Study of the Λ–Λ interaction with femtoscopy correlations in pp and p–Pb collisions at the LHC

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Study

of

the



–



interaction

with

femtoscopy

correlations

in

pp and

p–Pb collisions

at

the

LHC

.

ALICE

Collaboration

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received24May2019

Receivedinrevisedform26July2019 Accepted30July2019

Availableonline1August2019 Editor:L.Rolandi

Thiswork presentsnewconstraintsontheexistenceandthebindingenergyofapossible–bound state, the H-dibaryon, derived from –femtoscopic measurements by the ALICE collaboration. The resultsareobtainedfromanewmeasurementusingthefemtoscopytechniqueinpp collisionsat√s= 13 TeVand p–Pb collisionsat√sNN=5.02 TeV, combined withpreviouslypublishedresults frompp collisionsat√s=7 TeV.The–scatteringparameterspace,spannedbytheinversescatteringlength f₀−1 and the effectiveranged0,isconstrained by comparingthe measured–correlation function withcalculationsobtainedwithintheLednickýmodel.Thedataarecompatiblewithhypernucleiresults and latticecomputations,bothpredictingashallow attractiveinteraction,and permittotest different theoreticalapproaches describingthe–interaction.Theregioninthe(f₀−1,d0) planewhichwould accommodatea–boundstateissubstantiallyrestrictedcomparedtopreviousstudies.Thebinding energyofthepossible–boundstateisestimatedwithinaneffective-rangeexpansionapproachand isfoundtobeB=3.2₋+12..64(stat)+

1.8

−1.0(syst) MeV.

©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

1. Introductionandphysicsmotivation

A detailed characterization of the



–



interaction is of fun-damentalinterestsinceitplays adecisiverole inthequantitative understanding of the hyperon(Y) appearance in dense neutron-richmatter,inproto-neutronandinneutronstars[1].Ifhyperons doappear atlarge densities andtheir fraction becomes sizeable, theY–Y interaction is expectedto play an importantrole in the equation ofstate of the system[2,3]. Evenif thehyperon densi-tiesin compact objects are negligible,the interplay betweenthe average separations and the



–



effective range determine the possible onset of phenomena such as fermion superfluidity, and henceinfluencethetransportpropertiesofthesystem[4–6].

Thecharacterizationofthe



–



interactionisstillanopen is-sue in experimental nuclear physics. The Nagara event, recently measured with the emulsion technique [7,8], reports a clear ev-idence fora double-



hypernucleus 6_He, witha small binding energy between the two



s of



B

=

0

.

67

±

0

.

17 MeV. This

value was obtainedby comparing thebinding energy ofthe two



sinsidethedoublehypernucleus(B

=

6

.

91

±

0

.

16 MeV)with

thebinding energy ofa single



in a single-hypernucleus, how-ever, it might be influenced by three-body forces. Nevertheless, thisresultwas usedtoseta lowerlimit forthemassofthe pre-dictedbutsofarnot observedH-dibaryon,apossibleboundstate composedofsixquarks(uuddss)[9].Severalexperimental collab-orations have been involved in the search for this state in the decaychannels H

→ 

p

π

andH

→ 

,in nuclear and

elemen-tary (e−e+) collisions, but no evidence has been found [10–12], even though an enhanced



–



production near threshold was measured byE224 andE522 atKEK-PS[13,14]. Theoretical calcu-lationsperformedwithinthechiralconstituentquarkmodelrelate theexistenceofaH-dibaryontoanoverbindingofthe6_He mea-suredintheNagaraevent [15,16].

Theoretical models constrained to the available nucleon– nucleonandhyperon-nucleonexperimental data,assuming either asoft[15–17] orahard [18,19] repulsivecoreforthe



–



inter-action,predictdifferentscatteringlengths( f0)andeffectiveranges

(d0). Throughoutthispaperthestandard signconvention in

fem-toscopy is used,accordingto which a positive f0 corresponds to

an attractive interaction, while a negative scattering length cor-responds eitherto a repulsive potential (d0

>

|

f0

|/

2) or abound

state (d0

<

|

f0

|/

2). It was reported that a smallvariation of the



–



repulsive core parametrization leads to inverse scattering lengthswithin

−

0

.

27 fm−1

<

f₀−1

<

4 fm−1 andeffective ranges up to 16 fm [20]. Other calculations are directly constrained to the Nagara event and result in rather small scattering lengths andmoderateeffectiveranges,liketheFG

(

f₀−1

=

1

.

3 fm−1

;

d0

=

6

.

59 fm

)

[21] and theHKMYY

(

f₀−1

=

1

.

74 fm−1

;

d0

=

6

.

45 fm

)

[22] models.Itisclearthatmoreexperimentaldataareneededto studytheprobleminamorequantitativeandmodel-independent way.

Analternativemethodtostudyhypernucleiistheinvestigation of momentum correlations of



–



pairs produced in hadron–

https://doi.org/10.1016/j.physletb.2019.134822

0370-2693/©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

hadroncollisionsviathefemtoscopytechnique[23].TheSTAR col-laboration reported a



–



scatteringlength and effective range of f₀−1

= −

0

.

91

±

0

.

31+₋0.07_0.56 fm−1 andd0

=

8

.

52

±

2

.

56+₋2.090.74 fm,

measuredinAu–Aucollisions at

√

sNN

=

200 GeV [24].These

val-uescorrespondto arepulsive interaction; however,itwas shown thatthevaluesandthesignofthescatteringparametersstrongly depend on the treatment of feed-downcontributions fromweak decaystothemeasuredcorrelation.Are-analysisofthedata out-sidetheSTARcollaborationcametodifferentconclusions[20] and resultedinashallowattractiveinteraction.

In a pioneeringstudy [25], the



–



interaction was studied employing the femtoscopy technique in pp collisions at

√

s

=

7 TeV.Thisstudydemonstratedthatthedataareconsistentwith ei-ther a bound state or an attractive interaction, however, due to the small data sample no quantitative results were obtained. In thisletter,thesestudiesareextendedbyanalyzingfinal-state mo-mentum correlations in pp collisions at

√

s

=

13 TeV and p–Pb collisionsat

√

sNN

=

5

.

02 TeV,recordedby ALICEduring LHCRun

2.Thesmallsystemsizeinpp and p–Pb givesrisetopronounced correlations fromstrong final-state interactions dueto the small relativedistanceatwhichparticlesareproduced.Hence,thelarge datasets enable a high-precision studyofthe



–



strong final-stateinteractionandprovidenewexperimentalconstraintsonthe scatteringparametersandtheexistenceofapossibleboundstate.

2. Dataanalysis

The analysis presented in this paper is based on the data samples collected by ALICE [26] during the Run 2 of the LHC (2015–2018) in pp collisions at

√

s

=

13 TeV and p–Pb collisions at

√

sNN

=

5

.

02 TeV,combinedwiththepreviouslyanalyzedRun1

datafrompp collisions at

√

s

=

7 TeV [25].The eventandparticle candidateselectioncriteriafollowcloselytheprocedureappliedin theRun1analysis [25].

The events are triggered using two V0 detectors, which are small-angle plasticscintillator arraysplacedon eitherside ofthe collisionvertexatpseudorapidities2

.

8

<

η

<

5

.

1 and

−

3

.

7

<

η

<

−

1

.

7 [27]. Minimum bias pp and p–Pb events are triggered by the requirement of coincidentsignals in both V0detectors, syn-chronouswiththe beamcrossingtime definedby the LHCclock. The V0 detector is also used to reject background events stem-ming fromthe interaction ofbeamparticles withthe beampipe materialsorbeam-gasinteractions.Pile-upeventswithmorethan one collision per bunch crossing are rejected by evaluating the presenceofsecondaryeventvertices[27].Chargedparticlesare re-constructedbytheInner TrackingSystem(ITS) [26] andtheTime ProjectionChamber(TPC) [28],bothimmersedina0.5 Tsolenoidal magnetic field directed along the beam axis.A uniform detector coverage is assured by requiring the maximal deviation between thereconstructedprimaryvertex(PV)andthenominalinteraction pointtobesmallerthan10 cm.ThePVcanbereconstructedwith thecombinedinformationof theITSandTPC,andindependently withtheSiliconPixelDetector (SPD- oneof thethree subdetec-torsoftheITS).Ifbothmethodsareavailable,thedifferenceofthe z-coordinate betweenbothverticesisrequiredtobesmallerthan 5 mm.Afterapplyingtheseselection criteriatheremaining num-ber ofeventsis 1

.

0

×

109 _{forthe pp at}

√

_s

₌

_{13 TeVsample and}

6

.

1

×

108 _{forp–Pb at}

√

_s

NN

=

5

.

02 TeV.Thiscorrespondstoabout

90%and84%ofallprocessedeventsinpp andp–Pb.

