The proton–Ω correlation function in Au + Au collisions at s NN =200GeV

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Physics

Letters

B

www.elsevier.com/locate/physletb

The

proton–

correlation

function

in

Au

+

Au

collisions

at

√

s

_NN

=

200 GeV

STAR

Collaboration

J. Adam

k

,

L. Adamczyk

a

,

J.R. Adams

ah

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J.K. Adkins

x

,

G. Agakishiev

v

,

M.M. Aggarwal

aj

,

Z. Ahammed

bd

,

N.N. Ajitanand

av

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I. Alekseev

b

,

ad

,

D.M. Anderson

ax

,

R. Aoyama

ba

,

A. Aparin

v

,

D. Arkhipkin

d

,

E.C. Aschenauer

d

,

M.U. Ashraf

az

,

F. Atetalla

w

,

A. Attri

aj

,

G.S. Averichev

v

,

X. Bai

i

,

V. Bairathi

ae

,

K. Barish

h

,

A.J. Bassill

h

,

A. Behera

av

,

R. Bellwied

q

,

A. Bhasin

u

,

A.K. Bhati

aj

,

J. Bielcik

l

,

J. Bielcikova

ag

,

L.C. Bland

d

,

I.G. Bordyuzhin

b

,

J.D. Brandenburg

ao

,

A.V. Brandin

ad

,

D. Brown

aa

,

J. Bryslawskyj

h

,

I. Bunzarov

v

,

J. Butterworth

ao

,

H. Caines

bg

,

M. Calderón de la Barca Sánchez

f

,

J.M. Campbell

ah

,

D. Cebra

f

,

I. Chakaberia

w

,

as

,

P. Chaloupka

l

,

Z. Chang

d

,

F.-H. Chang

af

,

N. Chankova-Bunzarova

v

,

A. Chatterjee

bd

,

S. Chattopadhyay

bd

,

J.H. Chen

o

,

at

,

X. Chen

s

,

X. Chen

ar

,

J. Cheng

az

,

M. Cherney

k

,

W. Christie

d

,

G. Contin

z

,

H.J. Crawford

e

,

S. Das

i

,

T.G. Dedovich

v

,

I.M. Deppner

p

,

A.A. Derevschikov

al

,

L. Didenko

d

,

C. Dilks

ak

,

X. Dong

z

,

J.L. Drachenberg

y

,

J.C. Dunlop

d

,

L.G. Efimov

v

,

N. Elsey

bf

,

J. Engelage

e

,

G. Eppley

ao

,

R. Esha

g

,

S. Esumi

ba

,

O. Evdokimov

j

,

J. Ewigleben

aa

,

O. Eyser

d

,

R. Fatemi

x

,

S. Fazio

d

,

P. Federic

ag

,

P. Federicova

l

,

J. Fedorisin

v

,

P. Filip

v

,

E. Finch

au

,

Y. Fisyak

d

,

C.E. Flores

f

,

L. Fulek

a

,

C.A. Gagliardi

ax

,

T. Galatyuk

m

,

F. Geurts

ao

,

A. Gibson

bc

,

D. Grosnick

bc

,

D.S. Gunarathne

aw

,

Y. Guo

w

,

A. Gupta

u

,

W. Guryn

d

,

A.I. Hamad

w

,

A. Hamed

ax

,

A. Harlenderova

l

,

J.W. Harris

bg

,

L. He

am

,

S. Heppelmann

f

,

S. Heppelmann

ak

,

N. Herrmann

p

,

A. Hirsch

am

,

L. Holub

l

,

S. Horvat

bg

,

B. Huang

j

,

X. Huang

az

,

S.L. Huang

av

,

T. Huang

af

,

H.Z. Huang

g

,

T.J. Humanic

ah

,

P. Huo

av

,

G. Igo

g

,

W.W. Jacobs

r

,

A. Jentsch

ay

,

J. Jia

d

,

av

,

K. Jiang

ar

,

S. Jowzaee

bf

,

E.G. Judd

e

,

S. Kabana

w

,

D. Kalinkin

r

,

K. Kang

az

,

D. Kapukchyan

h

,

K. Kauder

d

,

H.W. Ke

d

,

D. Keane

w

,

A. Kechechyan

v

,

D.P. Kikoła

be

,

C. Kim

h

,

T.A. Kinghorn

f

,

I. Kisel

n

,

A. Kisiel

be

,

L. Kochenda

ad

,

L.K. Kosarzewski

be

,

A.F. Kraishan

aw

,

L. Kramarik

l

,

L. Krauth

h

,

P. Kravtsov

ad

,

K. Krueger

c

,

N. Kulathunga

q

,

S. Kumar

aj

,

L. Kumar

aj

,

R. Kunnawalkam Elayavalli

bf

,

J. Kvapil

l

,

J.H. Kwasizur

r

,

R. Lacey

av

,

J.M. Landgraf

d

,

J. Lauret

d

,

A. Lebedev

d

,

R. Lednicky

v

,

J.H. Lee

d

,

Y. Li

az

,

W. Li

at

,

C. Li

ar

,

X. Li

ar

,

Y. Liang

w

,

J. Lidrych

l

,

T. Lin

ax

,

A. Lipiec

be

,

M.A. Lisa

ah

,

H. Liu

r

,

P. Liu

av

,

F. Liu

i

,

Y. Liu

ax

,

T. Ljubicic

d

,

W.J. Llope

bf

,

M. Lomnitz

z

,

R.S. Longacre

d

,

S. Luo

j

,

X. Luo

i

,

L. Ma

o

,

G.L. Ma

o

,

at

,

R. Ma

d

,

Y.G. Ma

o

,

at

,

N. Magdy

av

,

R. Majka

bg

,

D. Mallick

ae

,

S. Margetis

w

,

C. Markert

ay

,

H.S. Matis

z

,

O. Matonoha

l

,

D. Mayes

h

,

J.A. Mazer

ap

,

K. Meehan

f

,

J.C. Mei

as

,

N.G. Minaev

al

,

S. Mioduszewski

