J/psi polarization in p plus p collisions at root s=200 GeV in STAR

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DOI: 10.1016/j.physletb.2014.10.049

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

J

/ψ

polarization

in

p

+

p collisions

at

√

s

=

200 GeV in

STAR

STAR

Collaboration

L. Adamczyk

a

,

J.K. Adkins

w

,

G. Agakishiev

u

,

M.M. Aggarwal

ai

,

Z. Ahammed

bb

,

I. Alekseev

s

,

J. Alford

v

,

C.D. Anson

af

,

A. Aparin

u

,

D. Arkhipkin

d

,

E.C. Aschenauer

d

,

G.S. Averichev

u

,

J. Balewski

aa

,

A. Banerjee

bb

,

Z. Barnovska

n

,

D.R. Beavis

d

,

R. Bellwied

ax

,

A. Bhasin

t

,

A.K. Bhati

ai

,

P. Bhattarai

aw

,

H. Bichsel

bd

,

J. Bielcik

m

,

J. Bielcikova

n

,

L.C. Bland

d

,

I.G. Bordyuzhin

s

,

W. Borowski

at

,

J. Bouchet

v

,

A.V. Brandin

ad

,

S.G. Brovko

f

,

S. Bültmann

ag

,

I. Bunzarov

u

,

T.P. Burton

d

,

J. Butterworth

ao

,

H. Caines

be

,

M. Calderón de la Barca Sánchez

f

,

D. Cebra

f

,

R. Cendejas

aj

,

M.C. Cervantes

av

,

P. Chaloupka

m

,

Z. Chang

av

,

S. Chattopadhyay

bb

,

H.F. Chen

aq

,

J.H. Chen

as

,

L. Chen

i

,

J. Cheng

ay

,

M. Cherney

l

,

A. Chikanian

be

,

W. Christie

d

,

J. Chwastowski

k

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M.J.M. Codrington

aw

,

R. Corliss

aa

,

J.G. Cramer

bd

,

H.J. Crawford

e

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X. Cui

aq

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S. Das

p

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A. Davila Leyva

aw

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L.C. De Silva

ax

,

R.R. Debbe

d

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T.G. Dedovich

u

,

J. Deng

ar

,

A.A. Derevschikov

ak

,

R. Derradi de Souza

h

,

S. Dhamija

r

,

B. di Ruzza

d

,

L. Didenko

d

,

C. Dilks

aj

,

F. Ding

f

,

P. Djawotho

av

,

X. Dong

z

,

J.L. Drachenberg

ba

,

J.E. Draper

f

,

C.M. Du

y

,

L.E. Dunkelberger

g

,

J.C. Dunlop

d

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L.G. Efimov

u

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J. Engelage

e

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K.S. Engle

az

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G. Eppley

ao

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L. Eun

z

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O. Evdokimov

j

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R. Fatemi

w

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S. Fazio

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J. Fedorisin

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P. Filip

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E. Finch

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Y. Fisyak

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C.E. Flores

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C.A. Gagliardi

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D.R. Gangadharan

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D. Garand

al

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F. Geurts

ao

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A. Gibson

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M. Girard

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S. Gliske

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D. Grosnick

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Y. Guo

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A. Gupta

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S. Gupta

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W. Guryn

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B. Haag

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O. Hajkova

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A. Hamed

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L.-X. Han

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R. Haque

ae

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J.W. Harris

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J.P. Hays-Wehle

aa

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S. Heppelmann

aj

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A. Hirsch

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G.W. Hoffmann

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D.J. Hofman

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S. Horvat

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B. Huang

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H.Z. Huang

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X. Huang

ay

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P. Huck

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T.J. Humanic

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G. Igo

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W.W. Jacobs

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H. Jang

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E.G. Judd

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S. Kabana

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D. Kalinkin

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K. Kang

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K. Kauder

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H.W. Ke

d

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D. Keane

v

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A. Kechechyan

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A. Kesich

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Z.H. Khan

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D.P. Kikola

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I. Kisel

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A. Kisiel

bc

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D.D. Koetke

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T. Kollegger

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J. Konzer

al

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I. Koralt

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W. Korsch

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L. Kotchenda

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P. Kravtsov

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K. Krueger

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I. Kulakov

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L. Kumar

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R.A. Kycia

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M.A.C. Lamont

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J.M. Landgraf

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J. Lauret

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A. Lebedev

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R. Lednicky

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J.H. Lee

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W. Leight

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M.J. LeVine

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F. Liu

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T. Ljubicic

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W.J. Llope

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R.S. Longacre

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X. Luo

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G.L. Ma

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Y.G. Ma

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D.M.M.D. Madagodagettige Don

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D.P. Mahapatra

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R. Majka

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S. Margetis

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C. Markert

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H.S. Matis

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D. McDonald

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T.S. McShane

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N.G. Minaev

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S. Mioduszewski

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B. Mohanty

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M.M. Mondal

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D.A. Morozov

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M.G. Munhoz

ap

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M.K. Mustafa

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B.K. Nandi

q

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Md. Nasim

ae

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T.K. Nayak

bb

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J.M. Nelson

c

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L.V. Nogach

ak

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S.Y. Noh

x

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J. Novak

ac

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S.B. Nurushev

ak

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G. Odyniec

z

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A. Ogawa

d

,

K. Oh

am

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A. Ohlson

be

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V. Okorokov

ad

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E.W. Oldag

aw

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R.A.N. Oliveira

ap

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M. Pachr

m

,

B.S. Page

r

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S.K. Pal

bb

,

Y.X. Pan

g

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Y. Pandit

j

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Y. Panebratsev

u

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T. Pawlak

bc

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B. Pawlik

ah

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H. Pei

i

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C. Perkins

e

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W. Peryt

bc

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P. Pile

d

,

M. Planinic

bf

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J. Pluta

bc

,

D. Plyku

ag

,

N. Poljak

bf

,

J. Porter

z

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A.M. Poskanzer

z

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N.K. Pruthi

ai

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M. Przybycien

a

,

P.R. Pujahari

q

,

H. Qiu

z

,

A. Quintero

v

,

S. Ramachandran

w

,

R. Raniwala

an

,

S. Raniwala

an

,

R.L. Ray

aw

,

C.K. Riley

be

,

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0370-2693/©2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/3.0/).Fundedby SCOAP3_.

