J/ψ production cross section and its dependence on charged-particle multiplicity in p + p collisions at s=200 GeV

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

J

/ψ

production

cross

section

and

its

dependence

on

charged-particle

multiplicity

in

p

+

p collisions

at

√

s

=

200 GeV

STAR

Collaboration

J. Adam

i

,

L. Adamczyk

a

,

J.R. Adams

ae

,

J.K. Adkins

u

,

G. Agakishiev

s

,

M.M. Aggarwal

ag

,

Z. Ahammed

bd

,

N.N. Ajitanand

ar

,

I. Alekseev

q

,

ab

,

D.M. Anderson

at

,

R. Aoyama

ax

,

A. Aparin

s

,

D. Arkhipkin

c

,

E.C. Aschenauer

c

,

M.U. Ashraf

aw

,

F. Atetalla

t

,

A. Attri

ag

,

G.S. Averichev

s

,

X. Bai

g

,

V. Bairathi

ac

,

K. Barish

az

,

A.J. Bassill

az

,

A. Behera

ar

,

R. Bellwied

av

,

A. Bhasin

r

,

A.K. Bhati

ag

,

J. Bielcik

j

,

J. Bielcikova

k

,

L.C. Bland

c

,

I.G. Bordyuzhin

q

,

J.D. Brandenburg

al

,

A.V. Brandin

ab

,

D. Brown

y

,

J. Bryslawskyj

az

,

I. Bunzarov

s

,

J. Butterworth

al

,

H. Caines

bg

,

M. Calderón de la Barca Sánchez

e

,

J.M. Campbell

ae

,

D. Cebra

e

,

I. Chakaberia

t

,

ap

,

P. Chaloupka

j

,

F.-H. Chang

ad

,

Z. Chang

c

,

N. Chankova-Bunzarova

s

,

A. Chatterjee

bd

,

S. Chattopadhyay

bd

,

J.H. Chen

aq

,

X. Chen

ao

,

X. Chen

w

,

J. Cheng

aw

,

M. Cherney

i

,

W. Christie

c

,

G. Contin

x

,

H.J. Crawford

d

,

S. Das

g

,

T.G. Dedovich

s

,

I.M. Deppner

ba

,

A.A. Derevschikov

ai

,

L. Didenko

c

,

C. Dilks

ah

,

X. Dong

x

,

J.L. Drachenberg

v

,

J.C. Dunlop

c

,

L.G. Efimov

s

,

N. Elsey

bf

,

J. Engelage

d

,

G. Eppley

al

,

R. Esha

f

,

S. Esumi

ax

,

O. Evdokimov

h

,

J. Ewigleben

y

,

O. Eyser

c

,

R. Fatemi

u

,

S. Fazio

c

,

P. Federic

k

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P. Federicova

j

,

J. Fedorisin

s

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P. Filip

s

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E. Finch

ay

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c

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a

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C. Markert

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at

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ac

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B. Mohanty

ac

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M.M. Mondal

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I. Mooney

bf

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D.A. Morozov

ai

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Md. Nasim

f

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d

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bg

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M. Nie

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G. Nigmatkulov

ab

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T. Niida

bf

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L.V. Nogach

ai

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T. Nonaka

ax

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S.B. Nurushev

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G. Odyniec

x

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A. Ogawa

c

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K. Oh

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S. Oh

bg

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V.A. Okorokov

ab

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D. Olvitt Jr.

as

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B.S. Page

c

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R. Pak

c

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Y. Panebratsev

s

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B. Pawlik

af

,

H. Pei

g

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C. Perkins

d

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J. Pluta

be

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J. Porter

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M. Posik

as

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E-mailaddress:yezhenyu@uic.edu(Z. Ye). https://doi.org/10.1016/j.physletb.2018.09.029