ax

,

D. Mishra

ae

,

B. Mohanty

ae

,

M.M. Mondal

t

,

I. Mooney

bf

,

D.A. Morozov

al

,

Md. Nasim

g

,

J.D. Negrete

h

,

J.M. Nelson

e

,

D.B. Nemes

bg

,

M. Nie

at

,

G. Nigmatkulov

ad

,

T. Niida

bf

,

L.V. Nogach

al

,

T. Nonaka

i

,

S.B. Nurushev

al

,

G. Odyniec

z

,

A. Ogawa

d

,

S. Oh

bg

,

K. Oh

an

,

V.A. Okorokov

ad

,

D. Olvitt Jr.

aw

,

B.S. Page

d

,

R. Pak

d

,

Y. Panebratsev

v

,

B. Pawlik

ai

,

H. Pei

i

,

C. Perkins

e

,

J. Pluta

be

,

J. Porter

z

,

M. Posik

aw

,

N.K. Pruthi

aj

,

M. Przybycien

a

,

J. Putschke

bf

,

A. Quintero

aw

,

S.K. Radhakrishnan

z

,

S. Ramachandran

x

,

R.L. Ray

ay

,

R. Reed

aa

,

H.G. Ritter

z

,

J.B. Roberts

ao

,

O.V. Rogachevskiy

v

,

https://doi.org/10.1016/j.physletb.2019.01.055

J.L. Romero

f

,

L. Ruan

d

,

J. Rusnak

ag

,

O. Rusnakova

l

,

N.R. Sahoo

ax

,

P.K. Sahu

t

,

S. Salur

ap

,

J. Sandweiss

bg

,

J. Schambach

ay

,

A.M. Schmah

z

,

W.B. Schmidke

d

,

N. Schmitz

ab

,

B.R. Schweid

av

,

F. Seck

m

,

J. Seger

k

,

M. Sergeeva

g

,

R. Seto

h

,

P. Seyboth

ab

,

N. Shah

at

,

1

,

E. Shahaliev

v

,

P.V. Shanmuganathan

aa

,

M. Shao

ar

,

W.Q. Shen

at

,

F. Shen

as

,

S.S. Shi

i

,

Q.Y. Shou

at

,

E.P. Sichtermann

z

,

S. Siejka

be

,

R. Sikora

a

,

M. Simko

ag

,

S. Singha

w

,

D. Smirnov

d

,

N. Smirnov

bg

,

W. Solyst

r

,

P. Sorensen

d

,

H.M. Spinka

c

,

B. Srivastava

am

,

T.D.S. Stanislaus

bc

,

D.J. Stewart

bg

,

M. Strikhanov

ad

,

B. Stringfellow

am

,

A.A.P. Suaide

aq

,

T. Sugiura

ba

,

M. Sumbera

ag

,

B. Summa

ak

,

X. Sun

i

,

Y. Sun

ar

,

X.M. Sun

i

,

B. Surrow

aw

,

D.N. Svirida

b

,

P. Szymanski

be

,

Z. Tang

ar

,

A.H. Tang

d

,

A. Taranenko

ad

,

T. Tarnowsky

ac

,

J.H. Thomas

z

,

A.R. Timmins

q

,

D. Tlusty

ao

,

T. Todoroki

d

,

M. Tokarev

v

,

C.A. Tomkiel

aa

,

S. Trentalange

g

,

R.E. Tribble

ax

,

P. Tribedy

d

,

S.K. Tripathy

t

,

O.D. Tsai

g

,

B. Tu

i

,

T. Ullrich

d

,

D.G. Underwood

c

,

I. Upsal

d

,

as

,

G. Van Buren

d

,

J. Vanek

ag

,

A.N. Vasiliev

al

,

I. Vassiliev

n

,

F. Videbæk

d

,

S. Vokal

v

,

S.A. Voloshin

bf

,

A. Vossen

r

,

F. Wang

am

,

G. Wang

g

,

Y. Wang

az

,

Y. Wang

i

,

J.C. Webb

d

,

L. Wen

g

,

G.D. Westfall

ac

,

H. Wieman

z

,

S.W. Wissink

r

,

R. Witt

bb

,

Y. Wu

w

,

Z.G. Xiao

az

,

W. Xie

am

,

G. Xie

j

,

Z. Xu

d

,

J. Xu

i

,

Y.F. Xu

at

,

N. Xu

z

,

Q.H. Xu

as

,

Y. Yang

af

,

C. Yang

as

,

S. Yang

d

,

Q. Yang

as

,

Z. Ye

j

,

Z. Ye

j

,

L. Yi

as

,

K. Yip

d

,

I.-K. Yoo

an

,

N. Yu

i

,

H. Zbroszczyk

be

,

W. Zha

ar

,

Z. Zhang

at

,

J. Zhang

s

,

L. Zhang

i

,

J. Zhang

z

,

Y. Zhang

ar

,

X.P. Zhang

az

,

S. Zhang

o

,

at

,

S. Zhang

ar

,

J. Zhao

am

,

C. Zhong

o

,

at

,

C. Zhou

at

,

L. Zhou

ar

,

Z. Zhu

as

,

X. Zhu

az

,

M. Zyzak

n

a_{AGHUniversityofScienceandTechnology,FPACS,Cracow30-059,Poland} b_{AlikhanovInstituteforTheoreticalandExperimentalPhysics,Moscow117218,Russia} c_{ArgonneNationalLaboratory,Argonne,IL 60439}

d_{BrookhavenNationalLaboratory,Upton,NY 11973} e_{UniversityofCalifornia,Berkeley,CA 94720} f_{UniversityofCalifornia,Davis,CA 95616} g_{UniversityofCalifornia,LosAngeles,CA 90095} h_{UniversityofCalifornia,Riverside,CA 92521} i_{CentralChinaNormalUniversity,Wuhan,Hubei430079} j_{UniversityofIllinoisatChicago,Chicago,IL 60607} k_{CreightonUniversity,Omaha,NE 68178}

l_{CzechTechnicalUniversityinPrague,FNSPE,Prague11519,CzechRepublic} m_{TechnischeUniversitätDarmstadt,Darmstadt64289,Germany} n_{FrankfurtInstituteforAdvancedStudiesFIAS,Frankfurt60438,Germany} o_{FudanUniversity,Shanghai,200433}