H.G. Ritter

z

,

J.B. Roberts

ao

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O.V. Rogachevskiy

u

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J.L. Romero

f

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J.F. Ross

l

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A. Roy

bb

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L. Ruan

d

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J. Rusnak

n

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N.R. Sahoo

bb

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P.K. Sahu

p

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I. Sakrejda

z

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S. Salur

z

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A. Sandacz

bc

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J. Sandweiss

be

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E. Sangaline

f

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A. Sarkar

q

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J. Schambach

aw

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R.P. Scharenberg

al

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A.M. Schmah

z

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W.B. Schmidke

d

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N. Schmitz

ab

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J. Seger

l

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P. Seyboth

ab

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N. Shah

g

,

E. Shahaliev

u

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P.V. Shanmuganathan

v

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M. Shao

aq

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B. Sharma

ai

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W.Q. Shen

as

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S.S. Shi

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Q.Y. Shou

as

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E.P. Sichtermann

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R.N. Singaraju

bb

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M.J. Skoby

r

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D. Smirnov

d

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N. Smirnov

be

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D. Solanki

an

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P. Sorensen

d

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U.G. deSouza

ap

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H.M. Spinka

b

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B. Srivastava

al

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T.D.S. Stanislaus

ba

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J.R. Stevens

aa

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R. Stock

o

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M. Strikhanov

ad

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B. Stringfellow

al

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A.A.P. Suaide

ap

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M. Sumbera

n

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X. Sun

z

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X.M. Sun

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Y. Sun

aq

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Z. Sun

y

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B. Surrow

au

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D.N. Svirida

s

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T.J.M. Symons

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A. Szanto de Toledo

ap

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J. Takahashi

h

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A.H. Tang

d

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Z. Tang

aq

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T. Tarnowsky

ac

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J.H. Thomas

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A.R. Timmins

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M. Tokarev

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B.A. Trzeciak

bc

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∗

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O.D. Tsai

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J. Turnau

ah

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T. Ullrich

d

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D.G. Underwood

b

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G. Van Buren

d

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G. van Nieuwenhuizen

aa

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J.A. Vanfossen Jr.

v

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R. Varma

q

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G.M.S. Vasconcelos

h

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A.N. Vasiliev

ak

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R. Vertesi

n

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F. Videbæk

d

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Y.P. Viyogi

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S. Vokal

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A. Vossen

r

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M. Wada

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M. Walker

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F. Wang

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G. Wang

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H. Wang

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J.S. Wang

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G. Webb

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J.C. Webb

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G.D. Westfall

ac

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S.W. Wissink

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Y.F. Wu

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W. Xie

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Z.P. Zhang

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C. Zhong

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X. Zhu

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Y.H. Zhu

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Y. Zoulkarneeva

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a_{AGHUniversityofScienceandTechnology,Cracow,Poland} b_{ArgonneNationalLaboratory,Argonne,IL 60439,USA} c_{UniversityofBirmingham,Birmingham,UnitedKingdom} d_{BrookhavenNationalLaboratory,Upton,NY 11973,USA} e_{UniversityofCalifornia,Berkeley,CA 94720,USA} f_{UniversityofCalifornia,Davis,CA 95616,USA} g_{UniversityofCalifornia,LosAngeles,CA 90095,USA} h_{UniversidadeEstadualdeCampinas,SaoPaulo,Brazil} i_{CentralChinaNormalUniversity(HZNU),Wuhan430079,China} j_{UniversityofIllinoisatChicago,Chicago,IL 60607,USA} k_{CracowUniversityofTechnology,Cracow,Poland} l_{CreightonUniversity,Omaha,NE 68178,USA}

m_{CzechTechnicalUniversityinPrague,FNSPE,Prague,11519,CzechRepublic} n_{NuclearPhysicsInstituteASCR,25068ˇRež/Prague,CzechRepublic} o_{FrankfurtInstituteforAdvancedStudiesFIAS,Germany} p_{InstituteofPhysics,Bhubaneswar751005,India} q_{IndianInstituteofTechnology,Mumbai,India} r_{IndianaUniversity,Bloomington,IN 47408,USA}

s_{AlikhanovInstituteforTheoreticalandExperimentalPhysics,Moscow,Russia} t_{UniversityofJammu,Jammu180001,India}

u_{JointInstituteforNuclearResearch,Dubna,141980,Russia} v_{KentStateUniversity,Kent,OH 44242,USA}

w_{UniversityofKentucky,Lexington,KY 40506-0055,USA}

x_{KoreaInstituteofScienceandTechnologyInformation,Daejeon,RepublicofKorea} y_{InstituteofModernPhysics,Lanzhou,China}

z_{LawrenceBerkeleyNationalLaboratory,Berkeley,CA 94720,USA} aa_{MassachusettsInstituteofTechnology,Cambridge,MA02139-4307,USA} ab_{Max-Planck-InstitutfürPhysik,Munich,Germany}

ac_{MichiganStateUniversity,EastLansing,MI 48824,USA} ad_{MoscowEngineeringPhysicsInstitute,Moscow,Russia}

ae_{NationalInstituteofScienceEducationandResearch,Bhubaneswar751005,India} af_{OhioStateUniversity,Columbus,OH 43210,USA}

ag_{OldDominionUniversity,Norfolk,VA23529,USA} ah_{InstituteofNuclearPhysicsPAN,Cracow,Poland} ai_{PanjabUniversity,Chandigarh160014,India}

aj_{PennsylvaniaStateUniversity,UniversityPark,PA 16802,USA} ak_{InstituteofHighEnergyPhysics,Protvino,Russia}

al_{PurdueUniversity,WestLafayette,IN 47907,USA} am_{PusanNationalUniversity,Pusan,RepublicofKorea} an_{UniversityofRajasthan,Jaipur302004,India} ao_{RiceUniversity,Houston,TX 77251,USA} ap_{UniversidadedeSaoPaulo,SaoPaulo,Brazil}

aq_{UniversityofScience&TechnologyofChina,Hefei230026,China} ar_{ShandongUniversity,Jinan,Shandong250100,China}

as_{ShanghaiInstituteofAppliedPhysics,Shanghai201800,China} at_{SUBATECH,Nantes,France}

au_{TempleUniversity,Philadelphia,PA 19122,USA} av_{TexasA&MUniversity,CollegeStation,TX 77843,USA} aw_{UniversityofTexas,Austin,TX 78712,USA} ax_{UniversityofHouston,Houston,TX77204,USA} ay_{TsinghuaUniversity,Beijing100084,China}

az_{UnitedStatesNavalAcademy,Annapolis,MD21402,USA} ba_{ValparaisoUniversity,Valparaiso,IN 46383,USA} bb_{VariableEnergyCyclotronCentre,Kolkata700064,India} bc_{WarsawUniversityofTechnology,Warsaw,Poland} bd_{UniversityofWashington,Seattle,WA 98195,USA} be_{YaleUniversity,NewHaven,CT 06520,USA} bf_{UniversityofZagreb,Zagreb,HR-10002,Croatia}

