1

Heavy quark system near Tc

Su Houng Lee In collaboration with Kenji Morita

Also, thanks to group members:

Present: T. Song, K.I. Kim, W.S. Park, H. Park, K. Jeong

Former: K. Ohnishi, S. Yasui, Y. Song

S H Lee 2

Early work on J/ (Hashimoto, Miyamura, Hirose, Kanki)

rr

rrV s )(

3

4)(

)(GeV 2

small

r

b decdec /)0()( TTTT

dec/TT

S H Lee 3

J/ in Quark-gluon plasma

• Matsui and Satz: J/ will dissolve at Tc due to color screening

• Lattice MEM : Asakawa, Hatsuda, Karsch, Petreczky ….

J/ will survive Tc and dissolve at 2 Tc

• Potential models (Wong …) :

Consistent with MEM Wong.

• Refined Potential models with lattice (Mocsy, Petreczky…)

: J/will dissolve slightly above Tc

• Lattice after zero mode subtraction (WHOT-QCD)

: J/wave function hardly changes at 2.3 Tc

• AdS/QCD (Kim, Lee, Fukushima ..)

: J/mass change

• And so on ……….

S H Lee 4

Comparison with experimental data of RHIC (√s=200 GeV at midrapidity)

T. Song (preliminary)

S H Lee 5

Some perspectives on sQGP and

relation to deconfinement

S H Lee 6

Some perspectives from Lattice data on ( , p) near Tc

Karsch hep-lat/0106019

pGGM

pGGM

3 8

11

ST

0

2

T

20

T2

Lattice data (Karsch et al) vs. Resummed perturbation (Blaizot et al.)

Operator representation: Gluon condensates

sQGPJ/

sQGP

S H Lee 7

)0()(4

100 MTMB c

02

02

4

1

4

1

4

1

4

3

MMp

MM

42 MeV 1898

9

4

1

G

0.3 0

2G

SHLee PRD40,2484(89)

Dominated by non perturbative change at Tc

M0 and Bag pressure

M0 and Gluon condensate 00

2

T

2

11

8 MGG

GeV4

T

2G

S H Lee 8

20

T

2

20T

2

4

3

9

2

4

3

9

2

MT

MB

MT

ME

s

s

Relation to Electric and Magnetic condensate

Relation to deconfinement

< E2 >T

< B2 >T =0

W(S-T)

W(S-S)

Time

Space

Space

L

L

OPE 1- </ E2> (ST)2 +…

OPE 1- </ B2> (SS)2 +…

exp(- V(T))

1

2

2

d

1

32

2

d

/

2

3

32

/

22

3

32

TEk

TEk

k

k

e

k

E

kB

e

mk

E

kE

Kaczmarek et al (prd04)

S H Lee 9

Heavy quark system in sQGP

OPE, QCD Stark Effect, and

QCD sum rules

S H Lee 10

MIT Bag

B

Vacuum with negative pressure

QCD vacuum

sQGP at Tc

0

2

Tc

2 7.0 GG

4

0

2 GeV 35.0G Large increase in E2

Heavy quark system near Tc

S H Lee 11

)0(),()( ccxccdxeq iqx

Heavy quark correlation function (q2)

..)12(4

),(...)(

2222

21

0

n

n Gqxqm

xqFdxq

• OPE makes sense when 2

vacuum

22 G 4 QCDqm

Definition

Operator product expansion (OPE)

qc

c

nG

2

medium

22 G 4 aTqm QCD

• Even at finite temperature or as long as

S H Lee 12

02 q

nn

n Gm

Cq

2

2

4)0(

222 2 4 QCDmqm

q2=0 : photo production of open charm

q2=m2J/ : OPE for bound state (Peskin 79)

c

c

nG

222 4 QCDQm

-q2 >0 : QCD sum rules for heavy quarks

22 4 QCDm

S H Lee 13

02 q

222 2 4 QCDmqm

q2=m2J/ : OPE for bound state (Peskin 79)

c

c

nG

S H Lee 14

qc

c

OPE for bound state: m infinity

)( || ),( 16/ 24220 mgOkmgOgNm c

QCD 2nd order Stark Effect : > qcd

T

J Emaxx

xdx

am 2

20

6

2/3

0

20

2/

1

)1(9

128

Attractive for ground state

T/Tc 1.0 1.05 0

mJ/ -44 MeV -105 MeV 311 MeV

m -4.3 MeV -10 MeV 580 MeV

)1( ))()((

)(2244

3242 O

mgmgmg

mgmgg

c

c

c

c

S H Lee 15

2nd order Stark effect from pNRQCD

LO Singlet potential from pNRQCD : Brambilla et al.