p_{UniversityofHeidelberg,Heidelberg69120,Germany} q_{UniversityofHouston,Houston,TX 77204} r_{IndianaUniversity,Bloomington,IN 47408}

s_{InstituteofModernPhysics,ChineseAcademyofSciences,Lanzhou,Gansu730000} t_{InstituteofPhysics,Bhubaneswar751005,India}

u_{UniversityofJammu,Jammu180001,India}

v_{JointInstituteforNuclearResearch,Dubna141980,Russia} w_{KentStateUniversity,Kent,OH 44242}

x_{UniversityofKentucky,Lexington,KY 40506-0055} y_{LamarUniversity,PhysicsDepartment,Beaumont,TX 77710} z_{LawrenceBerkeleyNationalLaboratory,Berkeley,CA 94720} aa_{LehighUniversity,Bethlehem,PA 18015}

ab_{Max-Planck-InstitutfurPhysik,Munich80805,Germany} ac_{MichiganStateUniversity,EastLansing,MI 48824}

ad_{NationalResearchNuclearUniversityMEPhI,Moscow115409,Russia} ae_{NationalInstituteofScienceEducationandResearch,HBNI,Jatni752050,India} af_{NationalChengKungUniversity,Tainan70101}

ag_{NuclearPhysicsInstituteASCR,Prague25068,CzechRepublic} ah_{OhioStateUniversity,Columbus,OH 43210}

ai_{InstituteofNuclearPhysicsPAN,Cracow31-342,Poland} aj_{PanjabUniversity,Chandigarh160014,India}

ak_{PennsylvaniaStateUniversity,UniversityPark,PA 16802} al_{InstituteofHighEnergyPhysics,Protvino142281,Russia} am_{PurdueUniversity,WestLafayette,IN 47907}

an_{PusanNationalUniversity,Pusan46241,RepublicofKorea} ao_{RiceUniversity,Houston,TX 77251}

ap_{RutgersUniversity,Piscataway,NJ 08854}

aq_{UniversidadedeSaoPaulo,SaoPaulo,05314-970,Brazil} ar_{UniversityofScienceandTechnologyofChina,Hefei,Anhui230026} as_{ShandongUniversity,Jinan,Shandong250100}

at_{ShanghaiInstituteofAppliedPhysics,ChineseAcademyofSciences,Shanghai201800} au_{SouthernConnecticutStateUniversity,NewHaven,CT 06515}

ax_{TexasA&MUniversity,CollegeStation,TX 77843} ay_{UniversityofTexas,Austin,TX 78712} az_{TsinghuaUniversity,Beijing100084}

ba_{UniversityofTsukuba,Tsukuba,Ibaraki305-8571,Japan} bb_{UnitedStatesNavalAcademy,Annapolis,MD 21402} bc_{ValparaisoUniversity,Valparaiso,IN 46383}

bd_{VariableEnergyCyclotronCentre,Kolkata700064,India} be_{WarsawUniversityofTechnology,Warsaw00-661,Poland} bf_{WayneStateUniversity,Detroit,MI 48201}

bg_{YaleUniversity,NewHaven,CT 06520}

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Articlehistory: Received7August2018

Receivedinrevisedform21December2018 Accepted28January2019

Availableonline31January2019 Editor:V.Metag

Keywords: Correlations Femtoscopy Ndibaryon

We present the first measurement of the proton–correlation function in heavy-ion collisions for the central (0–40%) and peripheral (40–80%) Au+Au collisions at √sNN=200 GeV by the STAR experiment

at the Relativistic Heavy-Ion Collider (RHIC). Predictions for the ratio of peripheral collisions to central collisions for the proton– correlation function are sensitive to the presence of a nucleon– bound state. These predictions are based on the proton–interaction extracted from (2 +1)-flavor lattice QCD calculations at the physical point. The measured ratio of the proton–correlation function between the peripheral (small system) and central (large system) collisions is less than unity for relative momentum smaller than 40 MeV/c.

Comparison of our measured correlation ratio with theoretical calculation slightly

favors a proton–bound system with a binding energy of ∼27 MeV.

©2019 Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3_.

1. Introduction

Thestudyofthenucleon–nucleon(NN),hyperon–nucleon(YN) andhyperon–hyperon (YY) interactions is offundamental impor-tance inunderstanding the relativistic heavy-ion collisions [1–3], modelingofneutronstars[4,7,5,6] andexaminingtheexistenceof variousexotichadrons[8–10].A significantamountofNN scatter-ingdataacquiredovertheyearsallowsustoconstructpreciseNN potentialmodels[11,12].TheavailabilityofnominalYNscattering dataandnoscatteringdataforthemulti-strangeYYsystemsmake the task of constructing YN and YY potentials very challenging. Withthedevelopment ofsophisticatedcomputational techniques, it has become possible to carry out the first principle calcula-tionsbasedonlatticeQuantumChromodynamics(QCD)toprovide constraints on some of the NN, YY and YN interactions [12–16]. Very often the experimental information on the bound states of strangebaryonsandnucleons (hypernuclei)isusedtoprovide in-formation on theYN interactions [17–19]. However, thismethod becomesdifficulttouseforthehypernucleicontaining morethan fourbaryonsduetothecontamination bythemany-bodyeffects, whichmakes itvery difficultto extractthe N



,N



, Y



andY



interactions.

High-energyheavy-ion collisions produce a sizablenumber of hyperons in each collision [20], which provides an excellent op-portunity tostudytheNN, YNandYYinteractions. Measurement of the two-particle correlations at low relative momentum, also knownasfemtoscopy,hasbeenusedtostudythespace–time dy-namics of the source created in heavy-ion collisions. In addition tothis, measurementofthetwo-particlecorrelationsatlow rela-tivemomentumcanbeusedtomeasurethefinalstateinteractions

(FSI) between NN, YN and YY. This approach has been used by

theSTAR experimentatRHIC toextract theFSI for



[21] and antiproton–antiproton [22]. Using a similar approach, the ALICE experimentattheLargeHandronCollider(LHC)reportedthe

mea-E-mailaddress:nehashah@iitp.ac.in(N. Shah).