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Articlehistory:

Received8November2013

Receivedinrevisedform7October2014 Accepted22October2014

Availableonline30October2014 Editor:M.Doser Keywords: Charmonia Polarization Spinalignment STAR RHIC

Wereportonapolarizationmeasurementofinclusive J/ψ mesonsinthedi-electrondecaychannelat mid-rapidityat2<pT<6 GeV/c in p +p collisions at√s=200 GeV.DataweretakenwiththeSTAR

detectoratRHIC.The J/ψpolarizationmeasurementshouldhelptodistinguishbetweendifferentmodels ofthe J/ψproductionmechanismsincetheypredictdifferent

p

T dependencesofthe J/ψ polarization.

Inthisanalysis, J/ψpolarizationisstudiedinthehelicityframe.Thepolarizationparameterλθmeasured atRHICbecomessmallertowardshigh

p

T,indicatingmorelongitudinal J/ψpolarizationas

p

T increases.

Theresultiscomparedwithpredictionsofpresentlyavailablemodels.

©2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/3.0/).FundedbySCOAP3_.

1. Introduction

The J

/ψ

is a bound state of charm (c) and anti-charm (c) quarks. Charmonia physical states have to be colorless, however theycanbeformedviaacolor-singletora color-octet intermediate

cc state.The first modelofcharmonia production,the Color Sin-gletModel(CSM)[1–8],assumedthat cc pairs arecreatedin the color-singletstateonly.Thisearlypredictionfailedtodescribethe measured charmoniacross-section whichhasled to the develop-mentofnewmodels.Forexample,Non-RelativisticQCD (NRQCD) [9]calculationswere proposedinwhichacc color-octet interme-diatestate,inadditiontoacolor-singletstate,can bindtoforma charmonium.

Different models of J

/ψ

production are able to describe the measured J

/ψ

production cross section reasonably well [10–17] and therefore other observables are needed to discriminate be-tweendifferent J

/ψ

productionmechanisms. J

/ψ

spinalignment, commonly known as polarization, can be used for this purpose, sincevariousmodelspredictdifferenttransversemomentum(pT) dependenceforthepolarization.Thepredictionsofdifferent mod-elsdeviate the mostathigh pT. Thereforea high-pT J

/ψ

polar-izationmeasurement is ofparticularinterest since it canhelp to discriminatebetweenthemodels.

NRQCDcalculations with color-octet contributions [18] are in goodagreementwithobserved J

/ψ

pT spectraindifferent exper-imentsatdifferentenergies,atthe RelativisticHeavyIonCollider (RHIC) [11,12], the Tevatron [13,14] and the Large Hadron Col-lider(LHC)[16,17,19].Butthecalculationsfailtodescribethe J

/ψ

polarizationathigh pT (pT

>

5 GeV

/

c)measured by theCDF ex-perimentat FermiLabat

√

s

=

1

.

96 TeV[20]. NRQCDcalculations predict transverse polarization for pT

>

5 GeV

/

c and the growth ofthepolarizationparameter

λ

θ withincreasingpT [21].However, the CDF polarization measurement becomes slightly longitudinal with increasing pT, for 5

<

pT

<

30 GeV

/

c [20]. Also, the CMS

*

Correspondingauthor.

E-mailaddress:[email protected](B.A. Trzeciak).

J

/ψ

polarizationmeasurement in p

+

p collisions at

√

s

=

7 TeV forhightransversemomenta[22]isindisagreementwithexisting next-to-leading-order (NLO) NRQCD calculations[21,23]. In addi-tion,the J

/ψ

polarization measurementsatthesameenergyand for lower pT were performed by ALICE (inclusive J

/ψ

produc-tion) [24] and LHCb (prompt J

/ψ

production) [25] experiments at forward rapidity. The ALICE experiment observed zero polar-izationwhileLHCb

λ

θ resultsindicatesmalllongitudinal polariza-tion(withothercoefficientsconsistentwithzero).Datafromboth experiments favor NLO NRQCD over NLO CSM [21,25]. At RHIC energies, at intermediate pT (1

.

5

<

pT



5 GeV

/

c) andfor mid-rapidity,thetunedleading-order(LO) NRQCDmodel[26]predicts slightly longitudinal J

/ψ

polarization and describes the PHENIX result[27]well.

InthecaseoftheColorSingletModel,theNext-to-Leading Or-dercalculations(NLO+CSM)[28]forthe pT spectrumareinnear agreementwiththeRHICdataatlowandmid pT andtheseCSM calculationspredictlongitudinal J

/ψ

polarization atintermediate

pT (1

.

5

<

pT

<

6 GeV

/

c) at mid-rapidity which is in agreement withthePHENIXresult[28].AttheTevatronandLHCenergies,the upperboundofNNLO* prediction[29]isvery closeto the exper-imental cross section data, similar to RHIC [28].Also, the upper edge ofthis predictionforthe polarization is ingood agreement withtheCDFdata[29].However,NLOCSMcalculations[21,25]do notdescribe J

/ψ

polarizationresultsfromALICEandLHCbwell.

