Exploring the N –N coupled system with high precision correlation techniques at the LHC

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Physics Letters B

www.elsevier.com/locate/physletb

Exploring the N –N coupled system with high precision correlation techniques at the LHC

.ALICE Collaboration

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

Articlehistory:

Received21February2022

Receivedinrevisedform27May2022 Accepted27June2022

Availableonline4July2022 Editor: M.Doser

Theinteractionofandhyperons(Y)withnucleons(N)isstronglyinfluencedbythecoupled-channel dynamics.DuetothesmallmassdifferenceoftheNandNsystems,thesizable couplingstrengthof the N↔^Nprocessesconstitutesacrucial elementinthe determinationof theNinteraction.In thisletterwepresentthemostprecisemeasurementsontheinteractionofppairs,fromzerorelative momentumuptothe openingoftheNchannel.The correlationfunctioninthe relativemomentum spaceforp⊕^ppairsmeasuredinhigh-multiplicitytriggeredppcollisions at√

s = ^{13 TeVatthe} LHCisreported.TheopeningoftheinelasticNchannelsisvisibleintheextractedcorrelationfunction asacusp-likestructureoccurringatrelativemomentumk^∗=^{289 MeV/c.Thisrepresentsthefirstdirect} experimentalobservationoftheN↔^Ncoupledchannelinthepsystem.Thecorrelationfunction is comparedwithrecent chiral effective fieldtheorycalculations, basedondifferent strengths ofthe N↔^Ntransitionpotential.Aweakercoupling,as possiblysupportedbythepresentmeasurement, wouldrequireamorerepulsivethree-bodyNNinteractionforaproperdescriptionofthein-medium properties,whichhasimplicationsonthe nuclearequationofstateand forthe presenceofhyperons insideneutronstars.

©^2022EuropeanOrganizationforNuclearResearch,ALICE.PublishedbyElsevierB.V.Thisisanopen accessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

The proton–Lambda (p) system is one of the best-known examples in hadron physics where the role of coupled-channel dynamics is crucial for the understanding of the two-body and three-body interaction,bothinvacuumandatfinitenuclearden- sities [1–4]. The couplingbetween the nucleon–Sigma (N) and Nsystems arisesfromthesepairs havingthe samestrangeness content and a small mass difference, and it is responsible for thedominantattractivepinteractioninthespin-tripletstateof coupled-channelpotentials [3,5,6].

The attractive natureof theinteraction betweena protonand a was established from measurements of binding energies of light -hypernuclei [7,8] and scattering experiments at low en- ergies [9–11]. However,the availablescatteringcross sectionsare characterisedbylargeuncertainties.Moreover, theyarelimitedto hyperon momenta above p_lab∼^{100 MeV/c. Thus, a reliable de-} termination of standard quantities like scattering lengths, which provide a simple quantitative measure for the strength of an interaction, is practically impossible. Furthermore, in the region p_lab≈^{640 MeV/c, where the n+} and p⁰ channels open, the momentum resolutionofthe existingdatais poor [12,13].Calcu- lations based on N-N coupled-channel potentials [2,3,6] pre-

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

dict a narrow but sizable enhancement of the p cross section in that region which reflects the strength of the channel cou- plingandalsothatoftheNinteraction.However,becauseofthe poorresolutionofthementionedscatteringdata,thepresence of such a structure could not be confirmed. New p data that be- came available recently [14] cover only energies well above the N threshold.Experimental observations ofa cusp-like structure at the N threshold stem only from studies of the p invari- ant mass (IM) spectrum in strangeness exchange processes such asK⁻d→π⁻p[15,16] andmorerecentlyfrommeasurementsof thereactionpp→^K+p[17,18].

It is known that the strength of the N↔^N conversion is relevantforthebehaviourofhyperonsininfinitenuclear mat- ter [19–21].ThishasbeenemphasisedinarecentstudyoftheYN interactionbasedonchiraleffectivefieldtheory(

χ

EFT) [3].Specif- ically, this work discussed the interplay between the N↔^N conversion,thein-mediumpropertiesoftheandtheroleplayed by three-body forces.The abundant data onhypernuclei allowed the determination of the average attraction (−^{30 MeV) experi-} encedbyahyperonwithinsymmetricnuclearmatteratthenu- clearsaturationdensity [22].However,theinteractionofhyperons withthesurroundingnucleons atlarger baryonicdensitiesis not knownempirically.Theoutcomeofpertinentcalculationsdepends ontheemployedNandNNinteractionsinvacuum.Thesecon- tributions are directlycorrelated to the N↔^Nconversion, as the parameters driving the coupling strength in the theory can

https://doi.org/10.1016/j.physletb.2022.137272

0370-2693/©^2022EuropeanOrganizationforNuclearResearch,ALICE.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

be tuned differently while still reproducing the existing experi- ments [3]. For example, compared to the original version of the next-to-leading order(NLO)

χ

EFT (NLO13) [2], the revisitedver- sion(NLO19) [3] involvesaweakerN↔^Ntransitionpotential.

