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

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Contents lists available atScienceDirect

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

r

a

c

t

Articlehistory:

Received16November2019

Receivedinrevisedform27March2020 Accepted6April2020

Availableonline9April2020 Editor: B.Betram

ThisLetterpresentstheﬁrstdirectinvestigationofthep–0interaction,usingthefemtoscopytechnique inhigh-multiplicityppcollisionsat√s=13 TeVmeasuredbytheALICEdetector.The0_is_{reconstructed} viathedecaychannelto

γ

,andthe subsequentdecayoftop

π

−.Thephotonisdetectedviathe conversioninmaterialtoe+e−pairsexploitingthecapabilityoftheALICEdetectortomeasureelectrons atlowtransversemomenta.Themeasuredp–0_correlation_indicates_a_shallow_strong_interaction._The comparison of the data to several theoretical predictions obtained employingthe Correlation Analysis Tool using the Schrödinger Equation (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.

1. Introduction

Aquantitative understanding of thehyperon–nucleon interac-tioninthestrangeness S

= −

1 sectorisfundamentaltopindown the role of strangeness within low energy quantum chromody-namics and to study the properties of baryonic matter at ﬁnite densities.Thepossiblepresenceoftheisoscalar

andthe isovec-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].The

hyperonsarerarely in-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

states in-volves neutral decay products [6], thus requiring high-resolution calorimeters.

_E-mail_address:_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-pectedtoprovideanadditionalattractivecontributioninthe two-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-mediumpropertiesaremostlydeterminedbytheoverall repul-sioninthe I

=

3

/

2 component [21,22]. Arepulsivecomponentin thehyperon–nucleoninteractionscouldshifttheonsetforhyperon productiontolargerdensities,above2–3timesthenormal

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

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tiondensity,thusleadingtostifferEoSwhichareabletodescribe theexperimentalconstraintofNS.

Tothisend,differenttheoreticalapproachesincludingchiral ef-fectiveﬁeldtheories(χEFT) [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.Recentab ini-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.Inthis Let-ter,thesestudiesareextendedtothe

sector.Theelectromagnetic decayofthe

0_is_exploited_for_the_ﬁrst_direct_measurement_of_the p–

0 interactioninppcollisions.Thisstudypavesthewayfor ex-tendingtheseinvestigationstothe charged

states,inparticular inlightofthelargerdatasamplesexpectedfromtheLHCRuns3 and4.

2. Data analysis

ThisLetterpresentsresultsobtainedfromadatasampleofpp collisionsat

√

s

=

13 TeVrecordedwiththeALICEdetector [30,31] duringtheLHCRun2(2015–2018).Thesamplewascollected em-ploying a high-multiplicity trigger with the V0 detectors, which consistoftwosmall-angleplasticscintillatorarrayslocatedon ei-therside ofthecollision vertexatpseudorapidities2

.

8

<

η

<

5

.

1 and

−

3

.

7

<

η

<

−

1

.

7 [32].Thehigh-multiplicitytriggerisdeﬁned bycoincidenthitsinbothV0detectorssynchronouswiththeLHC bunchcrossingandbyadditionallyrequiringthesumofthe mea-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 withatleastonecharged par-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 increasesthe probabil-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-particletrackingwithintheALICEcentralbarrelis con-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 ofhigh position-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)is con-ductedviathemeasurementofthespeciﬁcionizationenergyloss (dE

/

dx)withup to159reconstructedspacepoints alongthe par-ticle trajectory. The Time-Of-Flight (TOF) [35] detector system is locatedataradialdistanceof3.7 mfromthenominalinteraction point andconsists ofMultigapResistive Plate Chambers covering thefullazimuthalanglein

|

η

|

<

0

.

9.PIDisaccomplishedby mea-suringtheparticle’svelocity

β

viathetimeofﬂightoftheparticles inconjunctionwiththeirtrajectory.Theeventcollisiontimeis pro-videdasa combinationofthe measurementsin theTOF andthe T0 detector,two Cherenkovcounter arrays placed atforward ra-pidity [36].

The primary eventvertex(PV)is reconstructedwiththe com-binedtrackinformationoftheITSandtheTPC,andindependently withSPDtracklets.Whenbothvertexreconstructionmethods are available, thedifference ofthecorresponding z coordinates is re-quired to be smallerthan 5 mm. Auniform detectorcoverage is assured byrestrictingthemaximaldeviationbetweenthe z

coor-dinateof thereconstructedPV andthe nominalinteractionpoint to

±

10 cm.Atotalof1

.