Forthelower pT rangeatRHICenergies,theLONRQCD calcu-lations [26] andNLO+ CSM[28] havesimilar predictions regard-ing the J

/ψ

polarization, whichis longitudinal,anddescribe the experimentalresults[27]well.However,thesemodelspredict dif-ferent pT dependence: in the caseofthe NRQCDprediction, the trend is towards the transverse polarization with increasing pT, whiletheNLO+ CSMshowsalmostno pT dependence.Thus,itis especiallyimportanttomeasurea pT dependenceofthe J

/ψ

po-larizationandgotohighpT.

In this paper, we report a J

/ψ

polarization measurement in

p

+

p collisionsat

√

s

=

200 GeV atrapidity( y)

|

y

|

<

1,inthepT range 2

<

pT

<

6 GeV

/

c from the STARexperiment atRHIC. The

analysisisdoneusingdatawithahigh-pT electron(so-calledHigh Tower)trigger.The J

/ψ

isreconstructedvia itsdi-electrondecay channel.Theangulardistributionparameter(polarization parame-ter)

λ

θ forelectron decayof the J

/ψ

isextractedin thehelicity frame [30] as a function of J

/ψ

pT, in three pT bins. The ob-tainedresultiscomparedwithpredictionsofNLO+ CSM[28] and LONRQCDcalculations(COM)[26].

1.1.Angulardistributionofdecayproducts

J

/ψ

polarizationisanalyzedviatheangulardistributionofthe decayelectrons inthehelicityframe[30].Inthisanalysis,we are interestedinthepolarangle

θ

.Itistheanglebetweenthepositron momentumvectorinthe J

/ψ

restframeandthe J

/ψ

momentum vectorinthelaboratoryframe.Thefullangulardistribution,which isderivedfromthedensitymatrixelementsoftheproduction am-plitudeusingparityconservationrules,isdescribedby:

d2N

d

(

cos

θ )

d

φ

∝

1

+ λθ

cos

2

_θ

_{+ λφ}

_sin2

_θ

_{cos 2}

_φ

+ λθ φ

sin 2

θ

cos

φ,

(1)

where

θ

and

φ

are polar and azimuthal angles, respectively;

λ

θ and

λ

φ are the angulardecay coefficients. The angular distri-butionintegratedovertheazimuthalangleisparametrizedas

dN

d

(

cos

θ )

∝

1

+ λθ

cos

2

_θ,

₍₂₎

where

λ

θ iscalledthepolarizationparameter.Thisparameter con-tainsboththelongitudinalandtransversecomponentsofthe J

/ψ

cross section;

λ

θ

=

1 indicates full transverse polarization, and

λ

θ

= −

1 correspondstofulllongitudinalpolarization.

The measurement presentedin this Letter islimited to the

θ

angle analysis due to statistical limitations. Extraction of the

λ

θ parameterinthehelicity frameallows one tocomparethe result withtheavailable model predictions anddrawmodel dependent conclusions. A measurement of the

θ

angle with a better preci-sion,aswell asthe

φ

angle,willbe possible withanewerSTAR dataat

√

s

=

500 GeV.Then, the frame invariant parameter, also in different referenceframes, can be calculated providing model independentinformationaboutthe J

/ψ

polarization[31].

2. Dataanalysis

2.1.Datasetandelectronidentification

The p

+

p 200 GeV data used inthis analysis were recorded bytheSTARexperimentintheyear2009.TheSTARdetector[32] is a multi-purpose detector. It consists of many subsystems and has cylindrical geometry and a large acceptance with a full az-imuthalcoverage.Themostimportantsubsystemsforthisanalysis are briefly described below. The Time Projection Chamber (TPC) [33] isthemain trackingdetectorforcharged particles.It isalso usedtoidentifyparticlesusingtheionizationenergyloss(dE

/

dx).

OutsidetheTPCistheTimeOfFlight(TOF)detector[34]which ex-tendsSTARparticleidentificationcapabilitiestomomentumranges whereTPC dE

/

dx alone isinadequate. Between theTOF andthe STARmagnetthereistheSTARBarrelElectromagneticCalorimeter (BEMC)[35].TheBEMC isconstructed sothat anelectron should depositall its energy inthe BEMC towers whilehadrons usually depositonly a fractionof their energy. The energy deposited by aparticleintheBEMC canthusbe usedtodiscriminatebetween electrons andhadrons, by looking atthe E

/

p ratio.The BEMC is alsousedto triggeronhigh-pT electrons.Together withtheTOF, theBEMC isutilizedto discriminateagainst pile-uptracks inthe

TPC, sincebothdetectorsarefast.MostoftheSTARdetector sub-systemsareenclosedinaroomtemperaturesolenoidmagnetwith auniformmagneticfieldofmaximumvalueof0.5T[36].

The analyzed data were collected with the High Tower (HT) trigger,whichrequirestransverseenergydepositedinatleastone single tower of the BEMC to be within 2

.

6

<

ET

≤

4

.

3 GeV. The HTtriggeralsorequiresacoincidencesignal fromtwoVertex Po-sition Detectors [37]. We have analyzed

∼

33 M events with the HTtriggerandwithaprimaryvertexz position

|

Vz

|

<

65 cm.This correspondstoanintegratedluminosityof

∼

1

.

6 pb−1.The J

/ψ

is reconstructedviaitsdi-electrondecaychannel, J

/ψ

→

e+e−,with thebranchingratio5

.

94%

±

0

.

06%[38].

Charged tracks are reconstructed using the STAR TPC which has 2

π

azimuthal coverage and apseudorapidity (

η

) coverage of

|η|

<

1.Tracksthat originatefromtheprimary vertexandhavea distance of closest approach (DCA) to the primary vertexof less than2 cmare used.In2009STARdidnothaveavertexdetector that would help to distinguish betweenprompt andnon-prompt

J

/ψ

,andTPCresolutionaloneisnotenoughtoselectnon-prompt

J

/ψ

fromB mesondecays.Inordertoensureagoodtrackquality, tracksarerequiredtohaveatleast15pointsusedinthetrack re-constructionintheTPC,andtohaveatleast52%ofthemaximum numberofpossibletrackreconstructionpoints.Cutsof

|η|

<

1 and

pT

>

0

.

