J/ψ production and elliptic flow in relativistic heavy-ion

collisions

Taesoo Song(Texas A&M Univ., USA)

Reference : T. Song, C. M. Ko, S. H. Lee and J. Xu, arXiv:1008.2730

Contents

1. Introduction2. Schematic model for fireball

expansion3. Thermal properties of charmonia 4. Charmonia in heavy-ion collisions5. Results6. Summary

1. introduction

QCD phase diagram

• Long time ago, J/ψ suppression was suggested by Matsui and Satz as a signature of QGP formation in heavy-ion collisions. (due to color screening between c and anti-c)

• The suppression was observed at SPS & RHIC.• LQCD suggests the dissociation temperature

of J/ψ higher than Tc.• J/ψ is still one of the promising diagnostic

probes for hot nuclear matter created by heavy-ion collisions.

J/ψ suppression

Phenomenological models

1. Statistical model (P. Braun-Munzinger)Low dissociation temperature of J/ψ Most J/ψ in heavy-on collisions are

regenerated ones.

2. Two-component model (R. Rapp)High dissociation temperature of J/ψ Some of J/ψ come from regeneration, some

of them come from initial production.

NJ/ψ vs. Npart

statistical model two-component model

NJ/ψ vs. Pt

statistical model two-component model

Questions

• How can both models successfully describe experimental data?

• How can both models be discriminated?

2. Schematic model for expanding fireball

• Initial condition• Equation of state (EoS)• modeling

2. 1. Glauber model

function. thickness; ),()(

ondistributiSaxon - Woods; e1

(r) where

),( ),( )(

collisionsbinary ofNumber 2.

)(1 1 )(

)(1 1 )()(

tsparticipan ofNumber 1.

,,

/)r-(r0

2

2

2

0

dxxbbT

zsbzszsdzddbN

sdsTsbTB

sdsbTsTAbN

BABA

C

BAincoll

AinAB

B

inBApart

b

s b-s

2. 2. Initial condition

GeV 200 at 11.0

GeV 130 at 09.0

2)1(

NN

NN

collpart

ppch

BAch

sx

sx

xNN

xd

dN

d

dN

Charged particle multiplicities PRC65, 061901 (2002) dAdNndAdNn

xnn

xV

Ss

collcollpartpart

collpart

00 / ,/ where

,2

)1(3.30

be toassumed is

stage initialin density entropy Local

EoS of QGP• Quasiparticle picture

Strongly interacting massless partons

Noninteracting massive partons to reproduce thermal quantities extracted from LQCD

05.1/ ,170 ,3

, 14.18

18),,(

,),,(ln)211(

48)( where

, 3

)( ,

632

)(

2)/(5.0

2

22

222

222

ccf

c

cTTc

cfc

qfc

g

TMeVTN

T

T

T

eTTF

TTFNNTg

TTgm

NNTTgm

C

P. Levai & U. Heinz PRC 57, 1879

(1998)

EoS of HG

• Resonance gas model 1. all mesons of masses lighter than

1.5 GeV & all baryons of masses lighter than 2.0 GeV are considered in HG phase.

2. They are assumed to have constant masses and to be noninteracting.

Energy density and pressure

0.15 0.20 0.25 0.30 0.350

4

8

12

16

e/T4

p/T4

e/T

4 , p/T

4

T (GeV)

)(

1

1

23

1)(

)(

12

)(

/22

23

/

223

22

22

TBepm

ppdTp

TB

e

pmpdT

Tpm

Tpm

Isothermal lines on transverse plane at τ0=0.6 fm/c

Temperature profiles at various impact parameters

2. 3. fireball expansion

• Radial acceleration in central collision

24.1

2

36.0mass inertia :

~area lcylindrica :

out-freezeat pressure :

)(

part

f

fr

NM

RA

pM

Appa

Parameterized to fit

experimental data <pt> of π, K, p at freeze-out

0 5 10 15 200.1

0.2

0.3

0.4

T (

GeV

)

t (fm/c)

0.2

0.4

0.6

0.8

v T (

c)

Assuming isentropic expansion, s(τ)=s0*v0/V(τ)

• Radial acceleration in non-central collision

3

2

3

22/1

2

2

2

2 sincos)()v( ,

sincos)(

shape, ellipticin expanding Fireball

2.2z , ,1

1

y

y

x

x

yx

xy

xyry

rx

R

v

R

vR

RRR

RR

RRzaa

zaa

Parameter to fit

experimental data v2 of π, K, p at freeze-out

0 2 4 6 8 10 12

4

6

8

10

Ry

Rx

Mixed

HGQGP

Rx,

Ry

(fm

)

(fm/c)

0.2

0.4

0.6

vy

v x, v

y (c

) vx

0.1

0.2

0.3

T (

GeV

)b=9 fm,

Blast wave model

TT

TpT

p

TT

TTT

T

T

TTT

T

pdyddN

pd

pdyddN

pd

v

dydpdN

dp

dydpdN

pdp

p

v

T

mK

T

pIrdrd

m

dydp

dN

22

22

2

22

22

1

1022

2cos

2cos

.tanh where

cosh

sinh

2

formula, Frye-Cooper usingby

0 100 200 300 4000

200

400

600

800

1000

pions kaons protons

<p T

> (

MeV

/c)