The



–



interactionisthemainfocusofthepresentstudy.As willbeexplainedinthenext section,thep–pcorrelationfunction isan essential inputforthe femtoscopicanalysisof



–



. There-fore, the reconstruction of both protons and



particles will be described in the following paragraphs. To increase the statistical

significance ofthe result, the anti-particle pairs are measured as well.

The selection of the proton candidates follows the analysis strategy used forthe pp collisions at

√

s

=

7 TeV [25]. The parti-cle identification(PID) is determined by thenumber of standard deviationsn

σ

betweenthehypothesisforaprotonandthe exper-imentalmeasurementofthespecificenergylossdE

/

dx intheTPC orthe timing informationfromtheTime-Of-Flight (TOF)detector [29]. Theanalyzedtracks areselectedwithin thekinematicrange 0

.

5

<

pT

<

4

.

05 GeV

/

c and

|

η

|

<

0

.

8. The PID is performedonly

withtheTPCfortrackswithp

<

0

.

75 GeV

/

c,byrequiring

|

n

σ

|

<

3. Tomaintain thepurityoftrackswith p

>

0

.

75 GeV

/

c,the

|

n

σ

|

is calculatedfromcombiningtheTPCandTOFinformation.The con-tributionofsecondaryparticles,whichstemfromelectromagnetic andweakdecaysorthedetectormaterial,areacontamination in thesignal.Thefractionsofprimary andsecondaryprotonsare ex-tracted using Monte Carlo (MC) template fits to the distance of closest approachoftheparticlesto thePV [30].TheMC distribu-tions are generated usingPythia8.2 [31] forthe pp andDPMJET 3.0.5 [32] for the p–Pb case, filteredthrough the ALICEdetector andreconstructionalgorithm[26].Theprotonpurityinpp (p–Pb) isfoundtobe99(97)%withaprimaryfractionof85(86)%.

The



particles are reconstructed via the decay



→

p

π

−, which hasabranching ratioof63.9%andc

τ

=

7

.

89 cm [33].For the reconstruction of the



the charge conjugate decay is em-ployed. The interaction rate of the LHC varied during different periods of the pp running. Tomaintain a constant purity that is independent of the interaction rate, in addition to the selection criteria usedfor the analysisof pp collisions at

√

s

=

7 TeV [25], the charged decay tracks must either have a hit in one of the SPD or Silicon Strip Detector (SSD- ITS subdetector) layers or a matched TOF signal. After applyingall selection criteria thefinal



and



candidatesareselectedina4 MeV

/

c2(

∼

3

σ

)mass win-dow aroundthenominalmass [33].Thefractions ofprimaryand secondary



particlesareextractedsimilarlyastheprotons,while the observable for thetemplate fits is the cosine ofthe opening angle

α

betweenthe



momentumandthevector pointingfrom thePVtothe



decayvertex. The



purityinpp (p–Pb)isfound tobe97(94)%withaprimaryfractionof59(50)%.Theexact com-position ofsecondaries, aswell as the



to

0 ratio,is fixed in the MC simulations, but is modeldependent. Therefore, the sys-tematicuncertaintiesincludea20% variationoftheratiosofthese contributions.

3. Analysisofthecorrelationfunction

The methodusedto investigatethe



–



interaction relieson particle pair correlations measured as a function of k



∗, defined asthe single-particlemomentum inthepairrestframe [23]. The observableofinterestC

(

p



1

,

p



2

)

isdefinedastheratioofthe

prob-ability of measuring simultaneously two particles with momenta



p1 andp



2,totheproductofthesingle-particleprobabilities: C

(

p



1

,

p



2

)

=

P

(

p



1

,

p



2

)

P

(

p



1

)

P

(

p



2

)

.

(1)

In the absence of correlations, the numerator factorizes and the correlationfunctionbecomesunity.Thefemtoscopyformalism [23] relates the correlation function for a pair of particles, to their effective two-particleemitting source function S

(

r

)

andthe two-particlewavefunction

( 

k∗

,



r

)

:

C

(

k∗

)

=



Table 1

Theweightparameters(Eq. (4))λppi andλ p–Pb

i oftheindividualcomponentsofthep–p,p–,p–−and–correlationfunctions.Thesub-indexesareusedtoindicate

themotherparticleincaseoffeed-down.Onlythenon-flatfeed-down(residual)contributionsarelistedindividually,whileallothercontributionsarelistedas“flatresiduals (res.)”.Allmisidentified(fake)pairsareassumedtobeuncorrelated,thusresultinginaflatcorrelationsignal.

p–p p– p–− – Pair λpp_i (%) λp_i–Pb (%) Pair λpp_i (%) λp_i–Pb (%) Pair λpp_i (%) λp_i–Pb (%) Pair λpp_i (%) λp_i–Pb (%) pp 74.8 72.8 p 50.3 41.5 p− 55.5 50.8  33.8 23.9 pp 15.1 16.1 p 0 16.8 13.8 p−₍₁₅₃₀₎− 8.8 8.1 p− 8.3 12.1

flat res. 8.1 8.0 flat res. 20.4 24.9 flat res. 30.3 28.3 flat res. 59.8 64.0

fakes 2.0 3.1 fakes 4.2 7.7 fakes 5.4 12.8 fakes 6.4 12.1

wherer istherelativedistancebetweenthepointsofemissionof thetwoparticles.ThisdefinitionofC

(

k∗

)

assumesthat the emis-sion source is not dependent on k∗, it is spherically symmetric andtheemissionofallparticles issimultaneous.TheEPOS trans-port model [34] predicts an emission source that does not fully satisfy the above assumptions. However, it was verified that the abovesimplificationsresultinverymilddeviationsinthe correla-tionfunctions,whicharenegligibleforthepresentanalysis.

Forasphericalsymmetricpotentialtheangulardependenceof thewave-functionistriviallyintegratedout.Thus thedirectionof



k∗ becomes irrelevant on the left-hand side of Eq. (2). Particles withlarge relative momentaq∗

=

2k∗ are not correlated, leading toC

(

k∗

→ ∞)

=

1.

The stronginteraction has a typical range ofa few femtome-tersandthusasignificantmodificationofthewavefunctionwith respecttoits asymptoticformisexpectedonlyforr



2 fm. Con-sequently,forsmallemissionsources thecorrelationfunctionwill be particularly sensitive to the strong interaction potential. Ex-perimentally, a small emission source can be formed in pp and p–Pb collisions[25,35].Inthecurrentanalysis, itisassumedthat theemission profile isGaussian andthat the p–p and



–



sys-temsarecharacterizedbyacommonsourcesizer0

=

rp–p

=

r–,

which is determined by fitting the p–p correlation function and thenusedfortheinvestigationofthe



–



interaction.Inpp colli-sionstheeffectofmini-jetsisonlypresentforbaryoncorrelations betweenparticleandanti-particle[25],hencetheinvestigateddata provideacleanenvironmenttoextractthefemtoscopicsignal.

Twodifferentframeworksareavailable forthe computationof C

(

k∗

)

.Thefirsttoolusedinthisanalysisisthe“Correlation Analy-sisToolusingtheSchrödingerequation”(CATS)[35].Here,alocal potentialV

(

r

)

isusedastheinputtoanumericalevaluationofthe wave function and the corresponding correlation function. CATS deliversan exactsolutionandthistool isusedto modelthep–p correlation using a Coulomb and an Argonne v18 potential [36]

forthe strong interaction.The known p–p interaction allows the sourcesizer0 tobeextractedfromthefittothemeasured

corre-lationfunction.

Thesecond tool is theLednický model[37], which assumesa Gaussianemission sourceandevaluates thewave function inthe effective-rangeexpansion. In thisapproach,the interactionis pa-rameterizedintermsofthescatteringlength f0 andtheeffective

ranged0. This approach produces a very accurate approximation

forC

(

k∗

)

in cased0



r0, while for smallervalues of r0 the

ap-proximatesolutionmaybecomeunstable,inparticularfornegative valuesof f0 [25]. However, it isknown that the Lednickýmodel

can be used to model the p–



correlation function even for a sourcesizeofr0

=

1

.

2 fm,withadeviationfromtheexactsolution

oflessthan 4% [35].It istherefore expectedthat thismodelcan successfullybeused tostudythe



–



interaction, eveninsmall collision systems.Nevertheless, thevalidity of the approximation willbefurtherverifiedinthenextsection.

Experimentally,thecorrelationfunctionisdefinedas

Cexp

(

k∗

)

=

N

Nsame

(

k∗

)

Nmixed

(

k∗

)

k∗→∞

−−−−→

1

,

(3)

where Nsame

(

k∗

)

and Nmixed

(

k∗

)

are the same and mixed event

distributions,while

N

isa normalizationconstant determinedby the condition that particlepairs withlarge relative momentaare notcorrelated.InsmallcollisionsystemsCexp

(

k∗

)

oftenhasa

long-rangetaildue tomomentum conservation,andarelated approx-imately linear non-femtoscopic background extending to low k∗ [25]. The latter isincorporated by includinga linear termin the fitfunction.