4 GeV

/

c arealsoapplied.Thetransversemomentumcutis chosentooptimizetheacceptanceincos

θ

andthesignificanceof the J

/ψ

signal.Applying higher pT cutcauses alossofstatistics at

|

cos

θ

|

∼

1 whilealower pT cutreducesthe J

/ψ

signal signifi-cance.EfficientidentificationofelectronswithlowpT waspossible usingavailableinformationfromtheTOF detector.Duringthe an-alyzedrunin2009,72%ofthefullTOFdetectorwasinstalled.The TOFpseudorapiditycoverageis

|η|

<

0

.

9.

In order to identify electrons and reject hadrons, information fromtheTPC, TOFandBEMC detectorsisused.TheTPCprovides informationaboutdE

/

dx ofaparticleinthedetector.Electron can-didates arerequired tohaven

σ

electron within

−

1

<

n

σ

electron

<

2,

wheren

σ

electron

=

log

[(

dE

/

dx

)/(

dE

/

dx

|

Bichsel

)

]/

σ

dE/dx,dE

/

dx isthe measured energy loss in the TPC, dE

/

dx

|

Bichsel is the expected

valueofdE

/

dx fromtheBichselfunctionprediction[39]and

σ

dE/dx is thedE

/

dx resolution. The Bichsel function isused to calculate the energy dependence of the most probable energyloss ofthe ionization spectrum from a detector. In a thin material such as theTPCgas,ithasbeenshownthattheBichselfunctionisavery goodapproximationforthedE

/

dx curves[40].Atlower momenta (p



1

.

5 GeV

/

c),whereelectronandhadrondE

/

dx bandsoverlap, theTOFdetectorisusedtorejectslowhadrons.Forp

<

1

.

4 GeV

/

c,

acutonthespeedofaparticle,

β

,of

|

1

/β

−

1

|

<

0

.

03 isapplied. Athighermomenta,theBEMC rejectshadronsefficiently.For mo-menta above 1.4 GeV/c,a cut on E

/

p

>

0

.

5c is usedfor electron identification, where E isthe energydeposited ina single BEMC tower (

η

× φ =

0

.

05

×

0

.

05). For electrons, the ratio of total energydepositedin theBEMCto theparticle’smomentum is ex-pected to be

≈

1. In the analysis we use energy deposited in a singleBEMCtowerbutan electroncandeposititsenergyinmore towers,thereforethevalueoftheE

/

p cutis0

.

5c.

It is alsorequired that at leastone of the electrons fromthe

J

/ψ

decay satisfies the HT trigger conditions. In order to en-sure that a selected electron indeed fired the trigger, an addi-tionalcut of pT

>

2

.

5 GeV

/

c isapplied forthat electron.The HT trigger requirements reduce significantly the combinatorial back-ground under the J

/ψ

signal and lead to a clear J

/ψ

signal at 2

<

pT

<

6 GeV

/

c.

Fig. 1. (Color online.) (a) Invariant mass distributions of unlike-sign (black cir-cles)andlike-sign(redtriangles)electron/positronpairs,for2<pT<6 GeV/c and |y|

<

1.(b) J/ψ signalafterthecombinatorialbackgroundsubtraction(closedblue circles)andMCsimulation(histogram).

2.2. J

/ψ

signalandcos

θ

distributions

Electrons and positrons that pass track quality and electron identification(eID) cutsare paired ineach event. Fig. 1(a) shows the invariant mass distribution fordi-electron pairs with

|

y

|

<

1 andpT of2–6 GeV/c.Theunlike-signpairsarerepresentedby cir-cles.Thecombinatorialbackgroundisestimatedusingthelike-sign technique, and is definedas a sum of all e+e+ and e−e− pairs inan event, representedbytriangles. The J

/ψ

signalis obtained bysubtractingthecombinatorialbackgroundfromtheunlike-sign pair distribution. Fig. 1(b) shows the invariant mass distribution for J

/ψ

ascircles,andthe histogramisthe J

/ψ

signal obtained fromaMonteCarlo(MC)simulation(seeSection2.3).Momentum resolution of electrons and positrons from the MC simulation is additionallysmearedinorderthatthesimulated J

/ψ

signalwidth matches the width of the J

/ψ

signal obtained from the data. The simulation does not include the J

/ψ

radiative decay chan-nel, J

/ψ

→

e+e−

γ

[11,38], leading to the discrepancy between

dataandsimulationforinvariant mass

∼

2

.

7–2

.

9 GeV

/

c2_.Thetail

inthedataatlowinvariantmassisduetoelectronbremsstrahlung andmissingphotonsinthecaseofthe J

/ψ

radiativedecay recon-struction. We select J

/ψ

candidates in the invariant mass range 2

.

9–3

.

3 GeV

/

c2 andsothediscrepancybetweenthedataandthe simulationforthelowermassrangedoesnotinfluenceourresult. Intheanalyzed rangesofrapidity,pT,andinvariantmass,the signaltobackgroundratiois15.Astrong J

/ψ

signalisseenwith a significanceof 26

σ

. Thenumber of J

/ψ

,obtainedby counting dataentriesinthe J

/ψ

masswindow,is791

±

30.Forthe polar-izationanalysis,wesplittheentire J

/ψ

sampleinto3pT binswith a comparablenumberof J

/ψ

ineach bin:2–3 GeV/c,3–4 GeV/c and4–6 GeV/c.

Rawcos

θ

distributionsfor J

/ψ

(after thecombinatorial back-groundsubtraction) areobtained bybin counting, using distribu-tionsfromthedata.Figs. 2(a)–(c)showuncorrectedcos

θ

distribu-tions(fullsquares).

2.3. Corrections

In order to obtain the cos

θ

corrections, unpolarized Monte Carlo J

/ψ

particles with uniform pT and rapidity distributions are embedded into real events, and the STAR detector response issimulated.Sincetheinput pT andrapidityshapesinfluence ef-ficiencies, J

/ψ

distributions are then weighted accordingto the

J

/ψ

pT andrapidityshapesobservedintheSTAR[11]andPHENIX [41]experiments.Correctedcos

θ

distributionsareobtainedby di-viding raw cos

θ

distributions by the corrections calculated as a functionofcos

θ

,ineachanalyzedpT bin.