However, itleads topracticallyidenticalresultsforNtwo-body scattering,buttoanenhancedattractivebehaviourinthemedium.

Thispointstoastrongerrepulsivethree-bodyforceneededwithin thelatterrealisation.TheinterplaybetweentheNandNNin- teractionisrelevanttothedebatedpresenceofhyperonsinside thecoreofneutronstars(NS) [22–24].Thehyperonpuzzle origi- nates fromthecontraposition betweentheenergeticallyfavoured production ofhyperonsin theinteriorof NS [25] and the subse- quentsoftening ofthecorresponding equation ofstate (EoS).The latterdoesnotsupporttheexistence oftheheaviestobserved NS ofupto2.2 solarmasses [26–28].ApplicationsoftheNLO19

χ

EFT potentials in calculationsof the EoS [4] demonstrated that a re- pulsive genuineNNinteractionsuppressesthe appearanceof hyperons inside NS, giving a more quantitative referencefor the solution of the hyperon puzzle. Thus new experimental data of high precision providing constraints on the N↔^N dynamics areneeded.

Recentstudiesoftwo-particlecorrelationsinpp,p–PbandPb–

Pb collisions havebeen successful in studying the final-state in- teraction (FSI) and in delivering high precision data on particle pairs of limited accessibility using traditional experimental tech- niques [29–39]. Performingsuch measurements insmallcollision systems resultsin a stronger sensitivityof theexperimental cor- relation to the coupled-channel dynamics, asrecently proven by meansofpK⁻correlations [35,40,41].Inthisletterwepresentthe combinedmeasurementofpandppairsinppcollisionswith ahigh-multiplicity(HM)triggerat√

s=13 TeV [42,43].

2. Dataanalysis

Therelevantobservableinthisanalysisisthetwo-particlecor- relationfunctionC(k^∗).Thisisrelatedtoaneffectiveparticleemis- sionsourceS(r^∗)andtothewavefunction(k^∗,r^∗)oftheparticle pair,bymeansoftherelationC(k^∗)=

S(r^∗)|(^k∗,r^∗)|^{2d3r∗ [44],} where the relative distancer^∗ and relative momentum q^∗=^2k∗ are evaluatedinthepairrestframe.Theexperimentalcorrelation isdefinedas

C

(

k^∗

) =

N

·

^N

(

k^∗

)/

M

(

k^∗

),

(1) where N(k^∗)isthedistributionofpairswherebothreconstructed particles aremeasured inthe sameevent, M(k^∗) isthereference distribution ofuncorrelatedpairs sampledfromdifferent(mixed) eventsandN ^isanormalisationfactor.Theuncorrelatedsamplein the denominator, M(k^∗), isobtainedby combiningparticles from oneeventwithparticlesfromasetofotherevents.Thetwoevents are requiredto have comparable number of charged particles at midrapidityandasimilarprimary vertexcoordinateV_z along the beamaxis(z).

TheALICEexperimentexcelsincorrelationstudiesthankstoits good tracking andparticle identification (PID) [42,43]. These ca- pabilitiesarerelatedto thethreesubdetectors,theinner tracking system(ITS) [45],thetimeprojection chamber(TPC) [46] andthe time-of-flight detector (TOF) [47]. The event trigger is based on the measured amplitudeinthe V0detector system, consistingof twoarraysofplasticscintillatorslocatedatforward(2.8<

η

<5.1) and backward (−³.7<

η

<−¹.7) pseudorapidities [48]. The se- lected HM eventscorrespond to 0.17% ofall eventswithat least onemeasuredchargedparticlewithin|