Toincrease thestatisticalsignificance ofCexp

(

k∗

)

the

particle-particle (PP) and antiparticle-antiparticle (PP) correlations are combinedusingtheir weighted meanCexp

(

k∗

)

=

N

PPCexp,PP

(

k∗

)

⊕

N

PPCexp,PP

(

k∗

)

, with the normalization performed in the range

240

<

k∗

<

340 MeV

/

c,whichisunaffectedbyfemtoscopic corre-lations.Itwasverifiedthat

N

PPCexp,PP

(

k∗

)

=

N

PPCexp,PP

(

k∗

)

within

thestatisticaluncertainties.

The systematic uncertainties of the experimental correlation functionareevaluatedbyvaryingtheselectioncriteriaofthe pro-ton and



candidates within 20%, following the procedure used fortheanalysisofthepp collisionsat

√

s

=

7 TeV [25]. Neverthe-less,byperformingaBarlowtest [38],thesystematicuncertainties were found to be insignificant compared to thestatistical uncer-tainties.

Momentum resolution effects modify the correlation function byatmost10% andareaccountedforbycorrectingthetheoretical correlation function [25]. The measured experimental correlation functioncontainsnotonlythecorrelationsignalofinterest,but ad-ditionallyaccumulatesresidualcontributionsfromfeed-down par-ticles. These are considered in the theoretical description of the correlationby usingthelineardecompositionofthetotal correla-tionfunctioninto

Ctot

(

k∗

)

=



i

λ

iCi

(

k∗

),

(4)

wherethe sumrunsover all contributions, the

λ

parameters are theweight factorsforthedifferentcontributionstothe total cor-relation and i

=

0 corresponds to the primary correlation. The

λ

coefficients are determined in a data-driven approach by per-forming Monte Carlo template fits to the data, using Pythia and DPMJET in pp and p–Pb collisions, respectively. The values ob-tainedaresummarizedinTable1.Thesystematicuncertaintiesare determined from the variation of the composition of secondary contributions, and the



to

0 _{ratio. The individual}

contribu-tionsCi

(

k∗

)

aremodeledeitherusingCATSortheLednickýmodel.

Thenon-genuine(i

=

0)contributionsincludeadditionalkinematic effects which lead to a smearing of their corresponding correla-tion functions [39]. As thecorrelation strength oftheseresiduals is strongly damped one can assume that Ci =0

(

k∗

)

≈

1 [40]. The

Fig. 1. Resultsforthefitofthepp dataat√s=13 TeV.Thep–pcorrelationfunction(leftpanel)isfittedwithCATS(blueline)andthe–correlationfunction(right panel)isfittedwiththeLednickýmodel(yellowline).ThedashedlinerepresentsthelinearbaselinefromEq.(5),whilethedarkdashed-dottedlineontopofthe–data showstheexpectedcorrelationbasedonquantumstatisticsalone,incaseofastronginteractionpotentialcompatiblewithzero.

onlysignificant contribution is p–



→

p–p, where thep–



inter-actionismodeledusingthescatteringparametersfroma next-to-leading order(NLO)

χ

EFT calculation [41] and thecorresponding correlation function is computed using the Lednický model. The remaining residuals are considered flat,apart from p–



−

→

p–



, p–

0

→

p–



andp–

(

1530

)

−

→

p–



−,wheretheinteractioncan bemodeled.Forthep–



− interactionarecentlatticeQCD poten-tial,fromtheHALQCDcollaboration [42,43],isused.Thep–

0 is modeledasin [44],whilep–

(

1530

)

−isevaluatedbytakingonly theCoulombinteractionintoaccount.

Afterall correctionshavebeenappliedtoCtot

(

k∗

)

,thefinal fit

functionis obtainedbymultiplying itwitha linearbaseline

(

a

+

bk∗

)

describingthenormalizationandnon-femtoscopybackground [25]

Cfit

(

k∗

)

= (

a

+

bk∗

)

Ctot

(

k∗

).

(5)

Fig. 1 shows an example of the p–p and



–



correlation func-tions measured in pp collisions at

√

s

=

13 TeV, together with the fit functions. The p–p experimental data show a flat behav-ior intherange200

<

k∗

<

400 MeV

/

c,thusbydefaulttheslope of the baseline is assumed to be zero (b

=

0) and the corre-lation is fitted in the range k∗

<

375 MeV

/

c. The resulting r0

values are 1

.

182

±

0

.

008(stat)+₋0.005_0.002(syst) fm in pp collisions at

√

s

=

13 TeVand1

.

427

±

0

.

007(stat)+₋0.001_0.014(syst) fminp–Pb colli-sionsat

√

sNN

=

5

.

02 TeV.Inpp collisionsat

√

s

=

7 TeVthesource

sizeisr0

=

1

.

125

±

0

.

018(stat)+₋0.0580.035(syst) fm [25].

Thesystematicuncertaintiesoftheradiusr0 areevaluated

fol-lowingtheprescriptionestablished during theanalysisofpp col-lisionsat

√

s

=

7 TeV [25].Theupperlimitofthefitrangeforthe p–ppairsisvaried withink∗

∈ {

350

,

375

,

400

}

MeV

/

c andthe in-puttothe

λ

parametersismodified by20%,keepingprimary and secondaryfractionsconstant.

Two further systematic variations are performed for the p–p correlation. The first concerns the possible effect of non-femto-scopy contributions to the correlation functions, which can be modeled by a linear baseline (see Eq. (5)) with the inclusion of b asafreefitparameter.Thefinalsystematicvariationistomodel thep–



feed-downcontributionbyusingaleading-order(LO)[41,

45] computationtomodeltheinteraction.The effectofthelatter isnegligible,asthetransformationtothe p–psystemsmearsthe differencesobservedinthepurep–



correlationfunctionout.

Toinvestigatethe



–



interactionthesourcesizesarefixedto the above results and the



–



correlations from all three data sets are fitted simultaneously in order to extract the scattering

parameters. The correlation functions show a slight non-flat be-havior atlarge k∗,especiallyforthe pp collisionsat

√

s

=

13 TeV (rightpanelinFig.1).Thusthefitisperformedbyallowinga non-zeroslope parameterb (seeEq. (5)).The fitrangeisextended to k∗

<

460 MeV

/

c in order to better constrain the linear baseline. Duetothesmallprimary

λ

parameters(seeTable1)the



–



cor-relationsignalisquiteweak andthefitshowsa slightsystematic enhancement comparedto theexpected Ctot

(

k∗

)

dueto quantum

statisticsonly,suggestiveofanattractiveinteraction.However,the current statisticaluncertainties donot allow the



–



scattering parameters to be extractedfromthe fit.Therefore, an alternative approach to study the



–



interaction will be presented in the nextsection.Systematicuncertaintiesrelatedtothe



–



emission sourcemayarisefromseveraldifferenteffects,whicharediscussed intherestofthissection.

Previousstudieshaverevealedthattheemissionsourcecanbe elongated along some of the spatial directions andhave a mul-tiplicity or mT dependence [46,47]. In the present analysis it is

assumed that the correlation function can be modeled by an ef-fective Gaussian source.The validity ofthis statement is verified by a simple toy MonteCarlo, inwhich a data-drivenmultiplicity dependenceisintroducedintothesourcefunctionandthe result-ing theoreticalp–pcorrelation functioncomputedwithCATS. The deviationsbetweenthisresultandacorrelationfunctionobtained withaneffectiveGaussiansourceprofilearenegligible.

Possibledifferencesintheeffectiveemittingsourcesofp–pand



–



pairs duetothestrong decaysofbroadresonances andmT

scaling are evaluated via simulations and estimated to have at mosta5% effectontheeffectivesourcesizer0.Thisistakeninto

account by includingan additional systematicuncertaintyon the r– valueextractedfromthefittothep–pcorrelation.

4. Results

Inordertoextractthe



–



scatteringparameters,the correla-tionfunctionsmeasuredinpp collisionsat

√

s

=

7,13 TeVaswell asinp–Pb collisionsat

√

sNN

=

5

.

02 TeVarefittedsimultaneously.

The rightpanel inFig.1showsthe



–



correlationfunction ob-tained in pp collisions at

√

s

=

13 TeV together with the result fromthefit.

Since the uncertainties of thescattering parameters are large, differentmodelpredictionsaretestedonthebasis oftheir agree-mentwiththemeasuredcorrelationfunctions.

