1

Su Houng Lee 1. Mesons with one heavy quark 2. Baryons with one heavy quark 3. Quarkonium

Arguments based on two point function can be generalized to higher point function

Heavy quark system and OPE

2

QCD

Chiral sym-metry break-

ing

Confinement

Phenomenol-ogy

One heavy quark

Two heavy quark

Heavy quark

3

1. Mesons with one heavy quark

4

Heavy quark propagator

mqqS

1)( where,...........)()()()( qSGqSqSqSG

Perturbative treatment are possible because

0for even qqm QCD

q

•

hh 2

121 Gm

5

..),(

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

......Tr0,)(

2

1

0

222

kmn

kmn

GmqLp

dxdp

Gpmqp

dplhqhlq

Perturbative treatment are possible when

222 1),( QCDxmqxxmqL

q

p

qp

which breaks down at x=0 due to light quark propaga-tor

One Heavy quark and one Light antiquark

6

n

Gh

mq

mqmqGG

qShqhq

22..

........

0,)(

Contribution from light quark condensate

222 QCDqm

q

qp

q

converges for large

7

.... 0,0, 2255

h

hiqx

mqm

hxhihxhidxe

Chiral order parameters

D(1870) D(2400)

qqm

qicxciqxdqcxcqxdc

mc2 )0(),()0(),( 5544

),(),( 0

s

msmsds DD

),( 0Dms ),( Dms

8

0 0||0d

V1

00||0Tr

11210||0Tr

0|1|00|1|0Tr21 0|1|0Tr0

4

0

55

xxx

mimi

imD

imDmD

m

Chasher-Banks formula

hh

h

iqxm

h

iqx

h

iqx

iqx

mm

xmD

xdxe

mimix

mDxdxe

mDxi

mDxi

mDxdxe

hxhihxhidxe

2 00||02

020||0|1|Tr

110||0|1|Tr

0|1|0|1|0|1|Tr

0,0,

0

55

55

9

Chasher-Banks formula –correlator with h-quark

h

hh

h

iqxm

h

iqx

h

iqx

iqx

m

mm

xmD

xdxe

mimix

mDxdxe

mDxi

mDxi

mDxdxe

hxhihxhidxe

8

0|00|08 02|00|4

020||0|1|Tr

110||0|1|Tr

0|1|0|1|0|1|Tr

0,0,

0

55

55

10

hh

h

iqxm

h

iqx

h

iqx

h

iqx

iqx

mm

xmD

xdxe

mimix

mDxdxe

mDx

mDx

mDxdxe

mDxi

mDxi

mDxdxe

hxhihxhidxe

2 00||01

00||0|1|Tr

110||0|1|Tr

0|1|0|1|0|1|Tr

0|1|0|1|0|1|Tr

0,0,

0

55

55

Chasher-Banks formula – with heavy quark

qqm

qicxciqxdqcxcqxdc

mc2 )0(),()0(),( 5544

11

• Direct observation of chiral symmetry restoration in medium

D(1870) 0-

D(2400) Belle

G > 200 MeV

0+

D 0qq

..0

)3.0 to2.0(1mn

qqqq

Hayashigaki (00)

Weise, Morath, Lee (99)

Generalization to other channels: Kampfer et a. (10), Mishra et.al., Z. Wang

• QCD sum rule approach: Hayashigaki, Weise, Morath, Lee

12

..12

1........

0,)(

0

022.. G

GG

G

GGGG

kmq

mqmqGG

qShqhq

n

Gh

but no convergence model approach

Heavy quark symmetry

ii

ki

ki

0

05

0

05 12

112

1

ii ik

ik

5

0

05

0

0 12

1112

11

D D*

D0 D1

near mass shell kmvq

13

Qq quark system in vacuum and medium: Chiral symme-try

D(1870)

0-

D(2400)2318 ?

0+

D*(2007)

1-

D1(2420)

1+

Ds(1968)

Ds(2317)

D*(2112)

Ds1(2460)

530448 ?

413 349348

0- 0+ 1- 1+

137 144

xxx? 396xxx 345

B(5279)

B(57xx)?

B*(5325)

B1(5721)

Bs(5366)

Bs(58xx)?