Npart

0 1 2 3 4

0

10

20

30

pT (GeV/c)

v 2 (%

)

0

10

20

30

pions kaons protons

baryonfor 3 meson,for 2

14.1 ,/exp

gmultiplyinafter (bottom)1

n

GeVcncpT

3. Thermal properties of charmonia

• Dissociation temperatures • Dissociation cross section in QGP and

in HG

3. 1. wavefunctions & binding energies & radii of charmonia at

finite T

Modified Cornell potentialF. Karsch, M.T. Mehr, H. Satz, Z phys. C. 37, 617 (1988)

σ=0.192 GeV2 : string tension

α=0.471 : Coulomb-like potential constant

μ(T) =√(Nc/3+Nf/6) gT : screening mass in pQCD

In the limit μ(T)→0,

rTrT er

eT

TrV )()(1)(

),(

rrTrV

),(

Ψ’(2S)χc (1P)

GeVGeV

J/ψ (1S)

Screening mass

289 MeV298 MeV306 MeV315 MeV323 MeV332 MeV340 MeV

GeV

Binding energies & radii of charmonia

Screening mass (MeV)

Bin

ding

ene

rgy

(GeV

)

Screening mass (MeV)

Rad

ius

(fm

)

3. 2. dissociation cross section

• Bethe-Salpeter amplitudeDefinition ;

Solution in NR limit ;

Leading Order (LO)

quark-induced Next to Leading Order (qNLO)

gluon-induced Next to Leading Order (gNLO)

Leading Order (LO)

quark-induced Next to Leading Order (qNLO)

gluon-induced Next to Leading Order (gNLO)

In QGP

σdiss= ∑j σ jpQCD

1. partons with thermal mass

2. temperature-dependent wavefunctions from modified Cornell potential are used.

In hadronic matterFactorization formula:

σdiss(p)= ∑ j ∫dx σ ipQCD (xp)Dj i(x)

Dj i(x) is PDF of parton i in hadron j interacting with charmonia

1. Massless partons

mass factorization, loop diagrams and renormalization remove collinear, infrared and UV divergence respectively

2. Coulomb wavefunctions are used.

4. Charmonia in heavy-ion collisions

• Cronin effect• Nuclear absorption (nuclear

destruction)• Thermal decay and leakage effect• Regeneration

Two-component model

Initial production of J/ψ through binary N-N collisions

Thermalization (QGP formation)≈ 0.6 fm/c

HadronizationT≈ 170 MeV

Regenerated J/ψ Thermal decay

in hadronic matter

Thermal decay in QGP

Nuclear absorption

detector

Kinetic freeze-outT≈ 120 MeV

Thermal decay in hadronic matter

Cronin effect

Beforecc production

4. 1. Cronin effect

1. Charmonia are produced mainly through g+g fusion

2. Different from in p+p collision, gluon in A+B collision can get additional Pt through g+N collision

3. It broadens Pt distribution of gluons

4. Subsequently, it broadens Pt distribution of J/ ψ in A+B collision, compared with in p+p collision

ABggN

gN

tpp

Jt

AB

Jt LP

PP

2

/

2

/

2

Primordial J/ψ is produced

Nucleus A

Nucleus B

4. 2. Nuclear destruction

'

2

),()1(exp

),()1(exp

)',(),(')(

1),(

z

nucBBB

z

nucAAA

BAAB

nucnuc

zsbdzB

zsdzA

zsbzsdzsdzdbT

bS

Primordial J/ψ is produced

Nucleus A

Nucleus B

Nuclear destruction cross

section is obtained from pA

collisionσdiss=1.5mb

4. 3. Thermal decay

J/ψ

QGP phase

Mixed phase(Assuming 1st order phase transition)

HG phase

J/ψ

J/ψ

Thermal decay widths in QGP & HG

phaseHG in )()(

phase mixedin )(*)1()(*)(

phase QGPin )()(

J/ ofsection crosson dissociati :

J/ and jbetween velocity relative :

J/ ngdissociatihardon or parton ofdensity :

)()(),()2( 3

3

HG

HGQGP

QGP

diss

rel

j

dissreljj

j

ff

v

n

TTvTnkd

g

Ψ’(2S)χc (1P)

J/ψ (1S)

The leakage effect

Thermal decay width =0

Thermal decay width ≠0

Thermal decay width : Γ→Γ*θ[R(τ)-r(τ)]

Considering feed-down from χc , Ψ’ to J/ψ, '/ 08.025.067.0

HGQGPHGQGPJ

HGQGPHGQGP SSSS c

')'(exp0

dS HGQGP

Survival probability from thermal decay

4. 4. Regeneration

• From Glauber model (dσccNN/dy=63.7(μb) from

pQCD),

• From Statistical model,

• Discrepancy between them is corrected with fugacity

• GCE is converted to CE because of small # of pairs

),(),()( 2BBBAAA

NNcc

ABcc zsbdzzsdzsdABbN

VnnN ChiddenopenABcc C

2

1

VnVnN ChiddenCopenABcc 2

2

1

VnVnI

VnIVnN hidden

open

openopen

ABcc C

2

C 0

C 1C ) (

) (

2

1

Canonical suppression

Relaxation factor for kinetic equilibrium

ionhadronizatat time the:

iparton by

charm-charm/anti ofsection cross scattering elastic :

iparton ofdensity number :

)/(1 timerelaxation where,

exp10 .