1 _{Also at Department of Physics, Indian Institute of Technology Patna, Bihar} 801106,India.

surement of the proton–proton and



correlation functions in

proton

+

protoncollisionsat

√

s

=

7 TeV [23].

Recent study of

(

2

+

1

)

-flavor lattice QCD simulations for the heavy quark masses showsthat the nucleon–



interaction (N



) is attractive atall distances [16]. Using thisN



interaction, it is shown that the shape of the two-particle correlation function at lowrelativemomentumchangessubstantiallywiththestrengthof theN



attraction [24].However,thepresenceoftheCoulomb in-teraction intheproton–



channel makesitdifficulttoaccessthe strong interaction directlyfromthe measured two-particle corre-lationfunction.Therefore,anewmeasure,namelytheratioofthe correlationfunctionbetweenperipheral(small)andcentral(large) collisionsystemsisproposedinRef. [24].Thisratioprovidesdirect accessto the stronginteraction betweenprotonand



, indepen-dentofthemodelusedfortheemissionsource.

The attractivenatureoftheN



interactionleadsto the possi-bleexistenceofanN



dibaryonwithstrangeness

= −

3,spin

=

2, andisospin

=

1

/

2,whichwas firstproposed inRef. [25].Suchan N



dibaryon is themost interesting candidate [25–29] after the H-dibaryon [8] as thePauli exclusionprinciple doesnot apply to quarks in the N



dibaryon andit is stable against strong decay [30,31].Severalattemptshavebeenmadetoestimate thebinding energyoftheN



stateindifferentQCDmotivatedmodels[16,32]. TheN



dibaryoncanbeproducedinhigh-energyheavy-ion colli-sionsthroughthecoalescencemechanism [33].IntheN



system, an S-wavehastwopossiblechannels,5_S

2 and3S1 (2s+1LJ,where the s, LandJdenote spin,L wave andtotalangular momentum, respectively). Forthe 5S2 channel thecouplingto



is dynam-ically suppressed, whereas in the 3_S

1 channel a sizablecoupling

to these octet–octet channels is possible through the rearrange-ment ofquarks [16]. Thismakes directsearches viathe invariant mass method very challenging in heavy-ion collisions. The mea-surement ofthe proton–



correlation function inperipheral and central Au

+

Au collisions at

√

sNN

=

200 GeV, presentedin this

Letter,willprovideinsightintotheexistenceofN



dibaryon. 2. Dataanalysis

Fig. 1. ProtonidentificationusingthetimeofflightandmomentumfromtheTOF andtheTPCdetectors,respectively.Thesolidlinesshowloweranduppercutsto selectprotons.

collisionsat

√

sNN

=

200 GeV in2011and2014. 5

.

30

×

108

mini-mumbiaseventsfrom2011and8

.

76

×

108 _{minimumbiasevents}

from 2014 were analyzed. The tracking and particle

identifica-tionforthemeasurements were providedby theTimeProjection Chamber (TPC) [35] and the Time-of-Flight (TOF) [36] detectors. These detectors are located in a 0.5 T magnetic field, and al-low determinationofthe momentum andcharge ofthe particles traversingthe TPC. Minimumbias triggered eventswere selected byrequiringcoincidentsignalsatforwardandbackwardrapidities intheVertex PositionDetectors (VPD) [37] andrequiringasignal atmid-rapidityintheTOF.Thecollisioncentralitywasdetermined fromthe uncorrected charged particle multiplicity dN/d

η

within

|

η

|

<

0

.

5 usinga MonteCarlo(MC) Glauber model [38]. The de-pendenceofdN/d

η

onthecollisionvertexpositionalongthebeam directionVz andthe beamluminosity hasbeen includedto take acceptanceandefficiencychangesonthemeasureddN/d

η

into ac-count.Tosuppresseventsfromcollisions withthebeampipe,the reconstructedprimaryvertexwasrequiredtoliewithina2 cm ra-dial distance from the centerof the beam pipe. In addition, the

z-positionofthevertexwas requiredtobewithin

±

40 cminthe centeroftheSTARTPCforthedatafromyear2011and

±

6 cmin thecenteroftheHeavyFlavorTracker(HFT) [39] forthedatafrom year2014,respectively.

2.1.Protonidentification

TheTOFandTPCdetectorswere usedforthe proton (antipro-ton)identification in the pseudorapidity range

|

η

|

<

1. A proton (antiproton)trackwas selected ifits distanceofclosest approach

(DCA) was less than 0.5 cm to the primary vertex, greater than

20 TPCpoints were measured out ofa maximum of 45,and the

numberofTPCpoints usedintrackreconstructiondividedbythe numberofpossiblepoints was greater than0.52inorderto pre-vent split tracks. The time offlight of the particles reaching the TOFdetectoralongwiththetrackinginformationfromtheTPC de-tector wasused tocalculatethe squareofthe particlemass(m2) to identify protons (antiprotons). Fig. 1 showsm2 _{from the TOF}

detectorversusmomentum fromtheTPC. Allcandidateswithm2

between0.75and1.10

(

GeV

/

c2

)

2 wereusedintheanalysis.