One optionis to usea localpotential and obtain C

(

k∗

)

based ontheexactsolutionfromCATS, withthesourcesizefixedtothe value obtainedfromthe fit to the p–p correlations. Manyof the

Fig. 2.–correlationsmeasuredinpp collisionsat√s=13 TeV(leftpanel)andp–Pb collisionsat√sNN=5.02 TeV(rightpanel)togetherwiththefunctionscomputed bythedifferentmodels [20].ThetestedpotentialsareconvertedtocorrelationfunctionsusingCATSandthebaselineisrefittedforeachmodel.Theeffectsofmomentum resolutionandresidualsareincludedinthetheorycurves.

existingmodelpredictionsaresummarizedin [20] andthe corre-spondingpotentials V

(

r

)

are parametrizedinalocalformusinga double-Gaussianfunction.Thecorrelationfunctiondependsonthe natureof the underlyinginteraction and Fig.2 showsthe exper-imental



–



correlations measured in pp collisions at

√

s

=

13 TeV (left panel) and p–Pb collisions at

√

sNN

=

5

.

02 TeV (right

panel)togetherwiththecorrelation functionsobtainedfor differ-entmeson-exchangeinteraction potentialsemployingCATS. Mod-els with a strongly attractive interaction ( f₀−1



1 and positive), liketheEhime[17] potential,resultinalargeenhancementofthe correlation function at low momenta which overshoots the data significantlybothinpp andp–Pb collisions.The sameisvalidfor potentialscorresponding to ashallow boundstate ( f₀−1

→

0 and negative),e.g.NF44[19].

Theother testedpotentialscorrespond eithertoabound state orashallowattractive( f₀−1



1)non-bindinginteraction.However, thosetwoverydifferentscenariosresultinsimilarcorrelationsand are difficult to separate. This isevident fromFig. 2 asall of the ESC08[48],HKMYY[22] andNijmegenND46[18] modelsproduce comparableresultsandarecompatiblewiththeexperimentaldata, eventhoughtheirscatteringparametersaredifferent.Inparticular, ND46predictsaboundstate,whiletheESC08andHKMYYmodels describeashallowattractivepotential andthelatterisconsistent withhypernucleidata[7,8].

TheLednickýmodelcanbeusedtocomputeC

(

k∗

)

forany f₀−1 andd0. Thus a scan over the scatteringparameters can be

pre-formedandtheagreementtotheexperimentaldatacanbe quan-tified.The Lednický model breaks down for source sizes smaller than the effective range, especially when dealing with repulsive interactions [25], as it produces unphysical negative correlation functions.As thereare norealistic models predicting such an in-teraction, thisstudy is not affected. Nevertheless,all models de-scribedin [20] are explicitlytested by comparingthe correlation functionsobtainedusingtheexactsolutionprovidedbyCATSwith theapproximatesolutionevaluatedusingtheLednickýmodel.The deviationsareonthepercentlevelandareneglected.

Anotherassumption,whichtheLednickýmodelisbasedon,is a Gaussian profile of the source. The EPOS [34] transportmodel predicts a non-Gaussian emission profile [35], andthe effects of short livedresonances are included. This source was adopted in CATS,by tuningitswidthsuch astodescribethep–p correlation function,andthepredictedC

(

k∗

)

foralloftheNDandNFmodels, showninFig.3,were comparedto the



–



correlation function inpp collisionsat

√

s

=

13 TeV.Thedeviationsin

χ

2_comparedto

thecaseofaGaussiansourcearewithintheuncertainty,justifying theuseofaGaussiansource.

Fig. 3. Exclusionplotforthe–scatteringparametersobtainedusingthe– correlationsfrom pp collisionsat √s=7 and13 TeVaswellasp–Pb collisions at√sNN=5.02 TeV.Thedifferentcolorsrepresenttheconfidencelevelof exclud-ingasetofparameters,giveninnσ.TheblackhashedregioniswheretheLednický modelproducesanunphysicalcorrelation.Thetwomodelsdenotedbycoloredstars arecompatiblewithhypernucleidata,whiletheredcrosscorrespondstothe pre-liminaryresultofthelatticecomputationperformedbytheHALQCDcollaboration. Fordetailsregardingthe regionat slightlynegative f−1

0 andd0<4,compatible withaboundstate,refertoFig.4.

Toquantifythe uncertainties of f₀−1 andd0,andestimate the

confidence levelof each parameterset, a MonteCarlomethod is used. In the currentwork the approach described in [49] is fol-lowed,whichiscloselyrelatedtotheBootstrapmethod.The strat-egy istouse theLednickýmodelto performa scan overthe pa-rameterspacespannedby f₀−1

∈ [−

2

,

5

]

fm−1 andd0

∈ [

0

,

18

]

fm

andrefitthe



–



correlationusingEq. (5) whenfixing the scat-teringparameterstoaspecificvalue

(

f₀−1

,

d0

)

i.Thecorresponding

χ

2

i is evaluatedby takingall datasets(pp at

√

s

=

7 and13 TeV andp–Pb at

√

sNN

=

5

.

02 TeV)intoaccount.Thedifferent

scatter-ingparameterscanbecomparedbyfindingthelowest(best)

χ

2 best

andevaluating



χ

2

i

=

χ

i2

−

χ

best2 foreachparameterset.This

ob-servable, andthe associated

(

f₀−1

,

d0

)

i, can be directly linked to

the confidencelevel [49]. This can be achievedeither by assum-ing normallydistributed uncertainties of

(

f₀−1

,

d0

)

, orinvokinga

moresophisticatedMonteCarlostudy,liketheBootstrapmethod. Thelatterisusedinthecurrentanalysis.

The resulting exclusion plot ispresented in Fig. 3, where the color code corresponds to the confidencelevel n

σ

for a specific choice ofscatteringparameters.In thecomputation onlythe sta-tisticaluncertaintiesaretakenintoaccount,asthesystematic un-certainties are negligible according to the Barlow criterion [38]. Thepredictedscatteringparameters ofalldiscussedpotentialsare

Fig. 4. Theregionofthe1σconfidencelevelfromFig.3,displayedinthe(B,d0) plane.The inner (dark) regioncorresponds tothe statisticaluncertainty ofthe method,whiletheouter(light)regionincludesthesystematicvariations.Thered starcorrespondstotheparameterswiththelowestχ2_.

highlightedwithdifferentmarkers andthe phasespaceregionin which the Lednický model produces an unphysical correlation is specified by the black hatched area. In this region the effective rangeexpansionbreaks downandtheLednickýequation leadsto a negative correlation function. While theSTAR result [24] is lo-catedinthisregion,all theoreticalmodels excludethepossibility of a repulsive



–



interaction withlarge effective range. More-overare-analysisoftheSTARdata [20] demonstratedthatamore realistic treatment of the residual correlations leads to an inver-sion of the signof the scattering length, that corresponds to an attractivepotential. Theimposed limiton thescatteringlengthis f₀−1

>

0

.

8 fm−1 [20]. This result can be tested within the cur-rent work, and Fig. 3 demonstrates that the ALICE data can ex-tendthoseconstraints.Inparticulartheregioncorrespondingtoa strongly attractive or a very weakly binding short-range interac-tion (small

|

f₀−1

|

andsmalld0) isexcluded by the data, whilea

shallowattractivepotential (large f₀−1)isinverygoodagreement withtheexperimentalresultsobtainedfromthisanalysis.A



–



boundstate wouldcorrespond tonegative f₀−1 andsmalld0

val-ues.Thepresentdataarecompatiblewithsuchascenario,butthe availablephasespaceisstronglyconstrained.TheHKMYY[22],FG [21] andHALQCD[50] valuesareofparticularinterest,asthefirst two models are tuned to describe the modern hypernuclei data, while the latter is the latest state-of-the-art lattice computation fromtheHALQCDcollaboration.Thelatticeresultsarepreliminary andpredictthescatteringparameters f₀−1

=

1

.

45

±

0

.

25 fm−1 and d0

=

5

.

16

±

0

.

82 fm[50].Allthreemodelsarecompatiblewiththe

ALICEdata,providingfurthersupportforashallowattractive



–



interactionpotential.

Apossibleboundstateisinvestigatedwithintheeffective-range expansion by computing the corresponding binding energy from therelation[51,52] B

=

1 md2₀



1

−



1

+

2d0f0−1



2

.

(6)

Thisrelationisonlyvalidforboundstates,whicharecharacterized bynegative f₀−1values.Further,thebindingenergyhastobeareal number,thustheexpression1

+

2d0f0−1 hastobepositive,which

impliesthat at leastone of the parameters f₀−1 ord0 hasto be

smallinabsolutevalue.WiththeserestrictionsEq. (6) transforms the observables in the exclusion plot (Fig. 3) from

(

f₀−1

,

d0

)

to

(

B

,

d0

)

,considering only theparameter spacecompatiblewith

aboundstate.ThisisdoneinFig.4,whereonlythe1

σ

confidence regionisshown,asitcorresponds totheuncertaintyof B.The

darkregionmarksthestatisticaluncertaintyofthefit.Theallowed

binding energy, independent of d0, is B

=

3

.