η

_|<1 (INEL>0).Thiscon- dition results in an average of 30charged particles in the range

|

η

|<0.5 [34]. Compared to a minimum-bias trigger, HM events provide not only a larger number of particles per event, but an

overallhigherproductionrateofparticles containing strangeness, such a hyperons [49]. Consequently, the HM sample offers a tenfold increase in the amount of p pairs reconstructed below k^∗ of 200 MeV/c, leading to a total of 1.3 million pairs within thesameeventsample.The reconstructedprimary vertex(PV)of the event is required to have a maximal displacement with re- spectto the nominalinteraction point of 10 cm along the beam axis,inordertoensureauniformacceptance.Pile-upeventswith multipleprimaryverticesareremovedfollowingtheprocedurede- scribedin [29,30,33,34]. Thefinal number ofselected HMevents reachesapproximately10⁹.Chargedparticles,suchasprotonsand pions, are directly measured, while the candidates are recon- structed based on the IM of the decayproducts. The correlation functionsobtained for particles (p) andanti-particles (p) are identicalwithinuncertainties, thusthefinal resultispresentedas theirweightedsump⊕^p.

Boththeprotonsandthecandidatesarereconstructedusing theproceduredescribed in [30], whiletherelatedsystematicun- certaintiesareevaluatedbyvaryingthekinematicandtopological observablesusedinthereconstruction.Forthepurposeofcorrela- tionstudiesit isessential todifferentiatebetweenprimary parti- cles,whichparticipateintheFSI,andsecondary(feed-down)parti- cles,whichstemfromweakorelectromagneticdecays.Experimen- tally,theformercanbeselectedbydemandingtheparticlecandi- datestobeclosetothePVoftheevent,whilethelatterhavetobe associatedwithasecondaryvertexwithintheevent.Inthefollow- ingtext,thesystematicvariationsareenclosedinparentheses.The primary proton candidates are selected in the momentum inter- val0.5(0.4, 0.6)<p_T<4.05 GeV/cand|

η

|<0.8(0.77, 0.85).To improvethequalityofthetracksaminimumof80(70,90)outof the159possible spatialpoints (hits) inside theTPCare required.

The candidates are selected by comparing the measurements in theTPCandTOFdetectorstotheexpecteddistributionsforapro- toncandidate.Theagreementisexpressedintermsofthedetector resolution

σ

(n^PIDσ ). Forprotonswith p_T<0.75 GeV/c the n^PIDσ is evaluatedonlybased ontheenergylossandtrackmeasurements inthe TPC, while for pT>0.75 GeV/c a combined TPCand TOF PIDselectionis applied(n^PIDσ =

n²σ,TPC+ⁿ²_σ,TOF^{).The nPID}_σ ^ofthe accepted candidates is required to be within 3 (2.5, 3.5). To re- jectnon-primaryparticles thedistanceof closestapproach (DCA) tothe PVof thetracks isrequired tobe lessthan 0.1 cm inthe transverseplane andlessthan0.2 cm along thebeamaxis.Nev- ertheless, duetothe limitedresolutionofthe reconstruction,the selectedprimaryprotoncandidateswillcontaincertainamountof secondaries,stemming from weak decays, andmisidentifications.

ThesecontributionsareextractedusingMonteCarlo(MC)template fitsto themeasured distributionsofthe DCAtothePV [29].The resultingprotonpurityis99.4% witha82.3% fractionofprimaries.

The candidates are reconstructed viathe weak decay → pπ⁻.Thesecondarydaughtertracksaresubjecttosimilarselection criteriaasfortheprimaryprotons.Inaddition,thedaughtertracks are requiredto havea DCAto the PVof atleast0.05 (0.06) cm.

The DCAofthe corresponding candidates to thePV hasto be below 1.5 (1.2) cm. The cosine of the pointing angle (CPA) be- tween thevector connecting the PVto thedecay vertexandthe three-momentumofthecandidateisrequiredtobelargerthan 0.99 (0.995).Torejectunphysicalsecondaryvertices,reconstructed with tracks stemming from collisions corresponding to different crossings of the beam, the decay tracks are required to possess a hit in one ofthe SPD orSSD detectors or a matched TOF sig- nal [31]. Thefinal candidatesare selectedina 4 MeV/c² mass window around the nominal mass [50], where the widthof the IMpeakisc.a.1.6 MeV/c².Thenumberofprimaryandsecondary contributions for are extracted similarly as for protons, using

Table 1

Weightparametersoftheindividualcomponentsofthepcorrelation function.Thetwolastrowscorrespondtothevaluesoftheλparame- terswithinthesystematicvariations.