2.2.



identification

The TPC was used for tracking, decay topology and identifi-cation of particles for



(

¯

) reconstruction in the pseudorapid-ity range

|

η

|

<

1. To reconstruct the



(

¯

), the decay channel

( ¯

)

→ 

K−

( ¯



K+

)

, with a branching ratioof 67.8%, with sub-sequentdecay

( ¯

)

→

p

π

−

(

p

¯

π

+

)

(branchingratioof 63.9%)was used [40]. The



(

¯

) candidates were formed from pairs of p

(

¯

p) and

π

− (

π

+) tracks whose trajectories pointed to a

com-mon secondarydecayvertex, which was wellseparated fromthe



(

¯

) vertex. These



(

¯

) candidateswere then combinedwith the bachelor K− (K+) tracks,which pointedtoa commondecay vertexwellseparatedfromtheprimary vertex.Themeanspecific energyloss measured by the TPCwas used forthe identification of the charged daughter particles (

π

±, K±, p, p) [

¯

41]. The de-cay length (DL) ofan



(

¯

) candidate was requiredto belarger than 4 cm from the primary vertex. As listed in Table 1, ad-ditional selection criteria on the DCA between the two



(

¯

) daughtertracks, betweenthe



(

¯

) and the bachelor track, and between the



(

¯

) and the primary vertex position were ap-plied to select



(

¯

). Furthermore, a cut on the pointing angle of the



(

¯

) candidate track with respect to the primary ver-tex (

|(

V

−

VP V

)

×

p

|

/

|

V

−

VP V

||

p

|

, where V is the

posi-tion ofthe



(

¯

) candidateandthe primary vertex, respectively and p isthe momentumof



(

¯

))was applied to selectan



(

¯

). To reduce the combinatorial background, the



(

¯

) candi-dateswereselectedintheinvariantmassrangebetween1.112and 1.120 GeV

/

c2. In addition, the

( ¯

)

candidates due to misiden-tification of the

π

− (

π

+) tracks asthe bachelor K− (K+) tracks

were removed by checking a



hypothesis. To check the



hy-pothesis,the

π

masswasassignedtoeachbachelortrackandthe

invariant mass was reconstructed for each pair of a



and the

bachelortrack.Ifthereconstructedinvariant massofthepairwas intherange1

.

306

<

Mass

<

1

.

336 GeV

/

c2,thepairwasrejected. Theinvariantmassdistributionsofcombined



and

¯

candidates for0–40% and40–80% Au

+

Aucollisionsat

√

sNN

=

200 GeVfor

thetransverse momentum(pT)ranges 1

.

5

<

pT

<

2

.

0 GeV/c and

Table 1

Selectioncriteriaforand ¯reconstruction.

Selectioncriteria 0–40% 40–80%

pT<2.5 GeV/c pT>2.5 GeV/c All pT

DCA <0.6 cm <0.7 cm <0.8 cm

DCA >0.4 cm >0.3 cm >0.3 cm

DL() >4.0 cm >4.0 cm >4.0 cm DL() >6.0 cm >6.0 cm >5.0 cm |(V−VP V)×p|/|V−VP V||p| <0.05 <0.08 <0.15

D L() <D L() Yes Yes Yes

proton DCA >0.8 cm >0.8 cm >0.6 cm pion DCA >2.0 cm >2.0 cm >1.8 cm bachelor DCA >1.2 cm >1.2 cm >1.0 cm proton to pion DCA <0.8 cm <0.8 cm <1.0 cm

Fig. 2. Reconstructedinvariantmass(M)distributionsofcombinedand

¯

samplefor0–40% Au+Aucollisionsat√sNN=200 GeVforthetransversemomentum(pT)range 1.5<pT<2.0 GeV/c (a)and3.0<pT<3.5 GeV/c (b).Theinvariantmassdistributionsofcombinedand ¯samplefor40–80% Au+Aucollisionsat√sNN=200 GeV forthetransversemomentum(pT)range1.5<pT<2.0 GeV/c (c)and3.0<pT<3.5 GeV/c (d).Thesolidlinesat1.665and1.679 GeV/c2showthemassregionofthe reconstructedand ¯candidatesusedforthemeasurementoftheproton–correlationfunction.

3

.

0

<

pT

<

3

.

5 GeV/c are shown in Fig. 2(a–d). The signal (S) tosignal

+

background(S

+

B) ratio,integratedover

±

3

σ

,is 0.2 forthe pT range1

.

5

<

pT

<

2

.

0 GeV/c and0.4 forthe pT range 3

.

0

<

pT

<

3

.

5 GeV/c in the 0–40% centralitybin, andis 0.3 for the pT range 1

.

5

<

pT

<

2

.

0 GeV/c and 0.7 for the pT range 3

.

0

<

pT

<

3

.

5 GeV/c inthe 40–80%centralitybin.All

( ¯

)

can-didateswiththeinvariant massbetween1.665 and1.679 GeV

/

c2

wereusedintheanalysis.

2.3. Two-particlecorrelationfunction

Thetwo-particlecorrelationfunctionisdefinedas:

Cmeasured

(

k∗

)

=

A

(

k∗

)

B

(

k∗

)

,

(1)

where A

(

k∗

)

isthe distribution ofthe invariant relative momen-tum,k∗

= | 

k∗

|

is the relative momentum of one of the particles inthepairrestframe,foraprotonand



pairoranti-protonand

¯

pair from the same event. B

(

k∗

)

is the referencedistribution generatedbymixingparticlesfromdifferenteventswiththesame centralityandwithapproximatelythesamevertexpositionalong the z-direction. The samesingle- and pair-particle cutswere ap-pliedfor the realand mixedevents.The data analysis was done

in nine centrality bins: 0–5%, 5–10%, 10–20%, 20–30%, 30–40%,

40–50%, 50–60%, 60–70% and 70–80% for both the same events

andthe mixedevents.The final resultswere combined and

pre-sented intwo centrality bins: 0–40% and 40–80%.The efficiency

andacceptanceeffectscanceledoutintheratio A

(

k∗

)/

B

(

k∗

)

.

Cor-rectionstotherawcorrelationfunctionswereappliedaccordingto theexpression:

C

(

k∗

)

=

Cmeasured

(

k

∗

₎

₋

₁

P

(

k∗

)

+

1

,

(2)

where the pair-purity, P

(

k∗

)

, was calculated as a product of S

/

(

S

+

B

)

forthe



(

¯

) andpurityofthe proton(antiproton). The selectedsample oftheprotoncandidatesalsoincludedsecondary protons from



,



and



decays.The estimatedfraction of the primary protons (antiprotons)fromthe thermalmodel [42] stud-iesis52%(48%) [43].Thepurityoftheprotonsampleisobtained as a product ofidentification probability andfraction ofprimary protons.Thepair-purityis0.2(0.36)forthe0–40%(40–80)% cen-tralitybinandisconstantovertheanalyzedrangeoftheinvariant

relativemomentum.