2+1.6₋2.4(stat) MeV,

where the central value corresponds to the lowest

χ

2 _{and the}

uncertainties aredetermined basedonthelowest andhighest al-lowed B valueswithinthe 1

σ

confidenceregion. Howeverthe

systematicuncertainties relatedto thesource sizes arenot taken into account, neither any possible biases related to the fit pro-cedure. Thus thecomputation ofthe exclusionplots (Figs. 3and

4) was repeated121 times,wherein eachre-iteration thesource sizes relatedtothedatasets arevariedwithin theassociated un-certainties, the fit ranges within k∗

∈ {

420

,

460

,

500

}

MeV

/

c and the bin widths of the experimental correlations are chosen as 12, 16 and 20 MeV

/

c. The resulting fluctuationsof the 1

σ

con-fidence region are marked in Fig. 4by the light region and rep-resent thetotal uncertainty. Assuming the latteris the quadratic sumofthestatisticalandsystematicuncertainty,thefinalresultis B

=

3

.

2+₋1.62.4(stat)+

1.8

−1.0(syst) MeV. 5. Summary

In this Letter, new data on p–p and



–



correlations in pp collisions at

√

s

=

13 TeV andp–Pb collisionsat

√

sNN

=

5

.

02 TeV

are presented.Together withthe resultsfroma pioneeringstudy ontwo-baryoncorrelationsinpp at

√

s

=

7 TeV,thesedataallow for a detailed studyof the



–



interaction with unprecedented precision.

Eachdatasetisanalyzedseparatelyby extractingthep–pand



–



correlation functions. The formerare used to constrain the size of the source r0, which is assumedto be the same for p–p

and



–



pairs.The



–



interactionistheninvestigatedby test-ing thecombinedcompatibilityofalldatasetstodifferentmodel predictionsandscatteringparameters.TheHKMYYandFGmodels, which are tuned to hypernuclei data,and thelattice calculations performed by the HAL QCD collaboration predict a shallow at-tractive interaction potential. The ALICE data manifest very good agreement with these predictions. Nevertheless, the data is also compatible with the existence of a bound state, givena binding energyofB

=

3

.

2+₋1.62.4(stat)+

1.8

−1.0(syst) MeV.TheRun3oftheLHC

is expected to further increase the statistical significance of the



–



correlation function andallow the scatteringparameters to beconstraintevenmorepreciselyinthefuture.

Acknowledgements

TheALICEcollaborationisgratefultotheHALQCDcollaboration forprovidinglatticeresultsregardingthe



–



interaction.Weare particularlythankfultoProf.TetsuoHatsudaandProf.KenjiSasaki fortheprecioussuggestionsandstimulatingdiscussions.

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 NacionaldeDesenvolvimentoCientíficoeTecnológico(CNPq), Uni-versidade Federaldo RioGrandedo Sul(UFRGS),Financiadorade EstudoseProjetos(Finep)andFundaçãodeAmparoàPesquisado

Estadode São Paulo(FAPESP),Brazil; MinistryofScience & Tech-nology of China (MSTC), National Natural Science Foundation of China (NSFC) andMinistry ofEducation ofChina (MOEC), China; Croatian Science Foundation and Ministryof Science and Educa-tion,Croatia;CentrodeAplicacionesTecnológicasyDesarrollo Nu-clear(CEADEN), Cubaenergía, Cuba; Ministryof Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish CouncilforIndependentResearch|NaturalSciences,theCarlsberg FoundationandDanishNationalResearchFoundation(DNRF), Den-mark;HelsinkiInstitute ofPhysics (HIP),Finland; Commissariatà l’EnergieAtomique(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;BundesministeriumfürBildungundForschung(BMBF)and GSIHelmholtzzentrum fürSchwerionenforschung, Germany; Gen-eralSecretariatforResearchandTechnology,MinistryofEducation, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy, GovernmentofIndia (DAE),DepartmentofScienceandTechnology, Government of India (DST), University Grants Commission, Gov-ernment of India (UGC) and Council of Scientific and Industrial Research(CSIR), India;IndonesianInstituteofSciences,Indonesia; CentroFermi- MuseoStoricodellaFisicaeCentroStudieRicerche EnricoFermiandIstitutoNazionalediFisicaNucleare(INFN),Italy; InstituteforInnovativeScienceandTechnology,Nagasaki Institute ofApplied Science(IIST), Japan Societyfor thePromotion of Sci-ence(JSPS)KAKENHIandJapaneseMinistryofEducation,Culture, Sports, Science and Technology (MEXT), Japan; Consejo Nacional deCiencia(CONACYT)yTecnología,throughFondodeCooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; NederlandseOrganisatievoorWetenschappelijkOnderzoek(NWO), Netherlands; The Research Council of Norway, Norway; Commis-sion on Science and Technology for Sustainable Development in theSouth(COMSATS),Pakistan;PontificiaUniversidadCatólicadel Perú,Peru;MinistryofScienceandHigherEducationandNational ScienceCentre,Poland;Korea Institute ofScience andTechnology InformationandNationalResearchFoundationofKorea(NRF), Re-publicofKorea;MinistryofEducationandScientific Research, In-stituteofAtomicPhysicsandMinistryofResearchandInnovation andInstituteofAtomicPhysics,Romania;JointInstituteforNuclear Research(JINR),MinistryofEducation andScience oftheRussian Federation, National Research Centre Kurchatov Institute, Russian Science Foundation and Russian Foundation for Basic Research, Russia;Ministry ofEducation,Science, Researchand Sportofthe Slovak Republic, Slovakia; National ResearchFoundation ofSouth Africa,SouthAfrica;SwedishResearchCouncil(VR)andKnut& Al-iceWallenbergFoundation(KAW),Sweden;EuropeanOrganization forNuclear Research, Switzerland; NationalScience and Technol-ogyDevelopment Agency (NSDTA), Suranaree University of Tech-nology(SUT)andOfficeoftheHigherEducationCommissionunder NRUprojectofThailand,Thailand;TurkishAtomic EnergyAgency (TAEK),Turkey;NationalAcademyofSciencesofUkraine,Ukraine; ScienceandTechnologyFacilitiesCouncil(STFC),UnitedKingdom; NationalScienceFoundationoftheUnitedStatesofAmerica(NSF) andUnitedStatesDepartmentofEnergy,OfficeofNuclearPhysics (DOENP),UnitedStatesofAmerica.

References

[1]M.Oertel,M.Hempel,T.Klähn,S.Typel,Equationsofstateforsupernovaeand compactstars,Rev.Mod.Phys.89(2017)015007,arXiv:1610.03361 [astro-ph. HE].

[2]J.Schaffner-Bielich,M.Hanauske,H.Stoecker,W.Greiner,Phasetransitionto hyperonmatterinneutronstars,Phys.Rev.Lett.89(2002)171101,arXiv:astro -ph/0005490 [astro-ph].

[3]S.Weissenborn,D.Chatterjee,J.Schaffner-Bielich,Hyperonsandmassive neu-tron stars: vector repulsion and SU(3) symmetry, Phys. Rev. C 85 (2012) 065802, arXiv:1112.0234 [astro-ph.HE], Erratum: Phys. Rev. C 90 (2014) 019904.

[4]J.Carlson,S.Gandolfi,A.Gezerlis,QuantumMonteCarloapproachestonuclear andatomicphysics,PTEP2012(2012)01A209,arXiv:1210.6659 [nucl-th]. [5]H.Güven,K.Bozkurt,E.Khan,J.Margueron,pairinginmulti-strange

hy-pernuclei,Phys.Rev.C98 (1)(2018)014318,arXiv:1803.05512 [nucl-th]. [6]T.Tanigawa,M.Matsuzaki,S.Chiba,PossibilityofLambdaLambdapairingand

itsdependenceonbackgrounddensityinrelativisticHartree-Bogoliubovmodel, Phys.Rev.C68(2003)015801,arXiv:nucl-th/0208035 [nucl-th].

[7]H.Takahashi,etal.,Observationofa(LambdaLambda)He-6double hypernu-cleus,Phys.Rev.Lett.87(2001)212502.

[8]E373(KEK-PS)Collaboration,J.K.Ahn,etal.,Double-hypernucleiobservedin ahybridemulsionexperiment,Phys.Rev.C88(2013)014003.

[9]R.L.Jaffe,Perhapsastabledihyperon,Phys.Rev.Lett.38(1977)195–198, Erra-tum:Phys.Rev.Lett.38(1977)617.

[10]ALICECollaboration,J.Adam,etal.,Searchforweaklydecayingn and

exoticboundstatesincentralPb-Pbcollisionsat√sNN=2.76TeV,Phys.Lett.

B752(2016)267–277,arXiv:1506.07499 [nucl-ex].

[11]BelleCollaboration,B.H.Kim,etal.,SearchforanH -dibaryonwithmassnear 2m inϒ(1S)andϒ(2S)decays,Phys.Rev.Lett.110(2013)222002,arXiv:

1302.4028 [hep-ex].