Efficienciesasafunctionofcos

θ

arecalculatedbyapplyingthe samecutsusedinthedataanalysistotheembedding(simulation) sample. Mostcorrectionsrelatedto theTPCresponse,suchasthe acceptance(withthepT and

η

cuts)andtrackingefficiency,andall BEMCefficiencies,areobtainedfromthesimulation.Then

σ

electron

andtheTOFresponsearenot simulatedaccurately inembedding. Thereforethen

σ

electron cutandTOFcutefficiencies arecalculated

usingthedata.

Forthecalculationofthen

σ

electron cut efficiency,then

σ

electron

distributionfromthedataisapproximatedwithasumofGaussian functions (oneGaussian function forelectrons andtwo Gaussian functions for hadrons), in narrow momentum bins. In order to improve the fitting, the TOF andBEMC eID cutsare applied and the positionofthe Gaussianfit forelectrons isconstrainedusing a high-purity (almost 100%) electron sample obtained by select-ingphotonicelectronsandsubtractingabackgroundfromlike-sign electron pairs.Photonic electronsare produced fromphoton con-version in the detector material and Dalitz decay of

π

0 _and

_η

mesons. These electrons are isolated using a cut on the invari-antmassofapairoftracksofme−e+

<

100 MeV

/

c2andadditional electronidentificationcuts:

|

1

/β

−

1

|

<

0

.

03 forp

<

1

.

5 GeV

/

c and E

/

p

>

0

.

5c formomentaabove1.5 GeV/c.

TOF matching efficiency is calculated using a low luminosity datasample (with almostnopile-up). SincetheTOF detectordid nothavefullcoveragein2009,theTOFmatchingefficiencyis ap-pliedinthetotalefficiencycalculationasafunctionof

η

.The effi-ciencyofthe1

/β

cutiscalculatedbyusingapureelectronsample obtainedbyselectingphotonicelectronswith

−

0

.

2

<

n

σ

e

<

2 and with theinvariant mass ofa pair oftracks lessthan 15 MeV

/

c2. The1

/β

cutefficiencyiscalculatedinnarrowmomentumbinsand then aconstant functionisfittedtoobtain thefinal 1

/β

cut effi-ciency.

Thetotal J

/ψ

efficiencycalculationsincludecontributionsfrom the acceptance, the tracking efficiency, the electron identifica-tion efficiency,and theHTtrigger efficiency,and areshown asa function of cos

θ

in Fig. 2(d)–(f) (blue triangles). The systematic

Fig. 2. (Coloronline.)Panels(a)–(c)showuncorrectedcosθdistributionsafterthecombinatorialbackgroundsubtraction,foreachanalyzedpT bin.Panels(d)–(f)showtotal

efficienciesasafunctionofcosθ.Systematicerrorsareshownasboxes.Panels(g)–(i)showdifferentefficienciesthatcontributetothetotalefficiency.

uncertainties (discussedinSubsection 3.2) onthe totalefficiency arealso showninthe figure.The right-hand panels,Fig. 2(g)–(i), show separately the efficiencies that contribute to the total effi-ciency.

The most important factor influencing the shape of the total efficiencyistheHTtriggerefficiency,whichisshownasgreen di-amondsinFig. 2(g)–(i).Atleastoneoftheelectronsfromthe J

/ψ

decayisrequired tosatisfy the triggerconditions andmusthave

pT above2.5 GeV/c.Due tothe decaykinematicsthiscut causes significantlossinthenumberofobserved J

/ψ

atlower J

/ψ

pT, andthe efficiencydecreases with decreasing

|

cos

θ

|

. This pattern is clearly visible in the HT trigger efficiency plot for 2

<

pT

<

3 GeV

/

c inFig. 2(g),whereall entriesatcos

θ

∼

0 are zero.With increasing J

/ψ

pT,thetriggerefficiencyincreases.Sincethe trig-gerhasalsoan upperthreshold(ET

≤

4

.

3 GeV), a decreaseofthe efficiencyat

|

cos

θ

|

∼

1 athigher pT isseen,asevidentinFig. 2(i).

3. Resultsanddiscussion

3.1.Correctedcos

θ

distributions

Thecorrectedcos

θ

distributionsarefittedwith

f

(

cos

θ )

=

C



1

+ λθ

cos2

θ



(3)

whereC is a normalizationfactor and

λ

θ is the polarization pa-rameter.The fittingprocedure is carried out withno constraints

applied to the fit parameters. The corrected cos

θ

distributions withthefitsare showninFig. 3.Theerrors shownarestatistical only.Thesolidlinerepresentsthemostlikelyfit.Thebandaround the lineis a 1

σ

uncertaintycontour on thefit, whichtakes into account uncertaintieson bothfit parametersandcorrelations be-tweenthem.Themeasuredvaluesofthepolarizationparameter,in each analyzed pT bin,arelisted inTable 1together witha mean

pT (

pT

)ineachbinandstatisticalandsystematicuncertainties.

3.2. Systematicuncertainties

The systematicuncertainties onthe polarizationparameter

λ

θ are summarizedinTable 2.Allsources, exceptthe lasttwo, con-tributetotheerroronthetotalefficiencyandareincludedinthe systematicuncertainties shownin Fig. 2(d)–(f). Each contribution is described below. Eachsystematic uncertaintyis the maximum deviationfromthe centralvalue of

λ

θ.The systematic uncertain-ties are combined assuming that they are uncorrelated, and are addedinquadrature.

3.2.1. Trackingefficiency

The systematic uncertainty on the tracking efficiency arises fromsmalldifferencesbetweenthesimulationoftheTPCresponse intheembedding calculationandthedata.Track properties,DCA andthenumberofpoints usedinthetrackreconstruction inthe TPC(fitPts),are comparedbetweensimulationanddata.The sys-tematicuncertaintyis duetoa shiftofthe fitPtsdistribution (by

Fig. 3. (Coloronline.)Correctedcosθdistributionsfittedwith thefunctioninEq.

(3).Theplottederrorsarestatistical.Thesolidbluelinesrepresentthemostlikely fits,andthehatchedbluebandsrepresentthe1σuncertaintyonthefits.

2 points)inthesimulation.Theuncertaintyisconsidered symmet-ric.

3.2.2. TPCeIDefficiency

The systematicuncertainty fromTPC electron identification is estimatedbychanging constraintsonthemean andwidthofthe Gaussianfitforelectronsandrecalculatingthetotalefficiency.The constraintsputonthemeanandwidthareallowedtovaryby3

σ

.