N.K. Pruthi

ag

,

M. Przybycien

a

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J. Putschke

bf

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A. Quintero

as

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S.K. Radhakrishnan

x

,

S. Ramachandran

u

,

R.L. Ray

au

,

R. Reed

y

,

H.G. Ritter

x

,

J.B. Roberts

al

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O.V. Rogachevskiy

s

,

J.L. Romero

e

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L. Ruan

c

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J. Rusnak

k

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O. Rusnakova

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S. Salur

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J. Sandweiss

bg

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au

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A.M. Schmah

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c

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N. Schmitz

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F. Seck

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J. Seger

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M. Sergeeva

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R. Seto

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aq

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P.V. Shanmuganathan

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W.Q. Shen

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W. Solyst

p

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bc

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bg

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ab

,

B. Stringfellow

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an

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T. Sugiura

ax

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ao

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X. Sun

g

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X.M. Sun

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B. Surrow

as

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D.N. Svirida

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P. Szymanski

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Z. Tang

ao

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A.H. Tang

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A. Taranenko

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m

a_{AGHUniversityofScienceandTechnology,FPACS,Cracow30-059,Poland} b_{ArgonneNationalLaboratory,Argonne,IL 60439}

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

j_{CzechTechnicalUniversityinPrague,FNSPE,Prague,11519,CzechRepublic} k_{NuclearPhysicsInstituteASCR,Prague25068,CzechRepublic}

l_{TechnischeUniversitatDarmstadt,Germany}

m_{FrankfurtInstituteforAdvancedStudiesFIAS,Frankfurt60438,Germany} n_{FudanUniversity,Shanghai,200433}

o_{InstituteofPhysics,Bhubaneswar751005,India} p_{IndianaUniversity,Bloomington,IN 47408}

q_{AlikhanovInstituteforTheoreticalandExperimentalPhysics,Moscow117218,Russia} r_{UniversityofJammu,Jammu180001,India}

s_{JointInstituteforNuclearResearch,Dubna,141980,Russia} t_{KentStateUniversity,Kent,OH 44242}

u_{UniversityofKentucky,Lexington,KY 40506-0055} v_{LamarUniversity,PhysicsDepartment,Beaumont,TX 77710}

w_{InstituteofModernPhysics,ChineseAcademyofSciences,Lanzhou,Gansu730000} x_{LawrenceBerkeleyNationalLaboratory,Berkeley,CA 94720}

y_{LehighUniversity,Bethlehem,PA 18015}

z_{Max-Planck-InstitutfurPhysik,Munich80805,Germany} aa_{MichiganStateUniversity,EastLansing,MI 48824}

ab_{NationalResearchNuclearUniversityMEPhI,Moscow115409,Russia} ac_{NationalInstituteofScienceEducationandResearch,HBNI,Jatni752050,India} ad_{NationalChengKungUniversity,Tainan70101}

ae_{OhioStateUniversity,Columbus,OH 43210}

af_{InstituteofNuclearPhysicsPAN,Cracow31-342,Poland} ag_{PanjabUniversity,Chandigarh160014,India} ah_{PennsylvaniaStateUniversity,UniversityPark,PA 16802} ai_{InstituteofHighEnergyPhysics,Protvino142281,Russia} aj_{PurdueUniversity,WestLafayette,IN 47907}

ak_{PusanNationalUniversity,Pusan46241,RepublicofKorea} al_{RiceUniversity,Houston,TX 77251}

am_{RutgersUniversity,Piscataway,NJ 08854}

an_{UniversidadedeSaoPaulo,SaoPaulo,05314-970,Brazil} ao_{UniversityofScienceandTechnologyofChina,Hefei,Anhui230026} ap_{ShandongUniversity,Jinan,Shandong250100}

aq_{ShanghaiInstituteofAppliedPhysics,ChineseAcademyofSciences,Shanghai201800} ar_{StateUniversityofNewYork,StonyBrook,NY 11794}

au_{UniversityofTexas,Austin,TX 78712} av_{UniversityofHouston,Houston,TX 77204} aw_{TsinghuaUniversity,Beijing100084}

ax_{UniversityofTsukuba,Tsukuba,Ibaraki305-8571,Japan} ay_{SouthernConnecticutStateUniversity,NewHaven,CT 06515} az_{UniversityofCalifornia,Riverside,CA 92521}

ba_{UniversityofHeidelberg,Heidelberg,69120,Germany} 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: Received11May2018

Receivedinrevisedform12September 2018

Accepted15September2018 Availableonline19September2018 Editor:H.Weerts

Keywords: Quarkonium p+p collisions

Multiplepartoninteractions Charged-particlemultiplicity

Wepresentameasurementofinclusive J/ψ productionatmid-rapidity(|y|

<

1)inp+p collisionsata center-of-massenergyof√s₌200 GeVwiththeSTARexperimentattheRelativisticHeavyIonCollider (RHIC). Thedifferentialproductioncross sectionfor J/ψ asafunctionoftransverse momentum(pT)

for0

<

pT<14 GeV/c andthetotalcrosssectionarereportedandcomparedtocalculationsfromthe

colorevaporationmodelandthenon-relativisticQuantumChromodynamicsmodel.Thedependenceof

J/ψ relativeyields inthree pT intervalsoncharged-particle multiplicity atmid-rapidityis measured

forthefirsttimeinp+p collisionsat√s=200 GeVandcomparedwiththatmeasuredat√s=7 TeV, PYTHIA8andEPOS3MonteCarlogenerators,andthePercolationmodelprediction.