0

×

109 _{high-multiplicity}_events_are_used 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.Thecorrespondingfractionof pri-maryandsecondaryprotonsareextractedusingMonteCarlo(MC) templateﬁtstothemeasureddistributionoftheDistanceof Clos-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 isreconstructedviathedecaychannel

0

→

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 betweenthe

andthe

0 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 conversionanalysisandthecorrespondingselectioncriteriaare de-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

(3)

Fig. 1. Invariantmassdistributionofthe

γ and

γ candidates,intwopTintervalsof1.5−2.0 GeV/c and6.5−7.0 GeV/c.ThesignalisdescribedbyasingleGaussian, andthebackgroundbyapolynomialofthirdorder.Thenumberof

0_candidates_is_evaluated_within_M

0(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

_mesons_is _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 _of_a _reﬁt_of _the_{reconstructed} _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(DCAz

<

0

.

5 cm).Afterapplicationoftheselection

criteria,about946

×

106

_γ

_candidates_with_a_purity_of_about_95.4% areavailableforfurtherprocessing.

The

particlecandidatesarereconstructedviathesubsequent decay

→

pπ−withabranchingratioof63.9% [6],followingthe procedures described in [27,28]. For the

the charge conjugate decayisexploited,andthesameselectioncriteriaareapplied.The decayproductsarereconstructedwiththeTPCandtheITSwithin

|

η

|

<

0

.

9.ThedaughtercandidatesareidentiﬁedbyabroadPID se-lectionintheTPC

|

nσ

|

<

5.Theresulting

candidateisobtained asthecombinationofthedaughtertracks.Thecontributionoffake candidatesis reduced by requesting a minimum pT

>

0

.

3 GeV/c. ThecoarsePIDselectionofthedaughtertracksintroducesa resid-ualK0_Scontaminationinthesampleofthe

candidates.This con-taminationisremovedbya 1

.

5σ rejectiononthe invariantmass assumingadecayinto

π

+

π

−,where

σ

correspondsto thewidth ofaGaussianﬁttedtotheK0_S signal.Topologicalselectionsfurther enhancethepurityofthe

sample.Theradialdistanceofthe de-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₎ _candidates_are _obtained_by _combining_all

₍

₎ and

γ

candidatesfromthesameevent,wherethenominalparticle masses [6] are assumedforthe daughters. Inparticular the tim-ingselectiononthedaughtertracksofthe

assuresthatthe

0

candidatesstemfromtherightbunchcrossing.Incaseadaughter trackisusedtoconstructtwo

γ

,

,and

candidates,ora combi-nationthereof,theone withthesmallerCPAisremovedfromthe sample.Inordertofurtheroptimizetheyieldandthepurityofthe sample,only

0candidateswithpT

>

1 GeV/c areused.

The resulting invariant mass spectrum is shown in Fig. 1 for two pT 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 pT 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

(

pT

)

±

3 MeV/c2.Thewidthoftheintervalischosenasa com-promisebetweenthe candidatecountsandpurity.In total,about 115

×

103 (110

×

103)

0 (

0₎ _candidates _are_found _at _a _purity of about 34.6%. Due to the enhanced combinatorial background at low pT, the purity increases from about20% at the lower pT 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

,the cor-responding

0 candidateisrejected.Sinceonly stronglydecaying resonancesfeedtothe

0 [6],allcandidatesareconsideredtobe primaryparticles.

3. Analysis of the correlation function

The experimental deﬁnition of the two-particle correlation function,forbothp–p andp–

0pairs,isgivenby [44],

C

(

k∗

)

=

N

×

Nsame

(

k

∗

₎

Nmixed

(

k∗

)

k∗→∞

−−−−→

1

,

(1)

withthesame(Nsame)andmixed(Nmixed)eventdistributionsofk∗ anda normalizationconstant

N

.The relative momentumof the pairk∗ isdeﬁnedask∗

=

1₂

× |

p∗₁

−

p∗₂

|

,wherep∗₁ and

p

∗₂ are the momenta ofthe twoparticles in thepair restframe, denotedby the∗.Thenormalizationisevaluatedink∗

∈ [

240

,

340

]

MeV/c for

(4)

p–p andink∗

∈ [

250

,

400

]

MeV/c forp–

0 _pairs,_where_effects_of ﬁnalstate interactionsare absentandhencethecorrelation func-tionapproachesunity.

The trajectories of the p–p and p–p pairs at low k∗ are al-mostcollinear,andmightthereforebeaffectedbydetectoreffects liketracksplittingandmerging [45].Accordingly, the reconstruc-tioneﬃciencyforpairsinthesameandmixedeventmightdiffer. To this end, a close-pair rejection criterion is employed remov-ingp–p andp–p pairsfulﬁlling

η

2

₊

_ϕ

∗2

_<

₀

_.