S O

Derivation

1/r > Binding > QCD,

• Take expectation value

• Large Nc limit

• Static condensate

• Energy

•

S H Lee 16

02 q

c

c

nG

222 4 QCDQm

-q2 >0 : QCD sum rules for heavy quarks

S H Lee 17

n

n

n Qs

sdsJQJ

dQ

dM

)(

)()0(),(

22

n

J

J

JJ

n

n

m

m

f

mmm

M

M

2'

2/

/

2/

2'2

/1

Q2=-q2>0, QCD sum rules for Heavy quark system

OPE

..

4!

)!4(1 22

2

c

nnm

G

n

naM

Phenomenological side

..

12

'

2/

/2/

n

JJn

J

n m

mcf

mM

s

J/

’

n

n

M

M 12with G

02 G

sum rule at T=0 : can take any Q2 >=0, 2

vacuum

22 G 4 QCDQm

S H Lee 18

Matching Mn-1/Mn from Phen to OPE

Obtain constraint for mJ/ and

OPE

.......................

4!

)!4(1 22

2

c

nnm

G

n

naM

Phenomenological side

222/

)(

sms

sfs

J

s

J/

’

<G2>+c<G2>

nn Qs

sdsM

)(

)(2

n

n

M

M 1

<G2

><G2>

sum rule near TcT

GQm 0

22 G 4

S H Lee 19

QCD sum rule constraint (Morita, Lee 08)

MeV

]

MeV

]mMeV]

mMeV]

)(

!

112

22

n

n

Qs

sdsQ

dQ

d

n

S H Lee 20

Summary

=constraint-m (Stark effect)

GeV

/JM

QCD sum rule limit with =0

m from QCD Stark Effect

GeV

/J

Mass and width of J/ near Tc (Morita, Lee 08)

NLO QCD Song (07)

T/Tc

(

MeV

)

S H Lee 21

Prediction from the bottom-up AdS/QCD model

YK, J.-P. Lee, and S. H. Lee, PRD (2007)

Deconfinement + temperature effects.Effect of gluon condensate is missing. So, above Tc detailed study about the competition between the temperature and

gluon condensate should be done .

S H Lee 22

SummaryS-wave vs. P-waves

OPE breaks down

S H Lee 23

Summary bb system

S H Lee 24

1. Expected mass shift for J/ is order 50 MeV at Tc

Experimental observation from RHIC is difficult at present

2. Larger effect for excited states

3. Small effect for but larger b

S H Lee 25

NN

NN

N

mxdxxGm

mm

0.45 ),( M

MeV 750 N|(Chiral)T|N M ,N|Op|N2

Op Op

22

000n.m.

• Linear density approximation

• Gluon condensate at finite density

n.m.0

22 0.061-1

GG

05

Gluon condensate in nuclear matter

RHIC energy scan

FAIR

S H Lee 26

Quantum numbers

QCD 2nd Stark eff.

Potential model

QCD sum rules

Effects of DD loop

c0-+ –8 MeV –5 MeV

(Klingl, SHL ,Weise,

Morita)

No effect

J/ 1-- –8 MeV(Peskin, Luke)

-10 MeV(Brodsky et al).

–7 MeV(Klingl,

SHL ,Weise, Morita)

<2 MeV(SHL, Ko)

c0,1,2++ -40 MeV -15 MeV

(Morita, Lee)

No effect on chi_1

(3686)

1-- -100 MeV < 30 MeV

(3770)

1-- -140 MeV < 30 MeV

Other approaches for mass shift in nuclear matter

S H Lee 27

Anti proton

4 to 6 GeV/ck

Heavy nuclei

3 2

11.2

0.17 5fm

fm fm

e

e

Observation of m through p-A reaction

Expected luminosity at GSI 2x 1032cm-2s-1

Can be done at J-PARC

S H Lee 28

1. Properties of QQ system in sQGP is still controversial

3. Partial observation at nuclear matter through p A reaction might be possible. FAIR, J-PARC

2. The mass and width will suddenly change at Tc different for s p wave and bottonium can probe confinement physics

Summary

4. A new constraint for heavy quark system near Tc