Pair p p(⁰) p() Flat feed-down p˜

λPair(%) 47.1 15.7 19.0 17.6 0.6

min{λPair} (%) 42.7 12.6 – – –

max{λPair} (%) 49.6 18.0 22.1 – –

the CPA asan observable forthe template fits. Theaverage frac- tion of primary hyperons is 57.6 (52.1, 60.6)% and19.2 (15.4, 21.9)%originatefromtheelectromagneticdecaysof⁰.Thenum- ber of ⁰ particles is related to their ratio to the hyperons, which is fixed to 0.33 (0.27, 0.40). These values are based on predictionsfromtheisospinsymmetry,thermalmodelcalculations usingtheThermal-FISTpackage [51] andmeasurementsofthecor- responding production ratios [52–54]. Further, each of the weak decays of ⁻ and ⁰ contributes with11.6 (13.5)% to the yield of hyperons.The purityof and was extracted by fitting, as a function ofk^∗,the IM spectra ofcandidates selected in the mixed-event sample. Thefits were performedin theIM rangeof 1088to1144MeV/c² usingadoubleGaussianforthesignalanda third-ordersplineforthebackground.Theresultwasaveragedfor k^∗<480 MeV/c, leading to a purity P=⁹⁵.3%. The systematic variationsincludeamodellingofthesignalusingthesumofthree Gaussians,leadingtoapurityof96.3%.Theeffectofmisidentified candidates(˜)canbeaccountedforbytherelations

C_exp

(

k^∗

) =

^PC_corrected

(

k^∗

) + (

1

−

^P

)

C_p˜

,

(2) C_corrected

(

k^∗

) =

^B

(

k^∗

)

λ

pCp

(

k^∗

) + λ

_p(0)C_p(0)

(

k^∗

) +λ

p()Cp()

(

k^∗

) + λ

_ff

+ λ

_p˜

,

(3)

where the signal is decomposed into its ingredients, weighted by thecorresponding λ parametersandcorrectedforthe non-FSI baseline B(k^∗).

Suchadecompositionisrequired [29],astheexperimentalsig- nal contains correlations complementing the genuine p signal Cp(k^∗). In the present analysis the contribution C_p˜ related to misidentified candidates (˜) is explicitly measured and sub- tracted from the total correlation Cexp(k^∗). This is achieved by performing asidebandanalysis [32], whichreliesonpurposefully selectingcandidatesincompatiblewiththetruemassbymore than5

σ

.

ThecorrectedcorrelationC_corrected(k^∗)hasaneffectivepurity of 100%, and the remaining contributions (Eq. (3)) are the gen- uine signal of interest C_p, the residual (feed-down) correlation C_p(0)ofparticlesoriginatingfromthedecayofa⁰,theresid- ual signal Cp() related to (⁻⊕⁰) decaying into , other sub-dominant(flat)sourcesoffeed-downcorrelationsC_ff≈^1,and contamination C_p˜ stemmingfrommisidentified protons.Eachof thesecontributionsisweightedbya statisticalfactorλ,evaluated astheproductofthepuritiesandfractions(primaryorsecondary) of theset particles [29]. Theseweight factorsare summarised in Table1.ThecontributionC_p˜cannotbemodelled,howevertheas- sociatedλ_p˜isonly0.6%,justifyingtheassumptionλ_p˜C_p˜≈λ_p˜ within theuncertainties ofCcorrected(k^∗). Bycontrast,theresidual correlations C_p(0) and Cp() are significant, but in these cases their interactions with protons can be described by theory. Re- cent correlation studies of the p⁰ system showed that this in- teraction is ratherweak [32]. Thischannel is modelledassuming either a flat function or employing the same

χ

EFT calculations used for the genuine p interaction [3]. The contribution from the p (p⁻⊕^p0) channel is modelled employing the lattice

potentialsfromtheHALQCDcollaboration [55].Theywereexperi- mentallyvalidatedbycomparisonwithprecisionmeasurementsof p⁻correlations [33,34].TheresidualcontributionsC_p(0)(k^∗)and Cp()(k^∗)areobtainedbytransformingthecorrespondinggenuine correlationfunctionstothebasisofthepinteraction,usingthe formalismdescribedin [29] and [56] appliedtothephasespaceof themeasuredpairs.

Thenon-FSIbackground(baseline)isparameterisedbyathird- orderpolynomial B(k^∗) constrainedto be flat atk^∗→^{0 and fit-} ted to the data (Eq. (3)). By default, the fit is performed for k^∗∈ [⁰,456] ^{MeV/c,withsystematicvariations oftheupperlimit} to 432 and480 MeV/c. Further, dueto the expectationof a flat baseline atlow k^∗,a systematic cross-check hasbeen performed byassumingthehypothesisofaconstantB(k^∗)andfittingthecor- relationfunctionfork^∗ below336 MeV/c.