Theeffectofmomentumresolutiononthecorrelationfunctions hasalsobeeninvestigatedusingsimulatedtracksfromthe



de-cay andthetracks forprotons,withknownmomenta,embedded

intotherealevents.Correlationfunctionshavebeencorrectedfor themomentumresolutioneffectusingtheexpression:

C

(

k∗

)

=

C



₍

_k∗

₎

_C in

(

k∗

)

Cres

(

k∗

)

,

(3)

where C

(

k∗

)

represents the corrected correlation function, and

Cin

(

k∗

)/

Cres

(

k∗

)

is the correction factor. Cin

(

k∗

)

was calculated

without taking into account the effect of momentum resolution

Fig. 3. Measuredcorrelationfunction(C(k∗))forproton–andantiproton–¯(P+ ¯P¯)for(0–40)% (a)and(40–80)% (b)Au+Aucollisionsat√sNN=200 GeV.Thetriangles representrawcorrelations,opencirclesrepresentpair-puritycorrected(PP)correlations,andsolidcirclesrepresentpair-purityandsmearingcorrected(PP+SC)correlations. Theerrorbarscorrespondtostatisticalerrorsandcapscorrespondtothesystematicerrors.ThepredictionsfromRef. [24] forproton–interactionpotentialsVI(red),VII (blue)andVIII(green)forsourcesizesRp=R=5 fmandRp=R=2.5 fmareshownin(a)and(b)respectively.

resolutiononthecorrelationfunctionsisnegligiblecomparedwith statisticalerrors.

To study the shape of the correlation function for the back-ground,thecandidatesfromtheside-bandsoftheinvariant mass of



were chosen in the range M

<

1

.

665 GeV/c2 _{and M}

_>

1

.

679 GeV/c2_{.Theseselectedcandidateswerethencombinedwith}

the proton tracks from the same eventto construct the relative

momentum for the same event. The relative momentum for the

mixed event is generated by combining the selected candidates fromtheside-bandsoftheinvariantmassof



withprotonsfrom differenteventswithapproximatelythesamevertexpositionalong thez-direction.

3. Resultsanddiscussion

After applying the selection criteria for the proton and



identification, as mentioned in the data analysis section, a to-tal of 38065

±

195 (8816

±

94) and 3037

±

55 (679

±

26) pairs of proton–



and antiproton–

¯

for k∗

<

0

.

2 (0.1) GeV/c are ob-served for 0–40% and 40–80% Au

+

Au collisions, respectively. The measured proton–



andantiproton–

¯

correlation functions, P



+ ¯

P

¯

,thecorrelationfunctionsaftercorrectionforpair-purity,

P



+ ¯

P

¯

(PP), andthe correlation functions aftercorrection for pair-purity and momentum smearing, P



+ ¯

P

¯

(PP

+

SC), for

0–40% and 40–80% Au

+

Au collisions at

√

sN N

=

200 GeV are

shownin Fig.3(a)and3(b).Thesystematicerrors forthe mea-suredproton–



correlationfunctionwereestimatedbyvaryingthe followingrequirementsfortheselectionof



candidates: the de-cay length, DCAof



to the primary vertex, pointing anglecuts andmassrange,whichaffectthepurityofthe



sample.TheDCA andm2 requirements were varied to estimate the systematic er-rorfromtheprotonpurity.Inaddition,thesystematicerrorsfrom normalizationand feed-down contributions were also estimated. The systematicerrors fromdifferentsources were then addedin quadrature.ThecombinedsystematicerrorsareshowninFig.3as capsforeachbinofthecorrelationfunction.

Predictionsfortheproton–



correlationfunctionfromRef. [24] fortheproton–



interactionpotentialsVI,VII andVIII forastatic source withsizes Rp

=

R

=

5

.

0 fm and Rp

=

R

=

2

.

5 fm are

also shown in Fig. 3(a) and Fig. 3(b). The selected source sizes are not fit to the experimental data. The choice of the poten-tials inRef. [24] is based onan attractive N



interaction in the

5_S

2 channel fromthe lattice QCD simulations withheavy u-, d-, s-quarks from Ref. [16]. The potential VII is obtained by fitting the lattice QCD data with a function V

(

r

)

=

b1e−b2r2

+

_b3

₍

₁

−

e−b4r2

₎₍

_e−b5r

_/

_r

₎

2_{, where b1 andb3 are negative andb2, b4 and} b5arepositive,whichrepresentsacasewithashallowN



bound

state. Twomorepotentials VI and VIII representcaseswithouta N



boundstateandwithadeepN



boundstate,respectively.The binding energies(Eb), scatteringlengths(a0) andeffectiveranges

(reff) forthe N



interactionpotentials VI, VII and VIII arelisted inTable2[24].ThemeasuredcorrelationfunctionforP



+ ¯

P

¯

is in agreement with the predicted trend with the interaction po-tentials VI, VII and VIII in 0–40% Au

+

Au collisions as shown in Fig. 3(a). However, due to limited statistics at the lower k∗, strong enhancement dueto the Coulomb interaction is not visi-blein40–80%Au

+

AucollisionsinFig.3(b).

The measured proton–



and antiproton–

¯

correlation func-tions include three effects coming from the elastic scattering in the5S2 channel,thestrongabsorptioninthe3S1 channelandthe long-rangeCoulombinteraction.TheCoulombinteractionbetween thepositivelychargedprotonandnegativelycharged



introduces astrongenhancement inthecorrelationfunction atthesmallk∗, asseeninFig.3.One canremove theCoulomb enhancement us-ing a Gamow factor [45], however, thissimple correction is not good enough to extract the characteristic feature of the correla-tionfunctionfromthestronginteraction.Afullcorrectionwiththe source-sizedependenceisneededtoisolatetheeffectofthestrong interactionfromtheCoulombenhancement.Therefore,theratioof thecorrelationfunctionbetweensmallandlargecollisionsystems, isproposedinRef. [24] asamodel-independentwaytoaccessthe strong interactionwith lesscontamination fromthe Coulomb in-teraction.