©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

1. Introduction

Quarkonia are bound states of heavy quark–antiquark pairs

( QQ ).

¯

Their production in p

+

p collisions can be factorized into hard and soft processes associated withshort and long distance stronginteractions, respectively[1]. Theformer isrelatedto pro-ductionof

Q

Q from

¯

hardpartonscatteringsandcanbecalculated byperturbative QuantumChromodynamics(pQCD). Thelatter in-volves evolution of QQ into

¯

bound quarkonium states and is

usually parameterized by phenomenological models such as the

Color-Evaporation Model (CEM), Color Singlet Model, and

Non-Relativistic Quantum Chromodynamics (NRQCD) including both

color singlet and octet intermediate states (for a recent review see [2]). With sizable theoretical uncertainties, these model

cal-culations can describe the measurement results of quarkonium

production cross sections from the Tevatron and Large Hadron

Collider(LHC)experiments[3–6].Precisemeasurementsof quarko-niumproductionoverawidekinematicrangeatRHICenergiescan provide new constraints on model calculations and insights into

thequarkoniumproductionmechanism.

RecentstudiesattheLHChaverevealedafaster-than-linear in-creasein J

/ψ

and D-meson relative yields withcharged-particle multiplicity(nch)atmid-rapidityin p

+

p collisions at

√

s

=

7 TeV [7,8],suggestingastrongcorrelationbetweenhardparton scatter-ingsproducingheavyflavorparticlesandsoftunderlyingprocesses producingall otherparticles.ByincludingMultiple-Partonic Inter-actions (MPI) [9–11], i.e. several interactions at the parton level occurringinasingle

p

+

p collision, PYTHIA8 [12] andEPOS3 [13] MonteCarlo(MC) generators can produce an increase in relative yields of heavy flavor particles with nch, but underestimate the observedyieldsatlarge

n

ch [8].Additionaleffectshavebeen sug-gestedto explainthe measurementresultsattheLHC.For exam-ple,collectiveexpansionimplementedinEPOS3MCgenerator [14] is found to modify the pT distribution of final state particles in highmultiplicity

p

+

p collisions at

√

s

=

7 TeV,producinga faster-than-linear increase for D-meson relative yields at intermediate

andhigh pT [8].Such an effect ishoweverexpectedto be small atRHIC energies. On the other hand,the percolationmodel [15] producesparticles throughinteractionsofcolorstrings,whichare

more suppressed for soft processes than hard processes due to

thedifferentsizeofthecolorstrings.Itcanalsoproducea faster-than-linearincreaseinrelativeyieldsofheavyflavorparticleswith

nch that is qualitatively consistent with theLHC results. Such an increaseispredictedtobesimilaratdifferentenergiesbythe per-colation model. Measurements of relative yields of heavy flavor particlesversus

n

ch atRHICenergiescanhelpconstrainmodel cal-culationsandprovideknowledgeoftheenergydependenceofMPI in

p

+

p collisions.

Inthisletter,wepresentnewresultsofinclusive J

/ψ

produc-tion atmid-rapidity(

|

y

|

<

1) in p

+

p collisions at

√

s

=

200 GeV withtheSTARexperimentatRHIC[16].Both thedifferential pro-ductioncrosssectionfor J

/ψ

asafunctionoftransverse momen-tum (pT) and the total cross section are obtained with higher precision than the previously published results [17,18]. The de-pendence of J

/ψ

relative yields on nch at mid-rapidity is also determined,forthefirsttime,for

p

+

p collisions atRHICenergies. Theseresultsarecomparedtocalculationsfromvarioustheoretical modelsandMCgenerators.