_01,_where_the azimuthalcoordinate

ϕ

∗considersthetrackcurvatureinthe mag-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

, and

0 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 statisticalﬂuctuationsisreducedbyevaluatingthesystematic un-certainties in intervalsof 100 MeV/c (20 MeV/c)in k∗ forp–

0

(p–p). Theresulting systematicuncertainties are parametrizedby anexponentialfunctionandinterpolatedtoobtaintheﬁnal point-by-pointuncertainties.Attherespectivelylowestk∗,thetotal sys-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, witha Gaus-sianshapedcoredensityprofileparametrizedbyaradiusr0,which isobtainedfromafittothep–p correlationfunction,similarlyas in [28,29].Followingthepremiseofacommonemissionsourcethe suchextractedradiusisthenusedasaninputtofitthep–

0 cor-relationfunction. Possiblemodifications ofthe sourceprofile due totheinfluenceofstronglydecayingresonances [47–49] are con-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,andadditionallyanysource distri-bution asinput tocompute the correlation function.For thep–p correlation function thestrong Argonne v18 potential [50] inthe

S,P ,andD wavesisusedasaninputtoCATS.

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

Weightparametersfortheindividualcomponentsofthemeasuredcorrelation func-tion.Contributions fromfeed-downcontainthe motherparticle listedas a sub-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–

channelisincorporatedbycomplexscattering parame-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,

Cmodel

(

k∗

)

=

1

+

i

λ

i

× (

Ci

(

k∗

)

−

1

),

(3)

wherethesumrunsoverallcontributions.Theirrelative contribu-tionisgivenbythe

λ

parameterscomputedinadata-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–

correlationfunctionismodeled us-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 applyingthe correspond-ingdecaymatrices [55].Allothercontributionsareassumedtobe

C

(

k∗

)

∼

1.Duetothechallengingreconstructionofthe

0,the ex-perimentalpurityofthe

0 sampleisratherlow,andadditionally exhibitsastrongdependenceonthetransversemomentum pT as demonstratedinFig.1.Theaverage pT ofthe

0 candidatesused to constructthecorrelation functionatk∗

<

200 MeV/c,however, is lowerthan the

pT

ofall inclusive

0 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 correlationfunctionstemsfromthecombinatorial back-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 orfrom feed-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

(5)

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

k∗

∈ [

0

,

375

]

MeV/c to determine 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,and sec-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 deviationofthetotal system-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

–πandK–Kcorrelationfunctionsat ultrarelativis-ticenergies inelementary [56] andheavy-ioncollisions [57] indi-cateasource distributionsigniﬁcantly deviatingfroma Gaussian. Indeed,stronglydecaying resonancesareknownto introduce sig-niﬁcantexponential tailsto thesource distribution,especially for

π–π

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

ρ

and

ω

,aresigniﬁcantlylonger-lived thanthosefeedingto protons(

) and

0 (

(1405)).Hence,itis notsurprisingthatthesourcedistributionfor

π

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

α

forthe ﬁttodetermine,the Gaussiansource shape(α

=

2) is re-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,whereitisconsistentand kine-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)_and system-aticuncertainties(boxes)areshownseparately.Thegraybanddenotesthep–(γ)

baseline.Thedataarecomparedwithdifferenttheoreticalmodels.The correspond-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 1σ 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 canonical ap-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 _function_is_shown inFig.3.Thek∗ valueofthedatapointsischosenaccordingtothe

k∗

ofthe sameevent distribution Nsame

(

k∗

)

in the correspond-ing interval. Therefore, due to the low number of counts in the ﬁrst bin,thedata pointis shiftedwithrespect tothe bincentre. Sincetheuncertaintiesofthedataaresizable,adirect determina-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

χEFT

atNext-to-LeadingOrder(NLO) [20].Thecorrelationfunction ismodeledusingtheLednický–Lyuboshitsapproach [51] consider-ingthecouplingsofthep–

0 systemtop–

andn-

+[52] with scatteringparametersextractedfromthefss2 model.Forthecase ofESC16,NSC97fand

χ

EFT,thewavefunctionofthep–

0_system, includingthecouplings,isusedasaninputtoCATStocomputethe correlationfunction.Thedegreeofconsistencyofthedatawiththe discussed models isexpressed by thenumber ofstandard devia-tionsnσ ,computedintherangek∗

<

150 MeV/c fromthep-value

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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 computedasonestandarddeviationofthecorresponding distribu-tion.Thedataare within (0.2