[12]R.E. Chrien, H particle searches at Brookhaven, Nucl. Phys. A 629(1998) 388C–397C.

[13]C.J.Yoon,etal.,SearchfortheH-dibaryonresonanceinC-12(K-,K+Lambda LambdaX),Phys.Rev.C75(2007)022201.

[14]KEK-PSE224 Collaboration,J.K.Ahn, et al., EnhancedLambdaLambda pro-ductionnearthresholdintheC-12(K-,K+)reaction,Phys. Lett.B444(1998) 267–272.

[15]P.M.M. Maessen,T.A.Rijken,J.J. deSwart,Soft corebaryonbaryonone bo-sonexchangemodels.2.Hyperon- nucleonpotential,Phys.Rev.C40(1989) 2226–2245.

[16]T.A.Rijken,V.G.J.Stoks,Y.Yamamoto,Softcorehyperon- nucleonpotentials, Phys.Rev.C59(1999)21–40,arXiv:nucl-th/9807082 [nucl-th].

[17]T.Ueda,K.Tominaga,M.Yamaguchi,N.Kijima,D.Okamoto,K.Miyagawa,T. Yamada,LambdaNand LambdaLambdainteractions inanOBEmodeland hypernuclei,Prog.Theor.Phys.99(1998)891–896.

[18]M.M.Nagels,T.A.Rijken,J.J.deSwart,Baryonbaryonscatteringinaoneboson exchangepotentialapproach.2.Hyperon-nucleonscattering,Phys.Rev.D15 (1977)2547.

[19]M.M.Nagels,T.A.Rijken,J.J.deSwart,Baryonbaryonscatteringinaone bo-sonexchangepotentialapproach.3.Anucleon-nucleonandhyperon- nucleon analysisincludingcontributionsofanonetofscalarmesons,Phys.Rev.D20 (1979)1633.

[20]K.Morita,T.Furumoto,A.Ohnishi,interactionfromrelativisticheavy-ion collisions,Phys.Rev.C91(2015)024916,arXiv:1408.6682 [nucl-th]. [21]I.N.Filikhin,A.Gal,Faddeev-Yakubovskycalculationsforlightlambdalambda

hypernuclei,Nucl.Phys.A707(2002)491–509,arXiv:nucl-th/0203036 [nucl -th].

[22]E.Hiyama,M.Kamimura,T.Motoba,T.Yamada,Y.Yamamoto,Four-bodycluster structureofA=7- 10doubleLambdahypernuclei,Phys. Rev.C66(2002) 024007,arXiv:nucl-th/0204059 [nucl-th].

[23]M.A.Lisa,S.Pratt,R.Soltz,U.Wiedemann,Femtoscopyinrelativisticheavyion collisions,Annu.Rev.Nucl.Part.Sci.55(2005)357–402,arXiv:nucl-ex/0505014 [nucl-ex].

[24]STARCollaboration,L.Adamczyk,etal.,correlationfunctioninAu+Au colli-sionsat√sN N=200GeV,Phys.Rev.Lett.114(2015)022301,arXiv:1408.4360 [nucl-ex].

[25]ALICECollaboration, S.Acharya,etal., p-p,p-and-correlations stud-iedviafemtoscopyinppreactionsat√s =7TeV,Phys.Rev.C99 (2)(2019) 024001,arXiv:1805.12455 [nucl-ex].

[26]ALICECollaboration,K.Aamodt,etal.,TheALICEexperimentattheCERNLHC, J.Instrum.3(2008)S08002.

[27]ALICECollaboration,B.Abelev,etal.,PerformanceoftheALICEexperimentat theCERNLHC,Int.J.Mod.Phys.A29(2014)1430044,arXiv:1402.4476 [nucl -ex].

[28]J.Alme,etal.,TheALICETPC,alarge3-dimensionaltrackingdevicewithfast readoutforultra-highmultiplicityevents,Nucl.Instrum.MethodsPhys.Res.A 622(Oct.2010)316–367,arXiv:1001.1950 [physics.ins-det].

[29] A.Akindinov,etal., PerformanceoftheALICE time-of-flightdetectorat the LHC,Eur.Phys.J.Plus128(Apr,2013)44,https://doi.org/10.1140/epjp/i2013 -13044-x.

[30]ALICECollaboration,K.Aamodt,etal.,Midrapidityantiproton-to-protonratioin ppcollisionsat√s=0.9 and7 TeVmeasuredbytheALICEexperiment,Phys. Rev.Lett.105(2010)072002,arXiv:1006.5432 [hep-ex].

[31] T.Sjöstrand,S.Mrenna,P.Skands,Pythia6.4physicsandmanual,J.High En-ergyPhys.2006(2006)026,http://stacks.iop.org/1126-6708/2006/i=05/a=026.

[32] S. Roesler, R. Engel, J. Ranft, The Monte Carlo event generator DPMJET-III, in: Advanced Monte Carlo for Radiation Physics, Particle Trans-port Simulation and Applications. Proceedings, Conference, MC2000, Lis-bon, Portugal, October 23-26, 2000, 2000, pp. 1033–1038, arXiv:hep-ph/ 0012252 [hep-ph], http://www-public.slac.stanford.edu/sciDoc/docMeta.aspx? slacPubNumber=SLAC-PUB-8740.

[33]Particle Data Group Collaboration, M. Tanabashi, et al., Review ofparticle physics,Phys.Rev.D98(2018)030001.

[34]T.Pierog,I.Karpenko,J.M.Katzy,E.Yatsenko,K.Werner,EPOSLHC:testof col-lectivehadronizationwithdatameasuredattheCERNLargeHadronCollider, Phys.Rev.C92(2015)034906,arXiv:1306.0121 [hep-ph].

[35]D.L.Mihaylov,V.MantovaniSarti,O.W.Arnold,L.Fabbietti,B.Hohlweger,A.M. Mathis,AfemtoscopiccorrelationanalysistoolusingtheSchrödingerequation (CATS),Eur.Phys.J.C78(2018)394,arXiv:1802.08481 [hep-ph].

[36]R.B.Wiringa,V.G.J.Stoks,R.Schiavilla,Anaccuratenucleon-nucleonpotential withchargeindependencebreaking,Phys.Rev.C51(1995)38–51,arXiv:nucl -th/9408016 [nucl-th].

[37]R.Lednicky,V.L.Lyuboshits,Finalstateinteractioneffectonpairingcorrelations betweenparticleswithsmallrelativemomenta,Sov.J.Nucl.Phys.35(1982) 770,Yad.Fiz.35(1981)1316.

[38]R.Barlow,Systematicerrors:factsandfictions,in:AdvancedStatistical Tech-niquesinParticlePhysics.Proceedings,Conference,Durham,UK,March18-22, 2002,2002,pp. 134–144,arXiv:hep-ex/0207026 [hep-ex].

[39]A.Kisiel,H.Zbroszczyk,M.Szyma ´nski,Extractingbaryon-antibaryonstrong in-teractionpotentialsfromp¯femtoscopiccorrelationfunctions,Phys.Rev.C89 (2014)054916,arXiv:1403.0433 [nucl-th].

[40]O.Arnold,StudyoftheHyperon-NucleonInteractionViaFemtoscopyin Ele-mentarySystemsWithHADESandALICE,PhDthesis,2017.

[41]J. Haidenbauer,S. Petschauer,N. Kaiser,U.G.Meissner,A.Nogga,W.Weise, Hyperon-nucleoninteractionatnext-to-leadingorderinchiraleffectivefield theory,Nucl.Phys.A915(2013)24–58,arXiv:1304.5339 [nucl-th].

[42]T.Hatsuda, K. Morita, A.Ohnishi, K. Sasaki, p− correlation inrelativistic heavyioncollisionswithnucleon-hyperoninteractionfromlatticeQCD,Nucl. Phys.A967(2017)856–859,arXiv:1704.05225 [nucl-th].

[43]K.Sasaki,etal.,BaryoninteractionsfromlatticeQCDwithphysicalmasses–

S= −2 sector–,PoSLATTICE2016(2017)116,arXiv:1702.06241 [hep-lat]. [44]A.Stavinskiy,K.Mikhailov,B.Erazmus,R.Lednicky,Residualcorrelations

be-tweendecayproductsofπ0_π0_andp 0_{systems,arXiv:0704.3290 [nucl-th].}

[45]H.Polinder, J. Haidenbauer,U.-G.Meissner,Hyperon-nucleoninteractions:a chiraleffectivefieldtheoryapproach,Nucl.Phys.A779(2006)244–266,arXiv: nucl-th/0605050 [nucl-th].

[46]ALICECollaboration,K.Aamodt,etal.,Femtoscopyofpp collisionsat√s=0.9 and7TeVattheLHCwithtwo-pionBose-Einsteincorrelations,Phys.Rev.D84 (2011)112004,arXiv:1101.3665 [hep-ex].