3.2.3. TOFefficiency

SincetheTOF detectordidnot havefullcoverage in2009,the TOF matchingefficiency isapplied in thetotal efficiency

calcula-Table 1

Thepolarizationparameter

λ

θ.

pT(GeV/c) pT(GeV/c) λθ 2<pT<3 2.48 0.15±0.33(stat.)±0.30(sys.) 3<pT<4 3.52 −0.48±0.16(stat.)±0.16(sys.) 4<pT<6 4.74 −0.62±0.18(stat.)±0.26(sys.) Table 2 Systematicuncertainties.

Source Systematic uncertainty onλθ,

in pT(GeV/c)bins 2–3 3–4 4–6 Tracking efficiency 0.024 0.009 0.008 TPC eID efficiency 0.009 0.006 0.012 TOF efficiency 0.057 0.018 0.014 BEMC efficiency 0.035 0.024 0.068 HT trigger efficiency 0.049 0.006 0.003 Input J/ψdistributions in the simulation 0.190 0.019 0.027 Errors from the simulation 0.077 0.028 0.004 Polarization of the continuum background 0.025 0.034 0.034

J/ψsignal extraction 0.195 0.149 0.246 Total ±0.297 ±0.160 ±0.260

tion asa function of

η

. The systematic uncertainty is estimated with the TOF matching efficiency also being a function of az-imuthal angle

φ

. The 1

/β

cut efficiency estimatedfromthe data insmall pT binsmaybe sensitivetofluctuations. The1

/β

distri-bution obtainedfrom thedata iswell described by theGaussian function.Sothesystematicuncertaintyonthe1

/β

cutefficiencyis estimatedbyapplyingtheefficiencycalculatedforthewhole mo-mentum rangeof0

.

4

<

p

<

1

.

4 GeV

/

c from aGaussian fitto the 1

/β

distribution.

3.2.4. BEMCefficiency

Differences between the simulated BEMC response and the BEMC response in the real data may affect the matching of a TPCtracktotheBEMCdetectorandtheefficiencyofthe E

/

p cut.

The matchingefficiencyofa TPCtracktotheBEMC andthe E

/

p

distribution are compared between data and simulation. A pure electron sample from the data is obtained by selecting photonic electrons with

−

0

.

2

<

n

σ

e

<

2 and withthe invariant mass of a pairoftracks lessthan 15 MeV

/

c2.Thesystematicuncertaintyof theBEMCefficiencyisestimatedby applyingBEMC matchingand

E

/

p cutefficienciesobtainedfromthedatainsteadofusing simu-latedBEMCresponse,inthetotalefficiencycalculation.

3.2.5. HTtriggerefficiency

HTtriggerresponseinthesimulation,energyinaBEMCtower, is comparedwiththeBEMC responseinthe data.Thesystematic uncertaintyontheHTtriggerefficiencyisestimatedbyvaryingthe triggerturn-onconditionsinthesimulationbythedifferenceseen betweendataandsimulation,whichis 3%.

3.2.6. Input J

/ψ

distributioninthesimulation

Sincetheinput J

/ψ

transversemomentumandrapidity distri-butions inthesimulationareflat,they needtobe weightedwith realistic pT andrapidity spectra. In order to estimate a system-aticuncertainty,the pT andrapidity weightsarechanged.The pT weightisvaried bychangingtherangesinwhichtheKaplan[42] functionisfittedtothepT spectrum.Theweightusedforrapidity isobtainedbyfittingaGaussianfunctiontotherapidityspectrum, andthesystematicuncertaintyisestimatedby assumingthat the rapidityshapeisflatatmid-rapidity.

Also, the J

/ψ

particles inthesimulation areunpolarized(the input cos

θ

distribution is flat). The acceptance of electron and

positronfromthe J

/ψ

decayinthedetectordependsonthe J

/ψ

polarization.Inorder toestimate theeffectofthe unknown J

/ψ

polarizationontheacceptancecalculation,fullytransverse(

λ

θ

=

1) andfully longitudinal(

λ

θ

= −

1) J

/ψ

polarization is assumedin theembeddinganalysis.Asystematicuncertaintyisestimatedasa differencebetweenthe resultobtainedwithnoinput J

/ψ

polar-izationandtheresultwhen J

/ψ

inthesimulationispolarized.An averageuncertaintyfromthe twoinput J

/ψ

polarizations, longi-tudinalandtransverse,istakenasasystematicuncertaintyinthis study.

3.2.7. Errorsfromthesimulation

Statisticalerrorsonthetotalefficiencies,determinedusingthe MCsimulation,areincludedinthesystematicuncertainties.

3.2.8. Polarizationofthecontinuumbackground

InFig. 1(b), it is seenthat there isstill some residual contin-uum background afterthe combinatorial background subtraction. Thisbackgroundconsistsofcorrelatedcc

→

e+e−andbb

→

e+e−. The continuum backgroundis about5% of the measured J

/ψ

in theanalyzed invariant massrange. Due to the smallstatistics of thecontinuumbackground,wearenotabletoestimatea polariza-tionofthecorrelatedbackgroundusingourdata.Instead,weuse the value obtained by the PHENIX experiment [27]. They found thatthecontinuumpolarizationisbetween

−

0

.

3 and0

.

3.We es-timate a systematicuncertainty by simulating cos

θ

distributions fortheresidualbackgroundtakingtwoextremevaluesof

λ

θ:

−

0

.

3 and0

.

3.Thenthosecos

θ

distributionsaresubtractedfromthe cor-rectedcos

θ

distributions fromthedata,assuming that the resid-ualbackground is 5% of the J

/ψ

yield,in order to estimate the influenceofthe continuum backgroundpolarization on the mea-sured

λ

θ.

3.2.9. J

/ψ

signalextraction

Thesystematicuncertaintyassociatedwiththe J

/ψ

signal ex-traction is estimated by counting the number of J

/ψ

particles usingthe simulated J

/ψ

signal shape. The J

/ψ

signal fromthe simulationisextractedineach pT andcos

θ

binandfittedtothe data.