The ratioof thecombined proton–



andantiproton–

¯

corre-lation function from the peripheral (40–80%) to central (0–40%) collisions,definedasR

=

C40–80/C0–40isshowninFig.4.The

Table 2

Bindingenergy(Eb),scatteringlength(a0)andeffective

range(reff)fortheSpin-2proton–potentials [24].

Spin-2 ppotentials VI VII VIII

Eb(MeV) – 6.3 26.9

a0(fm) −1.12 5.79 1.29

reff(fm) 1.16 0.96 0.65

Fig. 4. Thesolidcirclerepresentstheratio(R)ofsmallsystem(40–80% collisions)tolargesystem(0–40% collisions)forproton–andantiproton–¯( P+ ¯P¯),whereboth thecorrelationfunctionsarecorrectedforpair-purityandmomentumsmearing.Theerrorbarscorrespondtothestatisticalerrorsandcapscorrespondtothesystematic errors.Theopencrossesrepresenttheratioforbackgroundcandidatesfromtheside-bandsofaninvariantmass.Predictionsfortheratioofthesmallsystemtolarge system [24,48] forproton–interactionpotentialsVI(red),VII(blue)andVIII(green)forstaticsourcewithdifferentsourcesizes(S,L)

= (

2,3),(2,4),(2.5,5)and(3,5)fm, whereSandLcorrespondingtosmallandlargesystems,areshownin(a),(b),(c)and(d)respectively.Inaddition,thepredictionfortheexpandingsourceisshownin(e).

ofthesourcesizes for

π

–

π

,K0_S–K0_S,proton–protonandproton–



correlationsshow that thesource sizedecrease asthetransverse massincreases [22,44,43,46,47].Usingthistransversemass depen-dence [47],theexpectedsourcesizeforproton–



is2–3 fmforthe peripheralcollisionsand3–5 fmforthecentralcollisions.The pre-dictionsfortheratioofthesmallsystemtothelargesystemfrom Refs. [24,48] for the proton–



interaction potentials VI, VII and VIII fora staticsource withdifferentsource sizes (S,L)

= (

2

,

3

)

,

(

2

,

4

)

,

(

2

.

5

,

5

)

and

(

3

,

5

)

fm,whereSandLcorrespondtothesmall andlarge collisionsystems,respectively,areshowninFig.4(a–d). Asmallvariationinthesourcesizedoesnotchangethe character-isticoftheratioforthechoiceofthreepotentials.

Predictionsforthe ratioof the smallsystemto the large sys-tem with the effects of collective expansion are also shown in Fig.4(e) [24].ThetransversesourcesizesaretakenasRtrp

=

Rtr

=

2

.

5 fmforthesmallsystemandRtrp

=

Rtr

=

5 fmforthelarge

sys-tem.Thetemperatureatthethermalfreeze-outisTp,

=

164 MeV

forthe peripheral collisions and Tp,

=

120 MeV forthe central

collisions [49,50] and the proper-time at the thermal freeze-out is

τ

p(

τ



)

=

3

(

2

)

fm/c for the peripheral collisions and

τ

p

(

τ



)

=

20

(

10

)

fm/c forthecentralcollisions [51].

The predictions with an expanding source for the proton–



interaction potentials VI and VII are 3

σ

larger than the data at k∗

=

20 MeV/c. The predictions forthe proton–



interaction po-tential VIII withan expandingsource or staticsource are within 1

σ

ofthedataatk∗

=

20 MeV/c.AsshowninFig.4,themeasured ratios atk∗

=

20 and 60 MeV/c are R

=

0

.

28

±

0

.

35stat

±

0

.

03sys (background

=

0

.

96

±

0

.

13stat) and R

=

0

.

81

±

0

.

22stat

±

0

.

08sys (background

=

0

.

97

±

0

.

05stat), respectively. The measured ratios atk∗

=

20 and 60 MeV/c arecomparedinFig. 5withthe model

calculations for the ratio of the correlation function for the pe-ripheraltothe centralcollisions andthe scatteringlength forthe proton–



interactionfromtheRef. [24].Fromthecomparison, we conclude that our data favora positive scattering length for the proton-



interaction.Thepositive scatteringlength andthe mea-sured ratio ofthe proton–



correlation function from peripheral to central collisions lessthanunity fork∗

<

40 MeV/c favorsthe proton–



interaction potential VIII withEb

∼

27 MeV forproton

and



. 4. Conclusions

The first measurement of the proton–



correlation functions in heavy-ion collisions is presented in this Letter. The measured ratiooftheproton–



correlationfunctionfromperipheralto

cen-tral Au

+

Au collisions at

√

sNN

=

200 GeV is compared with

thepredictionsbasedontheproton–



interactionextractedfrom

(

2

+

1

)

-flavor lattice QCD simulations. At present, dueto limited statistics, it is not possible to extract the interaction parameters.

However the measured ratio of the proton–



correlation

func-tion fromperipheralto centralcollisions lessthan unityfork∗

<

40 MeV/c within1

σ

indicatesthatthescatteringlengthispositive fortheproton–



interactionandfavorstheproton–



boundstate hypothesis.

Acknowledgements

Fig. 5. Themeasuredratioofthecorrelationfunctionsbetween40–80%collisions and0–40%collisions,R,fork∗=20 (red)and60(blue)MeV/c arecomparedwith predictionsfromRef. [24] fortheratioasafunctionof1/a0,wherea0isscattering length.Thebandsrepresentstatisticalerrorsonthemeasurement.

BNL,theNERSCCenteratLBNL,andtheOpenScienceGrid consor-tiumforprovidingresourcesandsupport.Thisworkwassupported inpart by the Office of Nuclear Physics within the U.S. DOE Of-ficeofScience,theU.S. NationalScience Foundation,theMinistry ofEducation andScienceoftheRussianFederation, National Nat-ural Science Foundation of China, Chinese Academy of Sciences,

the Ministry of Science and Technology of China (973 Program

No. 2014CB845400, 2015CB856900) and the Chinese Ministry of

Education,the NationalResearchFoundation of Korea, Czech Sci-enceFoundation andMinistry of Education, Youth andSports of theCzechRepublic,DepartmentofAtomicEnergyandDepartment of Science and Technology of the Government of India, the Na-tionalScienceCentreofPoland,theMinistryofScience,Education andSportsoftheRepublicofCroatia,ROSATOM ofRussiaand Ger-manBundesministeriumfürBildung,Wissenschaft,Forschungund Technologie (BMBF)andtheHelmholtzAssociation.