H

i

i

reli

iirelax

relax

n

vn

dR

H

the number of regenerated J/ψ

NJ/ψrec=

VRγ2 {nJ/ψSJ/ψHG +Br(χc)*nχc *Sχc

HG + Br(ψ’) *nψ’* Sψ’HG }

• nJ/ψ, nχc , nψ’ : number densities of charmonia

• SJ/ψHG, Sχc

HG , Sψ’HG : survival rate of charmonia in HG

• Br(χc), Br(ψ’) : branching ratios of χc, ψ’ to J/ψ• R : relaxation factor• γ : fugacity

5. Results

• RAA vs. Npart

• RAA vs. pT

• <pT>

• V2

• Higher-order corrections in pQCD

5. 1. RAA of J/ψ

enhenced. is J/ 1, R

.suppressed is J/ 1, R

1

factoron modificatiNuclear

AA

AA

/

//

Jnn

JAA

coll

JAA N

N

NR

From RHIC near midrapidty at √sNN=200

GeV

RAA of J/ψ as a function of Npart

(near midrapidity in Au+Au collision at √s=200

GeV)

Regeneration

The role of coupling constant g in our model

1. ‘g’ determines dissociation temperatures of charmonia

(screening mass μ=√(Nc/3+Nf/6) gT) TJ/ψ=386 MeV, Tχc =199 MeV, TΨ’=185 MeV with

g=1.5

2. ‘g’ determines the thermal widths of charmonia (Г∼g2 in LO, and Г∼g4 in NLO)

3. ‘g’ determines the relaxation factor of charm quarks

W/O initial dissociation of J/ψ

without

RAA of J/ψ as a Function of pt

(For J/ψ, Tf=160 MeV)

<Pt2> of J/ψ

v2 of J/ψ (b=9 fm)

<Assumption>1. Elastic cross section

of J/ψ(color singlet) in QGP is much smaller than that of charm quark.

2. For J/ψ, inelastic collision is more effective than elastic collision in QGP because of its small binding energy and large radius at high T.

RAA of J/ψ as a function of Npart

(near midrapidity in Cu+Cu collision at √s=200 GeV)

Regeneration

Applying to Pb+Pb collision at √sNN=5.5 TeV (LHC) with the modified

parameters• by extrapolation,

Entropy dS/dη= 30.3{(1-x)Npart/2+xNcoll}

to 78.5{(1-x)Npart/2+xNcoll}, where x=0.11

J/ψ production cross section per rapidity in p+p collision

dσJ/ψpp/dy= 0.774 μb to 6.4 μb

• from pQCD,

cc production cross section per rapidity in p+p collision

dσccpp/dy= 63.7 μb to 639 μb

Ref. is NPA 789, 334 (2007)

7.36 μb at 7 TeV (Nov. 2010)

RAA of J/ψ as a function of Npart

(near midrapidity in Pb+Pb collision at √s=5.5 TeV)

Regeneration

5. 2. Higher-order corrections

• Dissociation cross section of charmonia σ [J/ψ+q(g)→c+c+q(g)] *A ; enhances decay of charmonia

• Elastic cross section of charm quarks σ [c+q(g)→c+q(g)] *B ; enhances regeneration of charmonia

Fractions of regenerated J/ψ

=(A,B)

RAA of J/ψ as a function of Npart

(near midrapidity in Au+Au collision at √s=200

GeV)

RAA of J/ψ as a Function of pt

<Pt2> of J/ψ

v2 of J/ψ (b=9 fm)

5. Summary

Summary of nuclear modification of charmonia in heavy-ion collision

• Before production; Cronin effect (pt↑)• After production; nuclear destruction (NJ/ψ↓) ; initial dissociation (NJ/ψ↓)• After thermalization; thermal decay (NJ/ψ↓); leakage effect (NJ/ψ↑, pt↑); regeneration (NJ/ψ↑); flow effect (pt↑)

Summary of results

• We reproduced successfully RAA of J/ψ in Au+Au and Cu+Cu collisions at RHIC and estimated RAA in Pb+Pb collision at LHC by using 2-component model.

• There seems to be a kink in RAA vs. Npart curve in Au+Au collision. → initial temperature begins to be over TJ/ψ?

• 2-component model vs. statistical model The number of J/ψ : the excessive number of J/ψ in 2-component

model is reduced by multiplying relaxation factor to regenerated J/ψ.

pt of J/ψ : In 2-component model, Cronin effect mainly enhances pt while in the statistical model, flow effect mainly enhances.

→ both models successfully describe RAA and pt of J/ψ in RHIC.

• Only v2 of J/ψ seems to be able to discriminate two models. → Precise measurement of v2 of J/ψ will reveal the fraction of

regenerated J/ψ