3.3.Polarizationparameter

λ

θ

Fig. 4showsthepolarizationparameter

λ

θ asafunctionof J

/ψ

pT for inclusive J

/ψ

production. The resultincludes direct J

/ψ

production,aswellas J

/ψ

fromfeed-downfromheavier charmo-niumstates,

ψ

and

χ

C (about40%oftheprompt J

/ψ

yield[43]), aswellasfromB mesondecays(non-prompt J

/ψ

)[11].The non-direct J

/ψ

production may influence the observed polarization. The STAR result (red stars) is compared with the PHENIX mid-rapidity(

|

y

|

<

0

.

35) J

/ψ

polarizationresultforinclusive J

/ψ

[27] (blacksolid circles).The bluelineisa linearfit,whichtakesinto account both statistical and systematic uncertainties, to all RHIC points.Thefitgivesanegativeslopeparameter

−

0

.

16

±

0

.

07 with

χ

2

_/

_ndf

₌

₁

_.

₅

_/

_{4.A trendtowardslongitudinal J}

_/ψ

_{polarizationis}

seenintheRHICdata.

STAR observes longitudinal J

/ψ

polarization in the helicity frameat pT

>

3 GeV

/

c.TheSTARandPHENIXmeasurements are consistentwitheachotherintheoverlappingpT region.Ourresult canbecomparedtothepolarizationmeasurementsfromCDF[20] andCMS[22] atmid-rapidity forprompt J

/ψ

.At pT

∼

5 GeV

/

c, CDF observes almost no polarization,

λ

θ

∼

0 (the polarization becomes slightly longitudinal as pT increases) while STAR ob-servesastronglongitudinalpolarizationinthat pT region.AtLHC

√

s

=

7 TeV,CMS reportszero polarization at mid-rapidity up to

pT

∼

70 GeV

/

c[22].Inaddition,theALICEexperimentalsoreports

Fig. 4. (Coloronline.)Polarizationparameter

λ

θasafunctionofJ/ψ pT (redstars)

for|y|

<

1.ThedataiscomparedwiththePHENIXresult(blacksolidcircles)[27]

andtwomodelpredictions:NLO+ ColorSingletModel(CSM)(greendashedlines representarangeof

λ

θforthedirect J/ψ,andthehatchedbluebandisan

extrap-olationof

λ

θforthepromptJ/ψ)[28]andLONRQCDcalculationswithcolor-octet

contributions(COM)[26](grayshadedarea).ThepTcoveragesoftheCSMandCOM

modelsare∼0.6–6.0 GeV/c and∼1.5–5.0 GeV/c,respectively.Thehorizontalerror barsrepresentwidthsofpT bins.Thebluelineisalinear fit( Ax+B)toRHIC

points.

very small polarization within 2

<

pT

<

8 GeV

/

c at forward ra-pidity[24].However,ifthe J

/ψ

productionisxT dependent[10], the RHICresult at pT

∼

2 GeV

/

c is comparablewiththeCDF re-sultatpT

∼

20 GeV

/

c and withtheCMSresultat pT

∼

70 GeV

/

c (xT

∼

0

.

02,xT

=

2pT

/

√

s).

The data are compared withtwo model predictions for

λ

θ at mid-rapidity: NLO+ CSM [28] and LO COM [26]. The prediction oftheCOM[26]fordirect J

/ψ

production,thegrayshadedarea, moves towards the transverse J

/ψ

polarization as pT increases [20].The trendseen inthe STAR and PHENIX resultsis towards longitudinal J

/ψ

polarizationwithincreasing pT,anda linearfit to the RHIC data has a negative slope parameter. The difference betweenthecentralvalue oftheCOMmodelcalculationsandthe STARdataintermsof

χ

2

_/

_{ndf ( P value)is6.7/3(8}

_.

₂

_×

₁₀−2_).The

COMfailedtodescribethepolarizationmeasurementsbytheCDF andCMSexperimentsathigherenergies.

Greendashedlines representarangeof

λ

θ forthedirect J

/ψ

productionfromtheNLO+CSMpredictionandanextrapolationof

λ

θ fortheprompt J

/ψ

productionis shownasthehatched blue band[28].ItpredictsaweakpT dependenceof

λ

θ,andwithinthe experimentalandtheoreticaluncertainties,theRHICresultis con-sistentwiththeNLO+CSMmodelprediction.Comparisonbetween thecentral value oftheNLO+ CSMprediction andthe STARdata gives

χ

2

_/

_{ndf ( P value)of3.0/3(3}

_.

₉

_×

₁₀−1_)and5.1/3(1

_.

₆

_×

₁₀−1₎

forthedirectandprompt J

/ψ

production,respectively.

4. Summaryandoutlook

This paperreports thefirst STAR measurement of J

/ψ

polar-izationandcontributestotheevolvingunderstanding ofthe J

/ψ

production mechanisms. J

/ψ

polarization is measured in p

+

p

collisions at

√

s

=

200 GeV in the helicity frame at

|

y

|

<

1 and 2

<

pT

<

6 GeV

/

c. RHIC data indicates a trend towards longitu-dinal J

/ψ

polarization as pT increases. The result is consistent, within experimentalandtheoreticaluncertainties, withthe NLO+ CSMmodel.

Newer data at

√

s

=

500 GeV, taken in 2011 with much higher luminosity,may help to further distinguish between J

/ψ

production models, and may permit analysis of the full angular distribution.Furthermore,uncertainties inthemodels needto be reducedin order to draw more precise conclusions from experi-mentalmeasurements.

Acknowledgements

We thank the RHIC Operations Group and RCF at BNL, the NERSC Center at LBNL, the KISTI Center in Korea and the Open ScienceGridconsortiumforprovidingresourcesandsupport.This workwas supported inpartbytheOffices ofNPandHEP within the U.S.DOE Officeof Science, theU.S. NSF, CNRS/IN2P3, FAPESP CNPqofBrazil,MinistryofEd.andSci. ofthe RussianFederation, NNSFC,CAS,MoSTandMoEofChina,theKoreanResearch Founda-tion,GAandMSMT oftheCzechRepublic, FIASofGermany, DAE, DST,andCSIRofIndia,NationalScienceCentreofPoland,National Research Foundation (NRF-2012004024), Ministryof Sci., Ed. and SportsoftheRep.ofCroatia,andRosAtomofRussia.

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