1

Heavy quark system in vacuum and in medium

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

Hadronic Physics at B-factory, LEPS and J-PARC

B-factory

Heavy quark physics

Heavy Exotics

LEPS:

Chiral, Exotics

J-PARC

D, anti-p, nuclear matter

Heavy Exotics

qq, Qq in nuclear matter Chiral symmetry breaking

QQ in nuclear matter confinement

S H Lee 3

Some perspectives on sQGP and

relation to deconfinement

K.Morita, SHL: PRL 100, 022301 (08)

K.Morita, SHL: PRC 77, 064904 (08)

SHL, K. Morita: PRD 79, 011501 (09)

Y.Song, SHL, K.Morita: PRC 79, 014907 (09)

S H Lee 4

QCD Phase transition: Lattice data on ( , p)

Rescaled pressure (Karsch 01) Karsch hep-lat/0106019

Lattice result for purge gauge (Boyd et al 96)

p/T4

/T4

Sudden increase in

Slow increase in p

Latest Lattice result (Bazavov et al 09)

sQGP

S H Lee 5

Two gluon operators (quenched case): M2 M0

2

8

9

4ST G

gGGT

pgpguuT 34

1

4

1

02 M4

1M

4

1 gguuT

• Operators

• Thermodynamics

• Energy momentum Tensor

Twist-2 Gluon Gluon condensate

pGG

TspBE

3 8

11M

3

2 M

0

2

T

20

T

222

sQGP

S H Lee 6

BTp

BT

QGP

QGP

4

g

4g

d

d 3

400 MeV 189)0()(4

1 MTMB c

EOS in terms of M0 M2Bag model EOS in QGP phase

02

02

M4

1M

4

1

M4

1M

4

3

p

Dominated by non perturbative change at Tc : SHL, PRD40,2484 (89)

Effects of dynamical quarks on M0

GeV4

T

2G

M0, M2 and Bag model EOS

8

11M

0

2

T

20

GG

S H Lee 7

02

T

2

02T

2

M9

2 M

4

3

M9

2 M

4

3

TB

TE

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))

Using s from Kaczmarek et al (prd04)

Deconfinement involves both perturbative (M2) and Non perturbative (M0) change

M0, M2 E2, B2 confinement

S H Lee 8

NN

NN

N

mxdxxGm

mm

0.9 ),(2 M

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

Op Op

22

000

• Linear density approximation

• Condensate at finite density

n.m.0

22 0.061-1

GG

Tc5

Tc

2

0

2

5

2

0

0.7

..

..

mn

mn

GGG• At = 5 x n.m.

167.0 2.0

167.0 2.0

2

2

s

s

B

E

M0, M2 in nuclear matter

S H Lee 9

QCD vacuum 40

2

0

2

0

2 GeV 35.022 EBG

Nuclear medium: 20% deconfinement

0Medium

2 M11

8 G

20Medium

2

20Medium

2

M4

3M

9

2

M4

3M

9

2

s

s

B

E

S H Lee 10

Approaches to Heavy quark system in medium

OPE, QCD Stark Effect, and

QCD sum rules

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 baTqm QCD

• Even in medium as long as

S H Lee 12

2q

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

2nd order Stark Effect

NLO width (Song, Lee 05)

Applicable cases

S H Lee 13

qc

c

OPE for bound state: m infinity

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

QCD 2nd order Stark Effect : > qcd

Medium

220

6

2/3

0

20

2/

1

)1(9

128E

maxx

xdx

amJ

Attractive for ground state

)1( ))()((

)(2244

3242 O

mgmgmg

mgmgg

c

c

c

c

S H Lee 14

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 15

2q

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

Constraint on (m,

Applicable cases

S H Lee 16

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 17

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 in mediumMedium0

22 G 4 GQm

S H Lee 18

• QCD sum rule constraint

Mass and width of J/ in nuclear Matter (Morita, Lee 08)

mb 2 with

MeV 3.1

/

//

NJ

NrelNJNJ v

/

2

2

/

MeV 2.3

J

NJN

NrelN

r

r

v

c

c

c

S H Lee 19

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++ -20 MeV -15 MeV

(Morita, Lee)