[47]CMSCollaboration,A.M.Sirunyan,etal.,Bose-Einsteincorrelationsinpp,pPb,

andPbPbcollisionsat√sN N=0.9−7 TeV,Phys.Rev.C97(2018)064912, arXiv:1712.07198 [hep-ex].

[48]T.A.Rijken,M.M.Nagels,Y.Yamamoto,Baryon-baryoninteractions:Nijmegen extended-soft-coremodels,Prog.Theor.Phys.Suppl.185(2010)14–71. [49]W.H.Press,S.A.Teukolsky,W.T.Vetterling,B.P.Flannery,NumericalRecipes3rd

Edition:TheArtofScientificComputing,3rded.,CambridgeUniversityPress, NewYork,NY,USA,2007,ch. 15.6.1.

[50]T.Hatsuda,Latticequantumchromodynamicsandbaryon-baryoninteractions, Front.Phys.(Beijing)13(2018)132105,theresultson–interactionsare privatecommunicationsbasedonthiswork.

[51]S.Gongyo,etal.,MoststrangedibaryonfromlatticeQCD,Phys.Rev.Lett.120 (2018)212001,arXiv:1709.00654 [hep-lat].

[52]P. Naidon,S. Endo, Efimov physics: a review, Rept. Prog. Phys. 80 (2017) 056001,arXiv:1610.09805 [quant-ph].