2. STARexperimentanddataanalysis

The data used in this measurement were collected with

minimum-bias (MB) and high-tower (HT) triggers in p

+

p

colli-sions at

√

s

=

200 GeVby theSTARexperimentin2012. TheMB triggersselectnon-singlediffractive p

+

p collisions witha coinci-dencesignalfromthetwoVertexPositionDetectors(VPD) [19] or thetwoBeamBeamCounters(BBC) [20].TheVPDandBBCare lo-catedonboth sidesofthe p

+

p collision region andcovering the pseudo-rapidity region of 4.4

<

|

η

|

<

4.9 or 3.3

<

|

η

|

<

5.0, re-spectively.TheVPD-triggeredMBeventsareanalyzedtostudythe

Fig. 1. (Coloronline.)Invariant massdistributionsforunlike-signpairs(blacksquares),like-signpairs(bluehistogram),anddifferencebetweenunlike- andlike-signpairs (redcircles)fromtheVPD- (left),HT0- (middle)andHT2-triggered(right)eventsinp+p collisionsat√s=200 GeVin2012.TheredcurveisthecombinedfitwithaCrystal Ball(CB)functionanda1st-orderpolynomialfunctionrepresentingsignalandresidualbackground,respectively.

10 nb−1) is significantly larger than that of the BBC-triggered MB events (about 2.66 million). The latter are used to obtain the nch distribution in MB p

+

p collisions, since the BBC has a much higher triggerefficiency than the VPD for low multiplicity

p

+

p collisions. TheHTtriggersselectp

+

p collisions producingat leastonehigh-pT particlewithlargeenergydepositioninthe Bar-relElectromagneticCalorimeter(BEMC) [21].Datacollectedbythe HT0(HT2)triggerwithanenergythresholdof

E

T

>

2.6 (4.2) GeV, corresponding to an integrated luminosity of 1.36 (23.5) pb−1, areanalyzedto study J

/ψ

productionwith pT

>

1.5 (4.0) GeV/c. The vertex positions of p

+

p collisions along the beam line di-rection can be reconstructed from TPC tracks (VT P C

z ) or from VPD signals (VV P D

z ). A cut of

|

VzT P C

|

<

50 cm is applied to en-suregoodTPCacceptance forallthe events.Anadditional cutof

|

VT P C

z

−

VzV P D

|

<

6 cmisappliedtoreducethepile-upbackground fromout-of-timecollisionsfortheVPD-triggeredMBevents.

ThemaindetectorsusedinthedataanalysisaretheTime Pro-jectionChamber(TPC) [22],Time-Of-Flightdetector(TOF) [23],and BEMC, all with full azimuthal coverage within

|

η

|

<

1. The TPC records trajectories of charged particles with pT

>

0.2 GeV/c in

a 0.5 T solenoid magnetic field and determines their momenta

andionization energylosses(dE/dx). Tracksare requiredto have amaximumdistanceoftheclosestapproachtothecollisionpoint of1cm,aminimumof20TPChits(outofamaximumof45),and a minimumof 11 TPChitsfor dE

/

dx calculation. The TOF (VPD) provides the stop (start) time of flight information for charged particles from the collision vertices to the TOF, while the BEMC measureselectromagneticenergydeposition.

J

/ψ

candidates are reconstructed through the J

/ψ

→

e+e−

channel, where electrons are identified usingthe specific energy lossinTPC,

dE

/

dx, thevelocity(β)calculatedfromthepathlength andtime offlight betweenthe collision vertexandTOF, andthe

ratiobetweenthemomentumandenergydepositionintheBEMC

(pc/E) [17].Thenormalized

dE

/

dx is definedas

n

σ

e

=

ln

(

dE

/

dx

)

−

ln

(

dE

/

dx

|

Bichsel

)

σ

ln(dE/dx)

,

(1)

where

dE

/

dx (dE

/

dx

|

Bichsel) isthemeasured(expected)value,and

σ

ln(dE/dx) is one standard deviation of the

ln

(

dE

/

dx

)

distribution.

The n

σ

e value is required to be within

(

−

1.9,3) forall electron candidates.

|

1/β

−

1

|

<

0.03 isrequiredforTOFassociatedelectron tracks,and0.3

<

pc

/

E

<

1.5 forBEMC-associatedcandidateswith

pT

>

1 GeV/c.Both daughtersof J

/ψ

candidates are requiredto passthe

n

σ

e requirement, andeitherthe

β

or pc

/

E requirement. ForHT-triggeredevents,at leastonedaughter of J

/ψ

candidates mustpassthe pc

/

E requirement andhaveanenergydepositionin

theBEMCthatishigherthanthecorrespondingHTtrigger thresh-old.