No effect on c1

(3686)

1-- -100 MeV < 30 MeV

(3770)

1-- -140 MeV < 30 MeV

Other approaches for mass shift in nuclear matter

S H Lee 20

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 21

Some perspectives on

Diquarks and

heavy exotics

F.Navara, M. Nielsen, SHL: PLB 649, 166 (07)

SHL, S.Yasui, W.Liu, CMKo: EPJC 54, 259 (08)

SHL, M. Nielsen et al: PLB 661, 28 (08)

SHL, K.Morita, M.Nielsen: PRD 78, 076001 (08), NPA 815,29 (09)

SHL, M.Nielsen, U. Wiedner: JKPS 55,424(09)

SHL, S. Yasui: EPJC (09) in press

S H Lee 22

JPC Special feature

QSR tetraquark

QSR molecule Others

X(3872) 1++ B(XJ)/B(X)=1

[AV][S] m=3.92(Nielsen ..)

DD* m=3.87 (Nielsen, ..)

QSR with (Morita) ,

Mixture with cc

Y 1–-

ISR

Belle 4260,4360,4660

BaBar 4260,4360

[V][S] q=s m=4.65

q=u,d m=4.49(Nielsen, et al)

Ds0Ds* m=4.42D0D* m=4.27DD1 m=4.19

(Nielsen et al )

Hybrid

Z+(4430) ?,0- ’ [PS][S] m=4.52

(Nielsen, et al)

D*D1 m=4.40(Nielsen, Lee et al )

Z+(4050,4250)

? D*D* m=4.15DD1=4.19(Nielsen, et al )

D*D*(4020)D1D(4285) threshold

effect

Newly observed states

,cq[AV] ,cq[V] ,cq[PS] ,cq[S] bTab5

Tab

Tab5

Ta CCCC

,cqD1 ,cqD* ,cqD ,cqD0 55 i

S H Lee 23

QCD sum rule results on X(3872), Z(4430)

In principle QCD can not distinguish between diquark configuration and molecular configuration

However, seems to favor molecular current for all states

S H Lee 24

Tetraquarks: Jaffe

color spin interaction: light scalar nonet

jj ji

aj

aijiH mm

ssC1 q3q1

q2 q4

diquark picture: Yasui, Lee,.. (EJP08,EJP09)

• Heavy Dibaryon Hc: (ud) (us) (uc) stable against (ud) u + (us) c

• Heavy Tetraquark with spin 0 or spin 1

S H Lee 25

color spin interaction: light scalar nonet

jj ji

aj

aijiH mm

ssC1 q3q1

q2 q4

Two heavy anti-quarks: explicitly exotic

Heavy and explicitly exotic tetraquarks

S H Lee 26

Belle: PRL 98, 082001 (07)

e+ e- J/ + X(3904)

D D*

Tcc (3800)

e+

e

c

c

SHL, S Yasui, W Liu, C Ko (08)

Can look for 1+ (Tcc)

Previous works on TccZ. Zouzou, B. Silverstre-Brac, C. Gilgnooux, J Richard (86), D. Janc, M. Rosina (04), Y. Cui,

S. L. Zhu (07)

QCD sum rules: F Navarra, M.Nielsen, SHLee, PLB 649, 166 (2007)

simple diquark: SHL, S. Yasui, W.Liu, C Ko EPJ C54, 259 (2008), SHL, S. Yasui: EPJ C (09) in press

c

c

S H Lee 27

1. QCD phase transition is characterized by Perturbative M2 and Non perturbative M0 change 20% effect at Nuclear matter

3. More work on X,Y, Z are needed.

2. Heavy quark system can probe these changes and study confinement physics FAIR, J-PARC

Summary

4. Explicitly Exotic heavy particles: Hc, Tcc, … FAIR, J-PARC

D, anti-proton etc..