ALICECollaboration

S. Acharya

141

,

D. Adamová

93

,

S.P. Adhya

141

,

A. Adler

74

,

J. Adolfsson

80

,

M.M. Aggarwal

98

,

G. Aglieri Rinella

34

,

M. Agnello

31

,

N. Agrawal

10

,

Z. Ahammed

141

,

S. Ahmad

17

,

S.U. Ahn

76

,

S. Aiola

146

,

A. Akindinov

64

,

M. Al-Turany

105

,

S.N. Alam

141

,

D.S.D. Albuquerque

122

,

D. Aleksandrov

87

,

B. Alessandro

58

,

H.M. Alfanda

6

,

R. Alfaro Molina

72

,

B. Ali

17

,

Y. Ali

15

,

A. Alici

10

,

53

,

27

,

A. Alkin

2

,

J. Alme

22

,

T. Alt

69

,

L. Altenkamper

22

,

I. Altsybeev

112

,

M.N. Anaam

6

,

C. Andrei

47

,

D. Andreou

34

,

H.A. Andrews

109

,

A. Andronic

144

,

M. Angeletti

34

,

V. Anguelov

102

,

C. Anson

16

,

T. Antiˇci ´c

106

,

F. Antinori

56

,

P. Antonioli

53

,

R. Anwar

126

,

N. Apadula

79

,

L. Aphecetche

114

,

H. Appelshäuser

69

,

S. Arcelli

27

,

R. Arnaldi

58

,

M. Arratia

79

,

I.C. Arsene

21

,

M. Arslandok

102

,

A. Augustinus

34

,

R. Averbeck

105

,

S. Aziz

61

,

M.D. Azmi

17

,

A. Badalà

55

,

Y.W. Baek

40

,

S. Bagnasco

58

,

X. Bai

105

,

R. Bailhache

69

,

R. Bala

99

,

A. Baldisseri

137

,

M. Ball

42

,

R.C. Baral

85

,

R. Barbera

28

,

L. Barioglio

26

,

G.G. Barnaföldi

145

,

L.S. Barnby

92

,

V. Barret

134

,

P. Bartalini

6

,

K. Barth

34

,

E. Bartsch

69

,

F. Baruffaldi

29

,

N. Bastid

134

,

S. Basu

143

,

G. Batigne

114

,

B. Batyunya

75

,

P.C. Batzing

21

,

D. Bauri

48

,

J.L. Bazo Alba

110

,

I.G. Bearden

88

,

C. Bedda

63

,

N.K. Behera

60

,

I. Belikov

136

,

F. Bellini

34

,

R. Bellwied

126

,

V. Belyaev

91

,

G. Bencedi

145

,

S. Beole

26

,

A. Bercuci

47

,

Y. Berdnikov

96

,

D. Berenyi

145

,

R.A. Bertens

130

,

D. Berzano

58

,

M.G. Besoiu

68

,

L. Betev

34

,

A. Bhasin

99

,

I.R. Bhat

99

,

H. Bhatt

48

,

B. Bhattacharjee

41

,

A. Bianchi

26

,

L. Bianchi

126

,

26

,

N. Bianchi

51

,

J. Bielˇcík

37

,

J. Bielˇcíková

93

,

A. Bilandzic

117

,

103

,

G. Biro

145

,

R. Biswas

3

,

S. Biswas

3

,

J.T. Blair

119

,

D. Blau

87

,

C. Blume

69

,

G. Boca

139

,

F. Bock

94

,

34

,

A. Bogdanov

91

,

L. Boldizsár

145

,

A. Bolozdynya

91

,

M. Bombara

38

,

G. Bonomi

140

,

H. Borel

137

,

A. Borissov

144

,

91

,

M. Borri

128

,

H. Bossi

146

,

E. Botta

26

,

C. Bourjau

88

,

L. Bratrud

69

,

P. Braun-Munzinger

105

,

M. Bregant

121

,

T.A. Broker

69

,

M. Broz

37

,

E.J. Brucken

43

,

E. Bruna

58

,

G.E. Bruno

33

,

104

,

M.D. Buckland

128

,

D. Budnikov

107

,

H. Buesching

69

,

S. Bufalino

31

,

O. Bugnon

114

,

P. Buhler

113

,

P. Buncic

34

,

Z. Buthelezi

73

,

J.B. Butt

15

,

J.T. Buxton

95

,

D. Caffarri

89

,

A. Caliva

105

,

E. Calvo Villar

110

,

R.S. Camacho

44

,

P. Camerini

25

,

A.A. Capon

113

,

F. Carnesecchi

10

,

J. Castillo Castellanos

137

,

A.J. Castro

130

,

E.A.R. Casula

54

,

F. Catalano

31

,

C. Ceballos Sanchez

52

,

P. Chakraborty

48

,

S. Chandra

141

,

B. Chang

127

,

W. Chang

6

,

S. Chapeland

34

,

M. Chartier

128

,

S. Chattopadhyay

141

,

S. Chattopadhyay

108

,

A. Chauvin

24

,

C. Cheshkov

135

,

B. Cheynis

135

,

V. Chibante Barroso

34

,

D.D. Chinellato

122

,

S. Cho

60

,

P. Chochula

34

,

T. Chowdhury

134

,

P. Christakoglou

89

,

C.H. Christensen

88

,

P. Christiansen

80

,

T. Chujo

133

,

C. Cicalo

54

,

L. Cifarelli

10

,

27

,

F. Cindolo

53

,

J. Cleymans

125

,

F. Colamaria

52

,

D. Colella

52

,

A. Collu

79

,

M. Colocci

27

,

M. Concas

58

,

ii

,

Y. Corrales Morales

58

,

26

,

P. Cortese

32

,

M.R. Cosentino

123

,

F. Costa

34

,

S. Costanza

139

,

J. Crkovská

61

,

P. Crochet

134

,

E. Cuautle

70

,

L. Cunqueiro

94

,

D. Dabrowski

142

,

T. Dahms

103

,

117

,

A. Dainese

56

,

F.P.A. Damas

137

,

114

,

S. Dani

66

,

M.C. Danisch

102

,

A. Danu

68

,

D. Das

108

,

I. Das

108

,

S. Das

3

,

A. Dash

85

,

S. Dash

48

,

A. Dashi

103

,

S. De

85

,

49

,

A. De Caro

30

,

G. de Cataldo

52

,

C. de Conti

121

,

J. de Cuveland

39

,

A. De Falco

24

,

D. De Gruttola

10

,

N. De Marco

58

,

S. De Pasquale

30

,

R.D. De Souza

122

,

S. Deb

49

,

H.F. Degenhardt

121

,

K.R. Deja

142

,

A. Deloff

84

,

S. Delsanto

131

,

26

,

P. Dhankher

48

,

D. Di Bari

33

,

A. Di Mauro

34

,

R.A. Diaz

8

,

T. Dietel

125

,

P. Dillenseger

69

,

Y. Ding

6

,

R. Divià

34

,

Ø. Djuvsland

22

,

U. Dmitrieva

62

,

A. Dobrin

34

,

68

,

B. Dönigus

69

,

O. Dordic

21

,

A.K. Dubey

141

,

A. Dubla

105

,

S. Dudi

98

,

M. Dukhishyam

85

,

P. Dupieux

134

,

R.J. Ehlers

146

,

D. Elia

52

,

H. Engel

74

,

E. Epple

146

,

B. Erazmus

114

,

F. Erhardt

97

,

A. Erokhin

112

,

M.R. Ersdal

22

,

B. Espagnon

61

,

G. Eulisse

34

,

J. Eum

18

,

D. Evans

109

,

S. Evdokimov

90

,

L. Fabbietti

117

,

103

,

M. Faggin

29

,

J. Faivre

78

,

A. Fantoni

51

,

M. Fasel

94

,

P. Fecchio

31

,

L. Feldkamp

144

,

A. Feliciello

58

,

G. Feofilov

112

,

A. Fernández Téllez

44

,

A. Ferrero

137

,

A. Ferretti

26

,

A. Festanti

34

,

V.J.G. Feuillard

102

,

J. Figiel

118

,

S. Filchagin

107

,

D. Finogeev

62

,

F.M. Fionda

22

,

G. Fiorenza

52

,

F. Flor

126

,

S. Foertsch

73

,

P. Foka

105

,

S. Fokin

87

,

E. Fragiacomo

59

,

U. Frankenfeld

105

,

G.G. Fronze

26

,

U. Fuchs

34

,

C. Furget

78

,

A. Furs

62

,

M. Fusco Girard

30

,

J.J. Gaardhøje

88

,

M. Gagliardi

26

,

A.M. Gago

110

,

A. Gal

136

,

C.D. Galvan

120

,

P. Ganoti

83

,

C. Garabatos

105

,

E. Garcia-Solis

11

,

K. Garg

28

,

C. Gargiulo

34

,

K. Garner

144

,

P. Gasik

103

,

117

,

E.F. Gauger

119

,

M.B. Gay Ducati

71

,

M. Germain

114

,

J. Ghosh

108

,

P. Ghosh

141

,

S.K. Ghosh

3

,

P. Gianotti

51

,

P. Giubellino

105

,

58

,

P. Giubilato

29

,

P. Glässel

102

,

D.M. Goméz Coral

72

,

A. Gomez Ramirez

74

,

V. Gonzalez

105

,

P. González-Zamora

44

,

S. Gorbunov

39

,

L. Görlich

118

,

S. Gotovac

35

,

V. Grabski

72

,

L.K. Graczykowski

142

,

K.L. Graham

109

,

L. Greiner

79

,

A. Grelli

63

,

C. Grigoras

34

,

V. Grigoriev

91

,

A. Grigoryan

1

,

S. Grigoryan

75

,

O.S. Groettvik

22

,

J.M. Gronefeld

105

,

F. Grosa

31

,

J.F. Grosse-Oetringhaus

34

,

R. Grosso

105

,

R. Guernane

78

,

B. Guerzoni

27

,

M. Guittiere

114

,

K. Gulbrandsen

88

,

T. Gunji

132

,

A. Gupta

99

,

R. Gupta

99

,

I.B. Guzman

44

,

R. Haake

34

,

146

,

M.K. Habib

105

,

C. Hadjidakis

61

,

H. Hamagaki

81

,

G. Hamar

145

,

M. Hamid

6

,

R. Hannigan

119

,

M.R. Haque

63

,

A. Harlenderova

105

,

J.W. Harris

146

,

A. Harton

11

,

J.A. Hasenbichler

34

,

H. Hassan

78

,

D. Hatzifotiadou

10

,

53

,

P. Hauer

42

,

S. Hayashi

132

,

S.T. Heckel

69

,

E. Hellbär

69

,

H. Helstrup

36

,

A. Herghelegiu

47

,

E.G. Hernandez

44

,

G. Herrera Corral

9

,

F. Herrmann

144

,

K.F. Hetland

36

,

T.E. Hilden

43

,

H. Hillemanns

34

,

C. Hills

128

,

B. Hippolyte

136

,

B. Hohlweger

103

,

D. Horak

37

,

S. Hornung

105

,

R. Hosokawa

133

,

P. Hristov

34

,

C. Huang

61

,

C. Hughes

130

,

P. Huhn

69

,

T.J. Humanic

95

,

H. Hushnud

108

,

L.A. Husova

144

,

N. Hussain

41

,

S.A. Hussain

15

,

T. Hussain

17

,

D. Hutter

39

,

D.S. Hwang

19

,

J.P. Iddon

128

,

34

,

R. Ilkaev

107

,

M. Inaba

133

,

M. Ippolitov

87

,

M.S. Islam

108

,

M. Ivanov

105

,

V. Ivanov

96

,

V. Izucheev

90

,

B. Jacak

79

,

N. Jacazio

27

,

P.M. Jacobs

79

,

M.B. Jadhav

48

,

S. Jadlovska

116

,

J. Jadlovsky

116

,

S. Jaelani

63

,

C. Jahnke

121

,

M.J. Jakubowska

142

,

M.A. Janik

142

,

M. Jercic

97

,

O. Jevons

109

,

R.T. Jimenez Bustamante

105

,

M. Jin

126

,

F. Jonas

144

,

94

,

P.G. Jones

109

,

A. Jusko

109

,

P. Kalinak

65

,

A. Kalweit

34

,

J.H. Kang

147

,

V. Kaplin

91

,

S. Kar

6

,

A. Karasu Uysal

77

,

O. Karavichev

62

,

T. Karavicheva

62

,

P. Karczmarczyk

34

,

E. Karpechev

62

,

U. Kebschull

74

,

R. Keidel

46

,

M. Keil

34

,

B. Ketzer

42

,

Z. Khabanova

89

,

A.M. Khan

6

,

S. Khan

17

,

S.A. Khan

141

,

A. Khanzadeev

96

,

Y. Kharlov

90

,

A. Khatun

17

,

A. Khuntia

118

,

49

,

B. Kileng

36

,

B. Kim

60

,

B. Kim

133

,

D. Kim

147

,

D.J. Kim

127

,

E.J. Kim

13

,

H. Kim

147

,

J. Kim

147

,

J.S. Kim

40

,

J. Kim

102

,

J. Kim

147

,

J. Kim

13

,

M. Kim

102

,

S. Kim

19

,

T. Kim

147

,

T. Kim

147

,

S. Kirsch

39

,

I. Kisel

39

,

S. Kiselev

64

,

A. Kisiel

142

,

J.L. Klay

5

,

C. Klein

69

,

J. Klein

58

,

S. Klein

79

,

C. Klein-Bösing

144

,

S. Klewin

102

,

A. Kluge

34

,

M.L. Knichel

34

,

A.G. Knospe

126

,

C. Kobdaj

115

,

M.K. Köhler

102

,

T. Kollegger

105

,

A. Kondratyev

75

,

N. Kondratyeva

91

,

E. Kondratyuk

90

,

P.J. Konopka

34

,

L. Koska

116

,

O. Kovalenko

84

,

V. Kovalenko

112

,

M. Kowalski

118

,

I. Králik

65

,

A. Kravˇcáková

38

,

L. Kreis

105

,

M. Krivda

109

,

65

,

F. Krizek

93

,

K. Krizkova Gajdosova

37

,

M. Krüger

69

,

E. Kryshen

96

,

M. Krzewicki

39

,

A.M. Kubera

95

,

V. Kuˇcera

60

,

C. Kuhn

136

,

P.G. Kuijer

89

,

L. Kumar

98

,

S. Kumar

48

,

S. Kundu

85

,

P. Kurashvili

84

,

A. Kurepin

62

,

A.B. Kurepin

62

,

S. Kushpil

93

,

J. Kvapil

109

,

M.J. Kweon

60

,

J.Y. Kwon

60

,

Y. Kwon

147

,

S.L. La Pointe

39

,

P. La Rocca

28

,

Y.S. Lai

79

,

R. Langoy

124

,

K. Lapidus

34

,

146

,

A. Lardeux

21

,

P. Larionov

51

,

E. Laudi

34

,

R. Lavicka

37

,

T. Lazareva

112

,

R. Lea

25

,

L. Leardini

102

,

S. Lee

147

,

F. Lehas

89

,

S. Lehner

113

,

J. Lehrbach

39

,

R.C. Lemmon

92

,

I. León Monzón

120

,

E.D. Lesser

20

,

M. Lettrich

34

,

P. Lévai

145

,

X. Li

12

,

X.L. Li

6

,

J. Lien

124

,

R. Lietava

109

,

B. Lim

18

,

S. Lindal

21

,

V. Lindenstruth

39

,

S.W. Lindsay

128

,

C. Lippmann

105

,

M.A. Lisa

95

,

V. Litichevskyi

43

,

A. Liu

79

,

S. Liu

95

,

W.J. Llope

143

,

I.M. Lofnes

22

,

V. Loginov

91

,

C. Loizides

94

,

P. Loncar

35

,

X. Lopez

134

,

E. López Torres

8

,

P. Luettig

69

,

J.R. Luhder

144

,

M. Lunardon

29

,

G. Luparello

59

,

M. Lupi

74

,

A. Maevskaya

62

,