Thecorrelation function (Eq. (3)) isgivenasafunction ofthe measured k^∗, which isnot identical tothe true relative momen- tumofthepairduetotheeffectsofmomentumresolution.Thus, to compare the experimental results with theoretical predictions an unfoldingof thedata isrequired.Both thesame- and mixed- eventsamples(N(k^∗),M(k^∗)) are biasedbythe resolutionofthe detector.Theyrelatetotheirtrueunderlyingdistributionsby

N

(

k^∗

) =

∞

0

T

(

k^∗

,

k^∗_true

)

N_true

(

k^∗_true

)

dk^∗_true (4)

and M

(

k^∗

) =

∞

0

T

(

k^∗

,

k^∗_true

)

M_true

(

k^∗_true

)

dk^∗_true

,

(5)

where T(k^∗,k^∗_true) isthedetectorresponse matrix.The latterisa two-dimensional matrixcorresponding to the probability of hav- ing a true value k^∗_true given a measured k^∗. Byusing a full scale simulation of the detector, involving Pythia 8 [57] as an event generatorandGeant3 [58] tomodelthedetectorresponse,thema- trixT(k^∗,k^∗_true)hasbeen determined.The resultingspreadinthe distribution ofk^∗ for a fixed k^∗_true is,on average, 4.2 MeV/c.Us- ing Ntrue(k^∗_true)=^Mtrue(k^∗_true)C(k^∗_true) and defining W(k^∗,k^∗_true)= T(k^∗,k^∗_true)Mtrue(k^∗_true)/M(k^∗),Eq. (1) becomesequivalentto

Cexp

(

k^∗

) =

N

∞ 0

W

(

k^∗

,

k^∗_true

)

Ctrue

(

k^∗_true

)

dk^∗_true

.

(6)

Inthe presentanalysis theunfolding is performedasa two-step process,firstobtainingMtrue(k^∗)fromEq. (5),secondusingEq. (6) toobtain C_true(k^∗).Eachstepisperformedbyusingacubicspline toparameterise thetruefunctions, whicharefittedtotheir mea- suredcounterparts. Thesplines are definedfork^∗<1000 MeV/c, usingatotalof32knots.Thequalityoftheprocedureisvalidated by transforming the unfolded functions backwards using Eq. (5) and Eq. (6), which ideally should restore the input distributions (

χ

²=^{0). In case the resulting}

χ

² per data point is larger than 0.2,thevalueofeach Ctrue(k^∗)binisperturbed usingabootstrap procedure [59],untilabetter

χ

² isachieved.Thisisiterativelyre- peated until obtaining the desired precision, and until no single bindeviatesbymorethanhalfoftheiruncertainty.

3. Resultsanddiscussion

The corrected and unfolded experimental correlation function for p ⊕ ^p is shown in Figs. 1 and 2. The correlation func- tion is measured with high-precision in the low momentum re- gion down to k^∗ =^{6 MeV/c, in contrast to existing p} scat-

Fig. 1.Upperpanels:pcorrelationfunction(circles)withstatistical(verticalbars)andsystematic(greyboxes)uncertainties.Middlepanels:zoomonthecusp-likesignal atk^∗=289 MeV/c.Lowerpanels:Thedeviationbetweendataandpredictions,expressedintermsofnσ.ThefitisperformedusingNLO13(red)χEFT potentialswith cut-off=600 MeV [2,3] andusingacubicbaseline(darkgrey).Theresidualp⁻⊕^p0(pink)andp⁰(royalblue)correlationsaremodelledusing,respectively,alattice potentialfromtheHALQCDcollaboration [33,55] andaχEFTpotential [2].Bothcontributionsareplottedrelativetothebaseline,whileinpanelb)thestronginteractionof p⁰isneglected.Thereducedχ²,fork^∗<300 MeV/c,amountsto2.2incasea)andto1.9incaseb).

Fig. 2.SimilarrepresentationasinFig.1,wherethepinteractionismodelledusingNLO19(cyan)χEFT potentialswithcut-off=600 MeV [2,3].Thisleadstoanimproved descriptionofthelowmomentumregion.Thereducedχ²,fork^∗<300 MeV/c,equals2.0incasethep⁰ismodelledbyχEFT (panela)and1.8incasethep⁰finalstate interactionisignored(panelb).

tering data which cover the region k^∗ >60 MeV/c. The preci- sion achieved for k^∗<110 MeV/c is better than 1%, which cor- responds to an improvement of factor up to 25 compared to previous scatteringdata [9–11]. The theoretical correlation func- tions in Eq. (3) were evaluated using the CATS framework [60].