3. J

/ψ

productioncrosssection

Theinvariantmassspectraofthereconstructed J

/ψ

candidates fromdifferenttriggeredsamplesareshowninFig.1.The J

/ψ

raw yields are extractedby subtracting the invariant mass spectra of like-signelectronpairs(Me±e±)fromtheunlike-signones(Me±e∓).

The remaining distribution is fit by a two-component function,

composed ofa J

/ψ

signaldistribution,theshapeofwhichis ob-tained from STAR detector simulation [24] with the Crystal-Ball function[25],togetherwitharesidualbackgrounddistribution pa-rameterizedbya1st-orderpolynomialfunction.The J

/ψ

signalto the residualbackground ratiosin themass rangeof 2.9

<

Mee

<

3.2 GeV/c2 _{are18,36,and42fortheVPDMB,HT0andHT2data,}

respectively,andhavenegligibledependenceon

n

ch.Thelarge val-uesofthisratioreflectthat theresidualbackgroundissmalland can be neglected forthe measurement ofthe nch-dependenceof

J

/ψ

relativeyields.

The J

/ψ

productioncross sectionsare obtainedby correcting the J

/ψ

rawyieldsforthedetectorgeometric acceptanceand ef-ficiency. The vertex finding, track reconstruction, BEMC electron identification, VPD,BBC andHTtrigger efficiencies are estimated fromdetectorsimulation,whiletheelectronidentification efficien-ciesby TPC

dE

/

dx and TOF1/β requirementsareestimatedfrom data.ThecrosssectionsfromtheVPDMB, HT0andHT2 dataare consistentwitheachotherintheoverlapping pT regions,andare used for 0

<

pT

<

1.5, 1.5

<

pT

<

4.0 and 4.0

<

pT

<

14 GeV/c, respectively.Hereunpolarized J

/ψ

isusedinsimulationwhen cal-culating the J

/ψ

acceptance andefficiency,whichis around 20% for theVPD MB data,0.6–12% fortheHT0 data, and1.5–30%for theHT2data,respectively.Thelattertwoincreaseasafunctionof

J

/ψ

pT duetotheincreasingHTtriggerefficiency.

Thetotalsystematicuncertaintyforthemeasuredcrosssection is obtainedfromthe square rootofthe quadraticsumofthe in-dividualsystematicuncertaintieslistedinTable1,whichgenerally depend on the J

/ψ

signal significance in each pT bin. The un-certainty in the raw J

/ψ

yield extraction, estimated by varying thefittedmassrange,by changingtheresidualbackgroundshape from a1st-order polynomial function to an exponential function, andby comparingthefit resultto thebincountsin2.9

<

Mee

<

3.2 GeV/c2 _{corrected fortheresidual backgroundandfor the}

Table 1

Systematic uncertainties for the measurement of the J/ψproductioncrosssection.Seetextfordetails.

Type Uncertainty (%)

Raw yield extraction 1–14 Tracking efficiency 3–15 Electron identification efficiency 4–14 TOF-EMC efficiency correlation 1–7 HT trigger efficiency 4–13 (HT) Normalization 10 (MB)

8.5 (HT)

are3–15%and4–14%,respectively.SincetheTOFefficiencyis cal-culatedfromtracksmatchedwithBEMChits,thereisacorrection appliedtotheTOFefficiencybytheratiooftrueTOFefficiencyto thatcalculatedwithBEMC-matched tracks.Thiscorrectioncauses anuncertaintyof1–7%.TheHTtriggerefficiencyuncertainty, esti-matedbyvarying thetriggerrequirementindataandsimulation, is4–13%. An8% normalizationuncertaintydue tothe luminosity determinationis appliedforboth the MB andHTresults.An ad-ditional6% (3%) normalization uncertainty for the VPD MB (HT) resultisaddedfortheVPD(BBC)triggerandvertexreconstruction efficiency,makingthetotalnormalizationuncertainty10%(8.5%).

