1

Charmonium states in QGP

Su Houng Lee, Yonsei Univ.

2

Lattice result for phase transitionsLattice result for phase transitions

Confinement: L=e-F Chiral sym: <qq>

EOS: , p Heavy quark V(r)

J/ suppressionMatsui Satz 86

3

2003: Asakawa and Hatsuda claimed J/ will survive up to 1.6 Tc

Quenched lattice calculation by Asakawa and Hatsuda using MEM

T< 1.6 Tc

T> 1.6 Tc

J/ peak at 3.1 GeV

J/J/in Quark Gluon Plasmain Quark Gluon Plasma

4

C. Y. Wong… : Deby screened potential

(Ge

V

)

0

-0.8

Tc 1.6xTc

J/ Binding energy as a function T J/ wave functions at finite T

Some more recent work- ISome more recent work- I

5

What happens to J/What happens to J/ at T at Tcc ? ?

We will use QCD sum rule to answer this question because on can relate

“Critical” behavior of p properties of J/

6

Few words on QCD sum ruleFew words on QCD sum rule

Based on Dispersion relation and OPE

nnnn

n

n Q

nOpCpert

Qs

sdsQ

dQ

dM

)(

)(

)()(

22

2

For Heavy quarks

1. Q2 (4mc2+Q2), expansion in

n

cn m

GeV

Q

nOp

2

5.0)(

)()( 2/ Jmsfs 3. Works well for cc states with

2

2

4

)(

cn m

G

Q

nOp 2. <Op> Gluon operators

only

22/

1 4 cJn

n mmM

M

predicted Mc<MJ/ before experiment

7

QSR for heavy quarks at finite TQSR for heavy quarks at finite T

Previous attempts: Furnstahl, Hatsuda, Lee (90) at high T

Klingl, Weise, Lee, Kim (99), Hayashigaki (99) at finite density

Near Tc : Morita, Lee (07)

1. All temperature effects in operator n

cn

T

m

cTGeV

Q

nOp

2

5.0)(

Phenn

n

OPEn

n

M

M

M

M 11 4. Extract temp dependence from

GGG , 2

2. <Op>T two Gluon operators

222 )()(

sms

sfs

J

3. Include possible width change

8

T dependence of condensates T dependence of condensates (Morita, Lee07)

2

2

)(G

g

gGGT

pgpguupguupT 34

1

4

1

02 4

1

4

1GgGguuT

9

T dependence of Mass and width T dependence of Mass and width (Morita Lee07)

Tc Tc

If =0 If m=0

10

T dependence of width from NLO QCDT dependence of width from NLO QCD

Thermal width of J/ in pure glue theory at NLO QCD Song (07)

T/Tc

(

MeV

)

(

MeV

)

mJ/y

QCD sum rule constraint for mass shift and thermal width of J/ : Morita, Lee (07)

Assuming = 50 MeV at Tc, the mass shift could be -150 MeV at T=1.04 Tc

11

Application to finite density Application to finite density (Klingl, Weise, Lee (99), .. Morita(07))

Assuming J/-N=2mb,

= (J/-N v N) =1.3 MeV

Mass shift 7 MeV

Using linear density approximation

12

Possible observation in anti proton project at GSIPossible observation in anti proton project at GSI

Anti proton

4 to 6 GeV/ck

Heavy nuclei

3 2

11.2

0.17 5fm

fm fm

e

e

13

SummarySummary

1. Critical behavior of J/ near Tc, mass shift and width broadening

possible observation at LHC? Or RHIC (di-electron)?

change in multiplicity of J/ ?

similar mass shift could be observed at GSI

2. Need to improve the calculation

include continuum to investigate higher temperature

extend to unquenched calculation