusedasaninputtofitthep–⁰cor- relationfunction. Possiblemodifications ofthe sourceprofile due totheinfluenceofstronglydecayingresonances [47–49] arecon- sideredintheevaluationofthesystematicuncertaintiesassociated withthefittingprocedure.

The genuine p–p correlation function is modeled using the CorrelationAnalysisToolusingtheSchrödingerequation (CATS) [46], which allows one to useeither a localpotential V(r) or directly thetwo-particlewavefunction,andadditionallyanysourcedistri- bution asinput tocompute the correlation function.For thep–p correlation function thestrong Argonne v18 potential [50] inthe S,P,andDwavesisusedasaninputtoCATS.

The theoretical correlation function for p–⁰ is modeled em- ploying two different approaches. On the one hand, in CATSthe correlation function iscomputedfrom theisospin-averaged wave functions obtained within a coupled-channel formalism. On the other hand, the Lednický–Lyuboshits approach [51] relies on the effective-range expansion usingscatteringparameters asinput to evaluate the correlation function. The coupling ofthe n-⁺ sys- temto p–⁰ considering thedifferentthresholds isexplicitly in- cludedby meansofa coupled-channelapproach,whilethe effect

Table 1

Weightparametersfortheindividualcomponentsofthemeasuredcorrelationfunc- tion.Contributions fromfeed-downcontainthe motherparticle listedas asub- index.Non-flatcontributionsarelistedindividually.

p–p p–⁰

Pair λparameter

(%)

Pair λparameter

(%)

p–p 67.0 p–⁰ 22.0

p–p 20.3 p–(γ) 73.1

Feed-down (flat) 11.6 Feed-down (flat) 4.7

Misidentification (flat) 1.1 Misidentification (flat) 0.2

ofthep–channelisincorporatedbycomplexscatteringparame- ters [52].Detailsoftheemployedmodelsaredescribedinthenext Section.

The experimental data are compared with the modeled cor- relation function considering the finite experimental momentum resolution [27].Inaddition tothe genuinecorrelation functionof interest, the measured correlation function also contains residual correlations due to protons coming from weak decays of other particles, such as and⁺ (feed-down), andmisidentifications.

Theseeffectsare includedbymodelingthetotalcorrelation func- tionasadecomposition,

C_model

(

k^∗

) =

¹

+

i

λ

i

× (

Ci

(

k^∗

) −

¹

),

(3)

wherethesumrunsoverallcontributions.Theirrelativecontribu- tionisgivenbythe λparameterscomputedinadata-drivenway from single-particleproperties such asthepurity andfeed-down fractions [27],andaresummarizedinTable1.

Apart fromthegenuine p–p correlation function, a significant contribution comes fromthe decayof particles feeding to the protonpair.Theresidual p–correlationfunctionismodeledus- ing either the Usmani potential [53], chiral effective field the- ory calculations at Leading (LO) [54], or Next-To-Leading order (NLO) [20]. The resultingcorrelation function istransformed into themomentumbasisofthep–p pairby applyingthecorrespond- ingdecaymatrices [55].Allothercontributionsareassumedtobe C(k^∗)∼^1.Duetothechallengingreconstructionofthe⁰,theex- perimentalpurityofthe⁰ sampleisratherlow,andadditionally exhibitsastrongdependenceonthetransversemomentum pT as demonstratedinFig.1.Theaverage p_T ofthe⁰ candidatesused to constructthecorrelation functionatk^∗<200 MeV/c,however, is lowerthan the^pT^{ofall inclusive0} candidates.Considering this effect, the ⁰ purity employed to compute the λ parame- ters is found to be 27.4%. Accordingly, the main contribution to thep–⁰ correlationfunctionstemsfromthecombinatorialback- groundappearing in theinvariant massspectrum around the ⁰ peak, whichinthefollowingisreferred toas(

γ

).Theshapeof the p–(

γ

) correlation function is extractedfrom the sidebands oftheinvariant massselection,andisfoundtobeindependentof the choice of mass window. The non-flat behavior ismainly de- termined by residual p– correlationswhich are smeared by an uncorrelated

γ

, anddefines the baseline of the measurement of the p–⁰ correlation function. The shape is parametrizedwith a Gaussian distribution and weighted by its λ parameter. Allother contributions stemming frommisidentifiedprotons orfromfeed- downareassumedtobeC(k^∗)∼1.