Fig.2showsthemeasured J

/ψ

productioncrosssectiontimes the J

/ψ

→

e+e− branching ratio (Bee) asa function of J

/ψ

pT. Thenewresultisconsistent withthepublished STAR [17] result, but has better statistical precision for pT

<

10 GeV/c. It is also consistent withthe published PHENIX [18] result, buthas better precisionfor

p

T

>

2 GeV/c.Thetotal J

/ψ

productioncrosssection timesthebranchingratioperrapidityunitisestimatedtobe

Bee

d

σ

dy

|

y=0

=

43

.

2

±

3

.

0

(

stat.

)

±

7

.

5

(

syst.

)

nb

.

(2)

Also shown in Fig. 2 are theoretical model calculations. The green band represents the resultfrom CEM calculations for 0

<

pT

<

14 GeV/c and

|

y

|

<

0.35 [3], the orange band shows that from Next-to-Leading Order (NLO) NRQCD calculations for 4

<

pT

<

14 GeV/c and

|

y

|

<

1 [4], the blue band depicts the re-sult fromNRQCD calculationsfor 0

<

pT

<

5 GeV/c and

|

y

|

<

1 whichincorporatesaColor-GlassCondensate(CGC)effectivetheory framework for small-x resummation[26], and the magentaband showsthatfromNLONRQCDcalculationsfor1.1

<

pT

<

10 GeV/c and

|

y

|

<

0.35 [5]. The CEM and NLO NRQCD calculations de-scribethe datareasonablywell fortheapplicable pT ranges.The CGC

+

NRQCDcalculationsareconsistentwiththedatawithin un-certainties, however, the data are close to the lower uncertainty boundary of the theoretical calculation. We note that the feed-downcontributionsfromhighercharmoniumstates

χ

c J and

ψ(2S)

areexplicitlyconsideredbythecalculationsinRefs. [4,26],butnot by the calculations in Refs. [3,5] where model parameters have been fitto inclusive J

/ψ

cross sections fromexperimental

mea-surements. We also note that the feed-down contribution from

bottom hadron decays is included in the experimental data but

notincludedinanyofthesecalculations,whichispredictedtobe approximately10–25%intherangeof4

<

pT

<

14 GeV/c [27,28]. Ascanbeseen,exceptforthetwobinsatthehighestpT,the un-certainties in the experimental results are smaller than those in thetheoreticalcalculations.Therefore,thenewSTARresultcanbe usedtoconstraintheoreticalmodelcalculations.

4. Dependenceof J

/ψ

productiononnch

The BBC-triggered MB data are used to characterize the nch distributionatmid-pseudorapidity(

|

η

| <

1)inMB p

+

p collisions.

The

n

ch distributionforp

+

p collisions producing J

/ψ

isobtained

Fig. 2. (Coloronline.)Top: J/ψ crosssectiontimesbranchingratioasafunctionofpT inp+p collisionsat√s=200 GeV.Solidcirclesarefromthisanalysisfor|y|<1;

Fig. 3. (Coloronline.)Thecorrectednchdistributionsatmid-rapidity(|η|<1)forMB

events(opencircles)and J/ψeventswith J/ψ pT greaterthan0(purplecircles),

1.5(bluesquares),and4GeV/c (redtriangles)inp+p collisionsat√s=200 GeV. Thefitfunctionisanegativebinomialfunction.Barsandboxesarestatisticaland systematicuncertainties,respectively.

by subtracting the nch distribution of eventscontaining like-sign electron pairs with2.9

<

Mee

<

3.2 GeV/c2 fromthat of unlike-sign pairs, both of which are reweighted by the inverse of the

J

/ψ

reconstruction efficiency. Here the raw nch for each event is obtained fromthe number of tracks reconstructed in the TPC witha matched hitin the TOF. UnliketheTPC, which is suscep-tible to pile-up tracks from out-of-time collisions, the TOF only records signals fromparticles produced from the triggered colli-sion.About1%oftracksfromout-of-timecollisionsmayrandomly matchaTOFhitandtheeffectofthesepile-uptracksisconsidered asasystematicuncertainty.Theraw

n

ch distributionsarecorrected forthetriggerandvertexfindingefficiencies,whichareimportant forlow multiplicity p

+

p collisions, and fortheTPC andTOF ac-ceptancesandefficienciesthrough aniterativeBayesianunfolding method[29]. The responsematrix usedforunfolding is obtained fromMCsamplesgeneratedwithPYTHIA8.183 [12] andconvoluted withthedetectoracceptancesandefficiencies.Herethetrue

n

ch in the response matrix is defined as the number of charged parti-cles produced promptly fromthe primary vertex, including pion, kaon,proton,electron,andmuonwith

|

η

|

<

1,

p

T

>

0 GeV/c,and notfrom

K

0_or

_

_{decays.Inaddition, J}

_/ψ

_{eventsrequirethatthe} J

/ψ-decay

electrons are within

|

η

|

<

1 and included in the nch calculations.