The size of the emitting source employed inthe calculation was fixedfromindependentstudiesofprotonpairs [30],whichdemon- strateacommonprimordial(core)Gaussiansourceforppandp pairswhenthecontributionofstronglydecayingresonancesisex- plicitly accountedfor [30]. Thissource exhibitsa pronouncedmT dependence andconsidering the average transversemass ^mT = 1.55 GeV ofthe measured ppairs a corresponding coresource radiusofrcore(mT)=¹.02±⁰.04 fmisobtained.Thetotalsource function can be approximated by an effective Gaussian emission source of size 1.23 fm. The genuine p correlation function is modelled by

χ

EFT hyperon-nucleon potentials, considering the leading-order(LO)interaction [1] andtwoNLOversions(NLO13 [2]

andNLO19 [3]). Forthe NLO interactions the variation withthe underlying cut-off parameter (cf. Ref. [2]) is explored, while =^{600 MeV is chosen as a default value. Both NLO versions} provide an excellent description of the available scattering data, havinga

χ

²_≈16 fortheconsidered36datapoints [3].

Figs.1and2showthetotalfitfunctions(redandcyan)tothe presentdata.Thenon-FSIbaseline B(k^∗)isdepictedasadarkgrey line,whiletheindividualcontributionsrelatedtofeed-downfrom F= {⁰,}^{aredrawnasroyalblueandpinklines,}corresponding to B(k^∗)

λp(F)Cp(F)(k^∗)+¹−λp(F)

. The latter relation is derived by setting all C_i terms within Eq. (3), apart fromC_p(F),equal to unity. The upper panels in Figs. 1 and 2 present the correlation functioninthewholek^∗ range,whilethemiddlepanelsshowthe regionwheretheNchannelsopen,clearlyvisibleasacuspstruc- tureoccurringatk^∗=^{289 MeV/c.Thedeviationbetweendataand} prediction,expressed interms of number of standard deviations nσ,isshowninthebottompanels.Thediscrepancybetweenthe-

Table 2

Thedeviation,expressedintermsofnσ,betweendataandpredic- tionforthedifferentinteractionhypothesesofpandp⁰,evaluated fork^∗∈ [0,110]MeV/c (firsttwocolumns)andk^∗∈ [0,300]MeV/c (lasttwocolumns).Thedefaultvaluescorrespondtothefitwith a cubicbaselineandthevaluesinparenthesesrepresenttheresultsus- ingaconstantbaseline.Thedefaultinteraction(inbold)istheχEFT NLO19potentialwithcut-off=600 MeV [3].Eachrowcorresponds toadifferentvariantoftheχEFTinteractionusedforevaluatingthe pcorrelation.Thefirstandthirdcolumncorrespondtothecaseof modellingthep⁰usingχEFT,whilethesecondandfourth column representthecaseofnegligiblep⁰finalstateinteraction.

Standard deviation (n_σ) k^∗∈ [0,110]MeV/c k^∗∈ [0,300]MeV/c p⁰(→⁾ χEFT Negligible χEFT Negligible

p(↓) p⁰FSI p⁰FSI

LO-600 4.7 (4.9) 6.1 (7.0) 7.2 (8.7) 10.3 (10.3) NLO13-500 5.9 (8.0) 4.3 (5.1) 6.6 (10.3) 4.9 (7.6) NLO13-550 4.5 (5.8) 3.1 (3.1) 4.1 (7.2) 2.8 (3.4) NLO13-600 4.5 (5.3) 3.2 (3.1) 3.9 (5.1) 2.9 (3.0) NLO13-650 4.2 (4.7) 2.8 (2.7) 3.6 (4.1) 2.8 (3.3) NLO19-500 4.2 (5.0) 2.7 (3.0) 4.4 (7.6) 3.4 (4.3) NLO19-550 3.6 (4.2) 2.4 (2.7) 3.0 (4.4) 2.2 (2.7) NLO19-600 3.2 (3.2) 2.2 (2.3) 3.1 (3.8) 2.6 (3.3) NLO19-650 3.2 (3.6) 2.3 (2.0) 2.8 (3.2) 2.7 (3.5)

ory anddataislargest inthemomentum regionk^∗<110 MeV/c, while, due to the presence of the N cusp, the sensitivity of thecorrelationfunctiontothepropertiesofthestronginteraction extends up to 300 MeV/c. The deviations forthe interaction hy- pothesesare summarisedinTable 2,wheretheleft two columns showthenσ onlyinthelowmomentumregion,andtherighttwo columnsrepresentthedeviationevaluatedfork^∗∈ [⁰,300]^MeV/c.