The total correlation function includingall correctionsis then multipliedbyapolynomialbaselineCnon-femto(k^∗),

C

(

k^∗

) =

^Cnon-femto

(

k^∗

) ×

^Cmodel

(

k^∗

),

(4) toaccountforthenormalizationandnon-femtoscopicbackground effects stemming e.g. from momentum and energy conserva- tion [27]. The p–p correlation function is fitted in the range

Fig. 2.Measuredcorrelationfunctionofp–p⊕p–p .Statistical(bars)andsystematic uncertainties(boxes)areshownseparately.Thewidthofthebandcorrespondsto onestandarddeviationofthesystematicuncertaintyofthefit.

k^∗∈ [⁰,375] ^{MeV/c todetermine} simultaneously thefemtoscopic radius r0 and the parameters of the baseline. To assess the sys- tematic uncertainties on r₀ related to the fitting procedure the upperlimitofthefitregionisvariedwithink^∗∈ [³⁵⁰,400]^MeV/c.

Thebaseline ismodeledasapolynomial ofzeroth,first,andsec- ond order. Additionally, as discussed above, all three models for the p– residual correlation function are employed, andthe in- putto the λ parameters is modified by ±^20%while maintaining aconstant sum ofthe primary andsecondary fractions. The p–p correlation function is shown in Fig. 2, where the width of the bandscorrespondsto onestandard deviationofthetotalsystem- atic uncertainty of the fit. The inset shows a zoom of the p–p correlation function at intermediate k^∗, where the effect of re- pulsionbecomes apparent. The femtoscopicfit yields a radius of r₀=¹.249±⁰.008(stat)⁺₋⁰₀^._.⁰²⁴₀₂₁(syst)fm.

Analysesof

π

–

π

andK–Kcorrelationfunctionsatultrarelativis- ticenergies inelementary [56] andheavy-ioncollisions [57] indi- cateasource distributionsignificantly deviatingfroma Gaussian.

Indeed,stronglydecaying resonancesareknownto introducesig- nificantexponential tailsto thesource distribution,especially for

π

–

π

pairs [47–49].Thisbecomesevidentwhenstudyingthecor- responding resonance contributions obtained from the statistical hadronizationmodelwithinthecanonicalapproach [58].Themain resonancesfeedingtopions,

ρ

and

ω

,aresignificantlylonger-lived thanthosefeedingto protons() and⁰ ((1405)).Hence,itis notsurprisingthatthesourcedistributionfor

π

–

π

deviates from aGaussian.Theseconclusionsareunderlinedwhenfittingthep–p correlationfunctionwithaLévy-stablesourcedistribution [59,60].

Leavingboththefemtoscopicradiusandthestabilityparameter

α

forthe fittodetermine,the Gaussiansource shape(

α

₌2) isre- covered.EmployingaCauchy-typesourcedistribution(

α

=^1),the datacannotbesatisfactorilydescribed.Therefore,thepremiseofa Gaussiansourceholdsforbaryon–baryonpairs.

Accordingly, a Gaussian source with femtoscopic radius r0 is usedto fit the p–⁰ correlation function. The parameters ofthe linearbaseline are obtainedfromafit tothe p–(

γ

) correlation functionink^∗∈ [²⁵⁰,600]^{MeV/c,whereitisconsistentandkine-} matically comparable with p–⁰, howeverfeaturing significantly smalleruncertainties. Theexperimentalp–⁰ correlationfunction isthenfittedintherangek^∗<550 MeV/c,andvaried duringthe fitting procedure within k^∗∈ [⁵⁰⁰,600] ^{MeV/c to determine the} systematic uncertainty. Additionally, the input to the λ parame- ters is modified by ±^{20% while} maintaining a constant sum of theprimaryandsecondaryfractions.Theparameters ofthe base-

Fig. 3.Measuredcorrelationfunctionofp–⁰⊕p–⁰.Statistical(bars)andsystem- aticuncertainties(boxes)areshownseparately.Thegraybanddenotesthep–(γ) baseline.Thedataarecomparedwithdifferenttheoreticalmodels.Thecorrespond- ingcorrelationfunctionsarecomputedusingCATS [46] forχEFT [20],NSC97f [26]

andESC16 [23],andusingtheLednický–Lyuboshitsapproach [51,52] forfss2 [24].