Fig. 3 shows the corrected nch distributions, together with a negative binomialdistribution (NBD) functionfittedto the distri-bution in MB p

+

p collisions. The average charged-particle mul-tiplicity per pseudo-rapidity unit obtained from the fit,



dN_chM B

/

d

η



=

2.9

±

0.3(stat.

)

±

0.2(model

)

±

0.4(syst.

),

is consistent with thepreviousSTARpublishedresult[24].Themodeluncertaintyis estimated from the difference between the average value of the

nchdistributionandtheNBDfitresult.Ascanbeseen,theaverage

nch for p

+

p collisions producing J

/ψ

increases with increasing

J

/ψ

pT andishigherthanthatforMBcollisions.

The corrected nch distributions are divided into five inter-vals: 0–5,6–10, 11–15, 16–21and22–31. The J

/ψ

relativeyield

NJ/ψ

/



NJ/ψ



and relative charged-particle multiplicity

(

dN_chM B

/

d

η

)/



dN_chM B

/

d

η



are estimated for each interval, where NJ/ψ

is the number of J

/ψ

produced per MB collision in a

multi-plicity interval, and



NJ/ψ



the average value over the whole

multiplicity range. The last bin in MB events is excluded due

to the large statistical uncertainty. The systematic uncertainties for

(

dNM B

ch

/

d

η

)/



dNchM B

/

d

η



and NJ/ψ

/



NJ/ψ



are summarized in

Table 2

Systematicuncertaintiesforthemeasurementof thedependenceofJ/ψrelativeyieldsonnch.See

textfordetails.

Type Uncertainty (%) dNM B ch/dη dNM B ch/dη NJ/ψ NJ/ψ Vertex finding 2 3 Tracking 4–5 4–23 Unfolding 2–7 1–30 Pile-up 2 1–10

Table 2. The vertex finding efficiency correction has 3%

uncer-tainty, estimated by the difference between the defaultPYTHIA8 tuneandtheSTARheavyflavortune [30].Thetrackreconstruction efficiency correction is obtained fromdetector simulation. It de-pendson

n

ch andhas4–5% uncertaintyforMBeventsand4–23% uncertainty for J

/ψ

events.The unfolding process uncertainty is studied by changing the numberof Bayesianunfolding iterations andthePYTHIAtune,andbyreweightingPYTHIA

n

ch distribution to match with the unfolded nch distribution from data. This un-certainty isfoundtobe2–7%and1–30%forMB and J

/ψ

events, respectively. Theeffectofpile-uptrackcontributionsisestimated

by the difference between the NBD fit and the actual nch

dis-tribution in MB p

+

p collisions, as well as by the difference in the nch distribution betweenthelowest andhighest Zero-Degree Calorimeter (ZDC) [31] coincidence rate.The ZDCrateranged be-tween1–13 kHzandisproportionaltotheinstantaneous luminos-ity. The uncertainty dueto pile-up trackcontributions is 2% and 1–10%forMBand J

/ψ

events,respectively.

Fig. 4 shows the dependence of the J

/ψ

relative yield on

the relativecharged-particle multiplicity for J

/ψ

pT

>

0,1.5and 4 GeV/c, respectively. A strong increase in J

/ψ

relative yields with nch is observed, which seems to be stronger at higher pT

as suggested by data. The result for J

/ψ

relative yield with

pT

>

0 GeV/c in p

+

p collisions at

√

s

=

200 GeV is compared

withthatat

√

s

=

7 TeV[7].Thetworesultsfollowasimilartrend despite morethanone orderofmagnitudedifferencein

√

s, sug-gestinga weak dependenceoftheunderlying mechanismon

√

s.