Thepresentedresultsarethefirstdirectexperimentalevidence oftheN↔^Ncouplinginatwo-bodyfinalstate.Thesignal of the cusp isdetermined by the properties ofthe interaction, and furthermodifiedbytherelativeamountofNandpinitialstate pairs leading tothe final state (measured)ppairs.The amount of initial state pairs was fixed by the above-mentioned : ra- tio,enabling a directtest of thestronginteraction. The LOchiral potential [1] predicts a too small N cusp with respect to the measurement, the green line in Fig. 1, while both NLO interac- tions provide a satisfactory description of the cusp structure. On theother hand,inthemomentumregionbelow110 MeV/c there is a tension betweenthe data and thetheory predictions forall considered interactions.In particular,theresultsforthe twoNLO potentials are not that well in line with the measured correla- tionfunction,despiteofthefactthattheseinteractions reproduce thelow-energypscatteringdataperfectly [3].Thebestresultis provided bythe NLO19 potentialwith=600–650 MeV,though the deviationofnσ=³.2 from theexperimentis substantial.For NLO13thisdeviationisevenlargerandamountstonσ=⁴.2.Fur- ther,itisobservedthatforNLO13andNLO19thebestagreement with the data is achievedwithin the same range of cut-off val- ues(550–650 MeV)whichalsoprovidethebestdescriptionofthe availablescatteringandhypertritondata [2,3].

The discrepancybetweenthedataand

χ

EFT atlow momenta couldbeanindicationforaweakergenuinepinteraction,butit couldalsosignalthatthep⁰ correlationisverysmall.Asvisible intherightpanelsofFigs.1,2andTable2,adoptingthehypoth- esis of a negligible p⁰ correlation leads to a better agreement withthepresentpdata(nσ=².2). Atthemomentitisimpos- sibletodifferentiatebetweenthesetwocasesbecausetheexisting directmeasurementofthep⁰ channel isnotpreciseenoughfor drawingpertinentconclusions [32].Thep⁰measurementiscom- patiblewithboththeNLO predictions(ofaweaklyattractivep⁰ interaction)andwithaflatcorrelation(negligiblep⁰interaction).

Aprecisionmeasurementofthegenuinep⁰channel,expectedto

beachievedintheupcomingLHCRun3 [61],shouldprovideclar- ification. Then the actual strength of the N interaction can be pinneddowninamodelindependentwaybyadedicatedtheoret- icalanalysisofthepdata.

Alltheconclusionsofthepresentanalysisremainthesameun- derthealternativehypothesisofaconstantbaseline,orincasethe deviationisevaluatedfork^∗<300 MeV/c.Withinthatmomentum region,the NLO19provides a satisfactorydescription ofthe data, with a deviation of nσ =².8, while the NLO13 still results in a largerdiscrepancy(nσ=³.6).

4. Summary

Inconclusion,two-particlecorrelationtechniqueswereusedto study the final state interaction in the N↔^N coupled sys- tem. This was achieved by studying the p correlation function at low relative momenta with an unprecedented precision. The significanceofthecouplingofptoNismanifested asacusp- likeenhancement presentatthe corresponding thresholdenergy, which is the first direct experimental observation of this struc- ture. Further, using different modellings for the p⁰ feed-down leadstoastatisticallysignificantmodificationofthemeasuredp correlation, implying an indirect sensitivity to the genuine p⁰ correlation.In the momentumrangek^∗∈ [¹¹⁰,300] ^{MeV/c allof} the tested NLO

χ

EFT interactions are compatible with the data, however a significant deviation is present at lower values. The detailed analysis, presented in Table 2, reveals a deviationof at leastnσ =³.2, for k^∗<110 MeV/c, forthe considered