Thewidthofthebandscorrespondstoonestandard deviationofthesystematic uncertaintyofthefit.Theabsolutecorrelateduncertaintyduetothemodelingof thep–(γ)baselineisshownseparatelyasthehatchedareaatthebottomofthe figure.

lineare varied within 1

σ

oftheir uncertainties considering their correlation, includingthe caseofa constant baseline. Finally,the femtoscopicradiusisvariedaccordingtoitsuncertainties.Possible variations ofthe p–⁰ sourceduetocontributions ofmT scaling andstrongdecaysare incorporatedbydecreasingr0 by 15%,sim- ilarly asin [28,29]. The correspondingresonance yieldsare taken fromthestatisticalhadronization modelwithinthe canonicalap- proach [58].

All correlation functions resulting from the above mentioned variationsoftheselectioncriteriaarefittedduring theprocedure, additionallyconsideringvariations ofthemasswindowtoextract thep–(

γ

)baseline.ThewidthofthebandsinFig.3corresponds toonestandarddeviationofthetotalsystematicuncertaintyofthe fit.Theabsolutecorrelateduncertaintyduetothemodelingofthe p–(

γ

) baseline correlation function is shown separately atthe bottomofthefigure.

4. Results

Theexperimental p–⁰ ⊕^p–0 correlation functionisshown inFig.3.Thek^∗ valueofthedatapointsischosenaccordingtothe ^{k∗ ofthe sameevent} distribution N_same(k^∗)in the correspond- ing interval. Therefore, due to the low number of counts in the first bin,thedata pointis shiftedwithrespect tothe bincentre.

Sincetheuncertaintiesofthedataaresizable,adirectdetermina- tion ofscatteringparametersvia afemtoscopicfit isnot feasible.

Instead,thedataaredirectlycomparedwiththevariousmodelsof the interaction.These include, onthe one hand,meson-exchange models,such asfss2 [24] andtwoversionsofsoft-core Nijmegen models(ESC16 [23],NSC97f [61]),andontheotherhandresultsof

χ

EFTatNext-to-LeadingOrder(NLO) [20].Thecorrelationfunction ismodeledusingtheLednický–Lyuboshitsapproach [51] consider- ingthecouplingsofthep–⁰ systemtop–andn-⁺[52] with scatteringparametersextractedfromthefss2 model.Forthecase ofESC16,NSC97fand

χ

EFT,thewavefunctionofthep–⁰system, includingthecouplings,isusedasaninputtoCATStocomputethe correlationfunction.Thedegreeofconsistencyofthedatawiththe discussed models isexpressed by thenumber ofstandard devia- tionsnσ,computedintherangek^∗<150 MeV/c fromthep-value

Table 2

Degreeofconsistencyofthedifferentmodels withthe experimentalcorrelation function.

Model p–(γ)

baseline

fss2 χEFT NSC97f ESC16

nσ (k^∗<150 MeV/c) 0.2−0.8 0.2−0.9 0.3−1.0 0.2−0.6 0.1−0.5

of the theoretical curves. The range of nσ shown in Table 2 is computedasonestandarddeviationofthecorrespondingdistribu- tion.Thedataare within (0.2−^0.8)

σ

consistentwiththep–(

γ

) baseline,indicating thepresence ofan overallshallowstrongpo- tentialinthep–⁰channel.Themainsourceofuncertaintyofthe modelingofthecorrelationfunctionistheparametrizationofthe p–(

γ

) baseline due the sizeable statistical uncertainties of the latter.

All employed models for the N– interaction potential suc- ceedinreproducing thescatteringdatainthe S= −1 sector [7].