Bs*(5415)

Bs1(5830)

4646

14

2. Baryons with one heavy quark

15

Chasher-Banks formula - <** >

2

'0

'

55

55

21

0|00|00|00|02

1

00||0'0|''|21Tr0|1|

110||'1

'10|''|

21Tr0|1|

0|1|0|1|0|1|Tr0|1|

0,0,

h

h

h

iqxm

h

iqx

h

iqx

TTTTiqx

m

m

xxmD

xdxe

mimix

mimix

mDxdxe

mDxi

mDxi

mDx

mDxdxe

hdCuxhCduhdCiuxhCdiudxe

),(),( *

smsmsds

16

3. Quarkonium

17

..),(

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

......Tr0,)(

2

1

0

222

kmn

kmn

GmqLp

dxdp

Gqpmp

dplhqhlq

Perturbative treatment are possible when 2222 412),( QCDqmqxmqL

2q

System with heavy quark anti-quark

p

qp

222 4 QCDqm

18

q2 process expansion parameter example

0 Photo-production of open charm

m2J/

> 0 Bound state properties

Formalism by Peskin (79)

J/ dissociation: NLOJ/ mass shift: LO

-Q2 < 0 QCD sum rules for heavy quarks

Predicted mhc <mJ/ before experiment

Perturbative treatment are possible when 222 4 QCDqm

2

2

4mQCD

22

2

4 QmQCD

2/

2

2

4 J

QCD

mm

0/

2

2

J

QCD

mm

19

n

nQCDn

nnn

FGqxqm

xqFdxq

..)12(4

),(...)(2222

21

0

2/

2Jmq

Subtlety for bound states Applequist, Dine, Muzinich (78), Peskin (79), Basis for pNRQCD ........

)1( ))()((

)(2244

3242 O

mgmgmgmgmgg

c

c

c

c=

42 1 ,1 , mgt

mga

pm

Separation scale

20

qc

c

OPE for bound state: m infinity

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

Mass shift: QCD 2nd order Stark Effect : Peskin 79 e > L qcd

Medium

220

6

2/3

0

20

2/1

)1(9128 E

maxxxdxamJ

Attractive for ground state

Separation scale

For small T modify matrix el-ement

21

Summary of analysis of Stark effect+ QCD sum rule (Morita-Lee)

• Due to the sudden change of condensate near Tc

</ B2

>T

</ E2 >T

G0

G2

• Abrupt changes for mass and width near Tc

(GeV)/Jm

22

• QCD sum rule for Quarkonia at nuclear matter: Klingl, Kim, SHL,Weise (99), Hayashigai (99)

• Contribution from complete dim 6 operators: Kim SHL (01)

mass shift at nuclear matter: -7 MeV (dim 4) -4 MeV (dim4+ dim6)

• QCD sum rule + MEM at finite temperature: Gubler, Oka, Morita

QCD sum rule for Quarkonia in medium

• looking forward to further work

23

W(S-T)=exp(-s ST)

Time

Space

Space

SW(S-T) = 1- </ E2> (ST)2 +..

W(S-S) = 1- </ B2> (SS)2 +..

OPE for Wilson lines: Shifman NPB73 (80)

<E2>, <B2> vs confinement potential

• Local vs non local behavior

W(S-S)= exp(-s SS)

T

• Behavior at T>Tc

W(SS)= exp(-s SS)

W(ST)= exp(- g(1/S)T)

</ B2

>T

</ E2 >T

24

rrrrV s s )(

34)(

)(GeV 2s

small s

r

b decdec /)0()( TTTT ss

dec/TT

T/Tc

sString Tension: QCD order pa-rameter

Early work on J/y at finite T (Hashimoto, Miyamura, Hirose, Kanki)

25

Chiral sym-metry break-

ing

Confinement

JPARCOne heavy

quark

Two heavy quark

Heavy quark

Analytic approaches

Lattice calculation

26

2. Correlators with one Heavy quark: lead to sum rules relating well known chiral operators to spectral density

+ others that will be worked out. b) Obtain Weinberg type sum rule c) Nuclear target ? Heavy ion at JPAR

1. All Chiral symmetry order parameters zero eigenvalue solutions in QCD

Summary

3. Correlators with heavy quarks only : Quarkonium in medium will give new insights into confinement problem

qqm

qicxciqxdqcxcqxdc

mc2 )0(),()0(),( 5544

..... )( ,)0()( , AAxVVxqq ss