χ

EFT in- teractions.TheresultforNLO19exhibitsanoverallbettercompat- ibility, compared to theNLO13 prediction. The formerinvolves a weakerN↔^Ntransitionpotential anda moreattractivetwo- bodyinteractionofthehyperoninthemedium.Thisrequiresa strongerrepulsiveNNthree-bodyforce,whichleadstoastiffen- ingoftheEoSatlargedensities [4] andadisfavouredproduction ofthesestrangehadronsinneutronstars.Thepresenteddatapro- videanopportunitytoimprovethetheoreticalcalculationsforthe N↔^Ncoupledsystem,includingthelow-energypropertiesof N.The successfuluseofcorrelation techniquesinthetwo-body sectorcan beextendedto measuredirectlythethree-body corre- lations [62]. The increased amount of statistics during the third runningperiodoftheLHC [61] willallowforsuchmeasurements.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompetingfinan- cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgements

The ALICE Collaboration wouldlike 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 followingfundingagencies fortheir support inbuildingandrun- ningtheALICEdetector: A.I. AlikhanyanNationalScienceLabora- tory(YerevanPhysics Institute)Foundation (ANSL),StateCommit- tee of Science and World Federation of Scientists (WFS), Arme- nia; Austrian Academy ofSciences, Austrian Science Fund (FWF):

[M 2467-N36]andNationalstiftungfürForschung,Technologieund Entwicklung,Austria;MinistryofCommunicationsandHighTech- nologies, National Nuclear Research Center, Azerbaijan; Conselho

Nacional de DesenvolvimentoCientífico e Tecnológico (CNPq), Fi- nanciadora de Estudos e Projetos (Finep), Fundac¸ão de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Ministry of Ed- ucation of China (MOEC), Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC),China;MinistryofScienceandEducationandCroatianSci- ence Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN),Cubaenergía, Cuba; Ministryof Ed- ucation, YouthandSports ofthe CzechRepublic, Czech Republic;

TheDanishCouncilforIndependentResearchNaturalSciences,the Villum Fonden andDanish NationalResearch Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commis- sariatàl’ÉnergieAtomique (CEA)andInstitutNationaldePhysique Nucléaire et de Physique des Particules (IN2P3) and Centre Na- tional de laRecherche Scientifique (CNRS), France; Bundesminis- terium fürBildungundForschung(BMBF)andGSIHelmholtzzen- trum für Schwerionenforschung GmbH, Germany; GeneralSecre- tariatforResearchandTechnology,MinistryofEducation,Research andReligions, Greece;NationalResearch,Development andInno- vationOffice,Hungary;DepartmentofAtomicEnergy,Government of India (DAE), Department of Science and Technology, Govern- ment ofIndia (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innova- tive ScienceandTechnology,NagasakiInstituteofAppliedScience (IIST),JapaneseMinistryofEducation,Culture,Sports,Scienceand Technology(MEXT)andJapanSocietyforthePromotionofScience (JSPS)KAKENHI, Japan;Consejo Nacionalde Ciencia(CONACYT)y Tecnología, through Fondo de Cooperación Internacionalen Cien- cia y Tecnología (FONCICYT) and Dirección General de Asuntos delPersonalAcadémico (DGAPA),Mexico;NederlandseOrganisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Re- search Council of Norway, Norway; Commission on Science and Technology forSustainableDevelopmentintheSouth(COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education andScience, National Science Centre andWUT ID- UB, Poland; Korea Institute of Science and Technology Informa- tion and National Research Foundation of Korea (NRF), Republic of Korea; Ministry ofEducation andScientific Research,Institute of Atomic Physics and Ministry of Research and Innovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research(JINR), MinistryofEducationandScienceofthe Russian Federation, NationalResearch Centre KurchatovInstitute, Russian Science Foundation and Russian Foundation for Basic Research, Russia; Ministryof Education,Science, ResearchandSportof the Slovak Republic, Slovakia; NationalResearch Foundation of South Africa,SouthAfrica;SwedishResearchCouncil(VR)andKnut&Al- iceWallenbergFoundation(KAW),Sweden;EuropeanOrganization forNuclearResearch,Switzerland;SuranareeUniversityofTechnol- ogy (SUT),NationalScience andTechnology Development Agency (NSDTA) and Office of the Higher Education Commission under NRU projectofThailand,Thailand;TurkishAtomicEnergy Agency (TAEK),Turkey;NationalAcademyofSciencesofUkraine,Ukraine;

ScienceandTechnologyFacilitiesCouncil(STFC),UnitedKingdom;

NationalScienceFoundationoftheUnitedStatesofAmerica(NSF) andUnitedStatesDepartmentofEnergy,OfficeofNuclear Physics (DOENP),UnitedStatesofAmerica.

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