AlsoshowninFig.4arecalculationsfromdifferentMCgenerators andthepercolationmodel.PYTHIA8.183 [12] withthecolor recon-nectionscenariodescribesMPIthroughpQCD,takingintoaccount thedependenceontheenergyandimpactparameter(thedistance between the colliding protons in the plane perpendicular to the beam direction)of p

+

p collisions. It can describe the J

/ψ

rela-tive yieldandpredictsstrongerincrease ofthe J

/ψ

relativeyield with nch at higher pT. EPOS3 [13] uses a Gribov–Regge multi-ple scattering framework to describe initial p

+

p collisions and thus includes MPI in both hard and softprocesses. Furthermore, itincorporatesfeatures ofhydrodynamicalevolution[14] in high-multiplicity p

+

p collisions, which is suggested to be important for p

+

p collisions at

√

s

=

7 TeV[8] buthaslittleeffectat

√

s

=

200 GeV.BecauseEPOS3doesnotimplement J

/ψ

production,we

compare our data with the prediction from EPOS3 on the open

charmproduction.Thelatterfor2

<

pT

<

4 (4

<

pT

<

8) GeV/c is

found to be in good agreement with the STAR J

/ψ

result for

pT

>

1.5 (pT

>

4) GeV/c. The Percolation model [15] adapts a framework ofcolorstringinteractions todescribe p

+

p collisions.

Fig. 4. (Coloronline.)Themultiplicitydependenceof J/ψproductioninp+p collisionsat√s=200 GeV.Purplecircles,bluesquares,andredtrianglesrepresenttheresults for J/ψwithpTgreaterthan0,1.5,and4GeV/c,respectively.Barsandopenboxesarestatisticalandsystematicuncertainties,respectively.TheALICEresult[7] isshownin

theleftpanel.Thepurple,blueandredbandsinthemiddlepanelaregeneratedfromPYTHIA8for J/ψwithpTgreaterthan0,1.5,and4GeV/c,respectively.Theblueand

redbandsintherightpanelarefromEPOS3modelcalculationsfor D0_with2<p

T<4 and4<pT<8 GeV/c,respectively,whilethegreencurveisfromthePercolation

modelfor J/ψ withpT>0 GeV/c.

5. Summary

Insummary,inclusive J

/ψ

productionatmid-rapidity

|

y

|

<

1 inp

+

p collisions at

√

s

=

200 GeVisstudiedthroughthe J

/ψ

→

e+e−channelwiththeSTARexperiment.Themeasureddifferential productioncrosssectionasafunctionof J

/ψ

pT canbedescribed withinexperimentalandtheoreticaluncertaintiesbyCEM calcula-tionsfor0

<

pT

<

14 GeV/c,NLONRQCDcalculationsfor4

<

pT

<

14 GeV/c, and CGC

+

NRQCD calculations for 0

<

pT

<

5 GeV/c. The total J

/ψ

production cross section per rapidity unit times

J

/ψ

→

e+e−branchingratiois43.2

±

3.0(stat.

)

±

7.5(syst.

)

nb.The

J

/ψ

relativeyieldisfoundtoincreasewithcharged-particle mul-tiplicityatmid-rapidity.Theincreaseisstrongerthanalinearrise, andseemstodependon J

/ψ

pT butweaklyonthecenter-of-mass energyofthe

p

+

p collisions whencomparedtotheexperimental resultat

√

s

=

7 TeV.The increase can be described by PYTHIA8 andEPOS3MCgeneratorstakingintoaccountMultiple-Partonic In-teractions,andbythePercolationmodel.

Acknowledgements

We thank the RHIC Operations Group and RCF at BNL, the

NERSC Center at LBNL, and the Open Science Grid consortium

forprovidingresources andsupport.This workwas supported in

partby the Office of Nuclear Physics within the U.S. DOE Office

ofScience, the U.S. NationalScience Foundation, the Ministry of Education and Science of the Russian Federation, National Nat-ural Science Foundation of China, Chinese Academy of Sciences, the Ministry of Science and Technology of the People’s Republic ofChina and theChinese MinistryofEducation,the National Re-searchFoundationofKorea,CzechScienceFoundationandMinistry ofEducation,YouthandSportsoftheCzechRepublic,Department

of Atomic Energy and Department of Science and Technology of

the Government of India,the National Science Centre of Poland, the Ministryof Science, Education andSports of the Republicof

Croatia, ROSATOM of Russia and German Bundesministerium für

Bildung,Wissenschaft,ForschungundTechnologie (BMBF)andthe HelmholtzAssociation.

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