Duetotheavailableexperimental constraints,theoveralldescrip- tionofthep–interactionyields aconsistentdescription.Onthe other hand, the corresponding p–⁰ correlation functions differ significantlyamongeachother.Thisdemonstratesthatfemtoscopic measurements candiscriminate andconstrain models,andthere- forerepresenta uniqueprobeto studythe N– interaction.Both fss2 and

χ

EFT exhibit an overall repulsionin N– atintermedi- atek^∗,whichmainlyoccursinthespinsinglet S=^0,I=¹/2 and spintriplet S=^1,I=³/2 components [20,24].Inthelowmomen- tumregion,belowroughly50 MeV/c,bothmodelsyieldattraction, which is reflected in the profile of the correlation function. The Nijmegenmodels,ontheotherhand,arecharacterizedbyarather constantattractionoverthewholerangeofk^∗.Inparticularatlow relativemomenta,however,thebehaviorofthetwomodelsdevi- atessignificantly.Theshapeofthecorrelationfunctionofthemost recentNijmegenmodel,ESC16,differssignificantlyfromthatofthe other calculations. This ismainly due tothe fact that the occur- rence ofboundstates inthestrangenesssector (S= −¹,−²,−³⁾ is not allowed in the model [23]. This leads to a repulsive core inall theN–channels, whichcan wellbe observedin Fig.3as thenon-monotonicbehavioratsmallrelativemomenta.Incontrast toallotherdiscussedmodels,NSC97fyieldsattractioninthespin triplet S=^1,I=³/2 channel [61].Accordingly,thecorresponding correlation function demonstrates the strongest attractionat low momenta.The ratherlarge differencesamong themodeled p–⁰ correlation functions demonstrate that the shape ofthe latteris verysensitivetodetailsofthestronginteraction,anddrivenbythe interplayofthedifferentspinandisospinchannels.Thisshowsthe strength of femtoscopic measurements, in particular in the N–

channel.

The underlying two-body N– interaction obtained within these models, however,translates into significantly differentval- uesforthein-mediumsingle-particlepotentialUwhenincluded inmany-bodycalculations. Boththefss2quark-model,along with

χ

EFT, deliver similar results at nuclear saturation density, lead- ing to an overall repulsive U of around 10–17 MeV [20,21,24].

This is in agreement with evidence from relativistic mean field calculations fittingexperimental data of ⁻ atoms [12] and the experimental absence of bound states in hypernuclei [16]. On the contrary, both Nijmegen models yield a slightly attractive single-particle potential, ranging from≈ −^{16 MeV for NSC97fto}

≈ −^{3 MeV forESC16. As alreadymentioned, however,the inter-} pretation of hypernuclear measurements introduces a significant model dependence.This concerns not only the extraction of the experimental results, relying for instance on the framework of the distorted-wave impulse approximation [17], but also the ex- trapolationoftheoreticalcalculationstofinitedensityvia e.g. the G-matrixapproach [62,63].

5. Summary

ThisLetterpresentsthefirstdirectinvestigationofthep–⁰in- teraction inhigh-multiplicitypp collisions at√

s=^{13 TeV, hence} proving the feasibility of femtoscopic studies in the N– sector.

Thep–⁰correlationfunctionisconsistentwiththep–(

γ

)base- line, andthereforethemeasurementindicates thepresence ofan overallshallowstrongpotential.Thedataarecomparedwithstate- of-the-artdescriptionsoftheinteraction,includingchiraleffective field theory and meson-exchange models. Due to the scarce ex- perimentalconstraintsintheN–sector,themodeled correlation functions differsignificantly among each other.The shape of the modeled correlationfunctionsappears tobevery sensitiveto de- tailsofthestronginteraction,andisdrivenbytheinterplayofthe different spin andisospin channels. This proves that femtoscopic measurements inhigh-energyppcollisions provideadirectstudy of the genuine two-body N– strong interaction. The presented femtoscopic data cannot discriminate between different models, which is also the case forthe available scattering and hypernu- cleidata.

Further femtoscopic studies enabled by the abouttwo orders ofmagnitudelargerpp datasamplesof6 pb⁻¹ inminimumbias collisions at √

s=⁵.5 TeV and of 200 pb⁻¹ in high-multiplicity at √

s=^{14 TeV,foreseen to be collected inthe LHC Runs 3and} 4 [64], will therefore shed light on the N– sector and provide constraintsonthemodelsdescribingtheinteraction.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompetingfinan- cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgements

TheALICECollaborationisgratefultoJ. HaidenbauerandT. Ri- jkenforvaluablediscussions andforprovidingthe theoreticalre- sultsforthep–⁰interaction.

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- 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 Desenvolvimento Científico e Tecnológico(CNPq), Fi- nanciadora de Estudose Projetos (Finep),Fundação de Amparo à Pesquisa do Estado de São Paulo(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; HelsinkiInstitute ofPhysics(HIP), Finland;Commissariatà