References

[1]A.R.Bodmer,Phys.Rev.D4(1971)1601. [2]E.Witten,Phys.Rev.D30(1984)272.

[3]J.H.Chen,D.Keane,Y.G.Ma,A.H.Tang,Z.B.Xu,Phys.Rep.760(2018)1. [4]M.Prakash,J.M.Lattimer,Nucl.Phys.A639(1998)433c.

[5]H.J.Schulze,A.Polls,A.Ramos,I.Vidana,Phys.Rev.C73(2006)058801. [6]S.Weissenborn,D.Chatterjee,J.Schaffner-Bielich,Nucl.Phys.A881(2012)62.

[7]S.Petschauer,J.Haidenbauer,N.Kaiser,U.-G.Maißner,W.Weise,Eur.Phys.J.A 52(2016)15.

[8]R.Jaffe,Phys.Rev.Lett.38(1977)195.

[9]V.G.J.Stoks,T.A.Rijken,Phys.Rev.C59(1999)3009.

[10]Z.Y.Zhang,Y.W.Yu,C.R.Ching,T.H.Ho,Z.D.Lu,Phys.Rev.C61(2000)065204. [11]R.Machleidt,I.Slaus,J.Phys.G27(2001)R69.

[12]T.Inoue,etal.,HALQCDCollaboration,Prog.Theor.Phys.124(2010)591. [13]S.R.Beane,etal.,NPLQCDCollaboration,Phys.Rev.Lett.106(2011)162001. [14]T.Inoue,etal.,HALQCDCollaboration,Phys.Rev.Lett.106(2011)162002. [15]T.Inoue,etal.,HALQCDCollaboration,Nucl.Phys.A881(2012)28. [16]F.Etminan,etal.,HALQCDCollaboration,Nucl.Phys.A928(2014)89. [17]B.I.Abelev,etal.,STARCollaboration,Science328(2010)58. [18]L.Adamczyk,etal.,STARCollaboration,Phys.Rev.C97(2018)054909. [19]A.Gal,E.V.Hungerford,D.J.Millener,Rev.Mod.Phys.88(2016)035004,and

referencestherein.

[20]J.Adams,etal.,STARCollaboration,Phys.Rev.Lett.98(2007)062301. [21]L.Adamczyk,etal.,STARCollaboration,Phys.Rev.Lett.114(2015)022301. [22]L.Adamczyk,etal.,STARCollaboration,Nature527(2015)345.

[23]S.Acharya,etal.,ALICECollaboration,arXiv:1805.12455.

[24]K.Morita,A.Ohnishi,F.Etminan,T.Hatsuda,Phys.Rev.C94(2016),031901 (R).

[25]T.Goldman,K.Maltman,G.J.Stephenson,K.E.Schmidt,F.Wang,Phys.Rev.Lett. 59(1987)627.

[26]B.Schwesinger,F.G.Scholtz,H.B.Geyer,Phys.Rev.D51(1995)1228. [27]M.Oka,Phys.Rev.D38(1988)298.

[28]H.Pang,J.Ping,F.Wang,T.Goldman,E.Zhao,Phys.Rev.C69(2004)065207. [29]H.Pang,J.Ping,L.Chen,F.Wang,T.Goldman,Phys.Rev.C70(2004)035201. [30]M.Chen,H.Huang,J.Ping,F.Wang,Phys.Rev.C83(2011)015202. [31]H.Huang,J.Ping,F.Wang,Phys.Rev.C92(2015)065202. [32]Q.B.Li,P.N.Shen,Eur.Phys.J.A8(2000)417.

[33]N.Shah,Y.G.Ma,J.H.Chen,S.Zhang,Phys.Lett.B754(2016)6.

[34]K.H. Ackermann, et al., STAR Collaboration, Nucl. Instrum. Methods A 499 (2003)624.

[35]M.Anderson,etal.,Nucl.Instrum.MethodsA499(2003)659.

[36]W.J.Llope,STARCollaboration,Nucl.Instrum.MethodsA661(2012)S110. [37]W.J.Llope,etal.,Nucl.Instrum.MethodsA759(2014)23.

[38]M.L.Miller,etal.,Annu.Rev.Nucl.Part.Sci.57(2007)205.

[39]L.Adamczyk,etal.,STARCollaboration,Phys.Rev.Lett.118(2017)212301; G.Contin,etal.,Nucl.Instrum.MethodsA907(2018)60.

[40]C.Patrignani,etal.,ParticleDataGroup,Chin.Phys.C40(2016)100001. [41]M.Shao,O.Y.Barannikova,X.Dong,Y.Fisyak,L.Ruan,P.Sorensen,Z.Xu,Nucl.

Instrum.MethodsA558(2006)419.

[42]P.Braun-Munzinger,J.Stachel,Nucl.Phys.A606(1996)320; P.Braun-Munzinger,I.Heppe,J.Stachel,Phys.Lett.B465(1999)15; P.Braun-Munzinger,D.Magestro,K.Redlich,J.Stachel,Phys.Lett.B518(2001) 41.

[43]J.Adams,etal.,STARCollaboration,Phys.Rev.C74(2006)064906. [44]J.Adams,etal.,STARCollaboration,Phys.Rev.C71(2005)044906. [45]UrsAchimWiedemann,UlrichHeinz,Phys.Rep.319(1999)145. [46]B.I.Abelev,etal.,STARCollaboration,Phys.Rev.C74(2006)054902. [47] H.Zbroszczyk,Studiesofbaryon–baryoncorrelationsinrelativisticnuclear

col-lisions registeredattheSTARexperiment,PhDthesis,https://drupal.star.bnl. gov/STAR/files/Zbroszczyk_Hanna.pdf.

[48] PrivatecommunicationswithKenjiMorita,AkiraOhnishi,FaisalEtminanand TetsuoHatsuda.