−

0.8)σ consistentwiththep–

(

γ

)

baseline,indicating thepresence ofan overallshallowstrong po-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,theoverall descrip-tionofthep–

interactionyields aconsistentdescription.Onthe other hand, the corresponding p–

0 correlation functions differ signiﬁcantlyamongeachother.Thisdemonstratesthatfemtoscopic measurements candiscriminate andconstrain models,and there-forerepresenta uniqueprobeto studythe N–

interaction.Both fss2 and

χ

EFT exhibit an overall repulsionin N–

at intermedi-atek∗,whichmainlyoccursinthespinsinglet S

=

0,I

=

1

/

2 and spintriplet S

=

1,I

=

3

/

2 components [20,24].Inthelow momen-tumregion,belowroughly50 MeV/c,bothmodelsyieldattraction, which is reflected in the profile of the correlation function. The Nijmegenmodels,ontheotherhand,arecharacterizedbyarather constantattractionoverthewholerangeofk∗.Inparticularatlow relativemomenta,however,thebehaviorofthetwomodels devi-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 different val-uesforthein-mediumsingle-particlepotentialUwhenincluded

inmany-bodycalculations. Boththefss2quark-model,along with

χEFT,

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–

0 in-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.Thedataarecomparedwith state-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.

Declaration of competing interest

Theauthorsdeclarethattheyhavenoknowncompeting ﬁnan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto inﬂuencetheworkreportedinthispaper.

Acknowledgements

TheALICECollaborationisgratefultoJ. HaidenbauerandT. Ri-jkenforvaluablediscussions andforprovidingthe theoretical re-sultsforthep–

0interaction.

The ALICECollaboration would like to thank all its engineers andtechniciansfortheirinvaluablecontributionstothe construc-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 buildingand run-ningtheALICEdetector: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;MinistryofCommunicationsandHigh Tech-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) andUniversidade Fed-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;CentrodeAplicacionesTecnológicasyDesarrollo Nu-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

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l’ÉnergieAtomique (CEA), Institut Nationalde Physique Nucléaire etde Physique des Particules (IN2P3) andCentre National de la Recherche Scientifique (CNRS) and Région des Pays de la Loire, France; Bundesministerium für Bildung und Forschung (BMBF) andGSIHelmholtzzentrumfürSchwerionenforschungGmbH, Ger-many;GeneralSecretariatforResearchandTechnology,Ministryof Education,Research andReligions,Greece; NationalResearch De-velopmentandInnovationOffice,Hungary;DepartmentofAtomic Energy, Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Com-mission,GovernmentofIndia(UGC) andCouncil ofScientificand IndustrialResearch (CSIR), India;IndonesianInstitute of Sciences, Indonesia;CentroFermi- MuseoStoricodellaFisicaeCentroStudi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica Nucle-are Sezione di Padova (INFN), Italy; Institute for Innovative Sci-enceandTechnology,NagasakiInstitute ofApplied Science(IIST), JapaneseMinistryofEducation,Culture, Sports,Science and Tech-nology (MEXT) and Japan Society for the Promotion of Science (JSPS)KAKENHI, Japan;ConsejoNacionalde Ciencia(CONACYT) y Tecnología, throughFondo de Cooperación Internacional en Cien-cia y Tecnología (FONCICYT) and Dirección General de Asuntos delPersonalAcademico(DGAPA),Mexico;NederlandseOrganisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Re-search Council of Norway, Norway; Commission on Science and TechnologyforSustainableDevelopmentintheSouth(COMSATS), Pakistan;PontificiaUniversidadCatólicadelPerú,Peru;Ministryof ScienceandHigherEducationandNationalScienceCentre,Poland; KoreaInstituteofScienceandTechnologyInformationandNational ResearchFoundation of Korea (NRF), Republic of Korea;Ministry of Education and Scientific Research, Institute of Atomic Physics andMinistry ofResearch andInnovation andInstitute of Atomic Physics,Romania; JointInstituteforNuclearResearch(JINR), Min-istryofEducationandScienceoftheRussianFederation,National Research Centre Kurchatov Institute, Russian Science Foundation andRussianFoundationforBasicResearch,Russia;Ministryof Ed-ucation,Science, Research and Sportof the Slovak Republic, Slo-vakia;NationalResearchFoundationofSouthAfrica,SouthAfrica; SwedishResearchCouncil(VR)andKnut&AliceWallenberg Foun-dation (KAW), Sweden; European Organization for Nuclear Re-search,Switzerland;SuranareeUniversityofTechnology(SUT), Na-tionalScience andTechnology Development Agency(NSDTA) and OfficeoftheHigher Education CommissionunderNRU projectof Thailand,Thailand;TurkishAtomicEnergyAgency(TAEK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and TechnologyFacilitiesCouncil(STFC),UnitedKingdom;National Sci-enceFoundationoftheUnitedStatesofAmerica(NSF)andUnited StatesDepartmentofEnergy, Office ofNuclear Physics(DOE NP), UnitedStatesofAmerica.

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