1

Su Houng Lee

1. Hadrons with one heavy quark

2. Multiquarks with one heavy quark

3. Quarkonium

Arguments based on two point function

can be generalized to higher point function

Hadron Physics with Heavy quarks

2

QCD

Chiral sym-metry break-

ing

Confinement

Phenomenol-ogy

One heavy quark

Two heavy quark

Heavy quark

3

1. Hadrons with one heavy quark

4

Heavy quark propagator

mqqS

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

Perturbative treatment are possible

because

0for even qqm QCD

q

•

hh 2

12

1G

m

5

..),(

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

......Tr0,)(

2

1

0

222

kmn

k

mn

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

.... 0,0,22

55

h

hiqx

mq

mhxhihxhidxe

Chiral order parameters

D(1870) D(2400)

qqm

qicxciqxdqcxcqxdc

mc2

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

),(),(

0

s

msmsds DD

),( 0Dms ),( Dms

8

• Direct observation of chiral symmetry restoration in medium

D(1870) 0-

D(2400) Belle

G > 200 MeV

0+

D p0qq

..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

9

..1

2

1........

0,)(

0

0

22..

kmq

mqmqGG

qShqhq

n

Gh

but no convergence model approach

Heavy quark symmetry

ii

ki

ki

0

05

0

05 1

2

11

2

1

ii ik

ik

5

0

05

0

0 1

2

11

1

2

11

D D*

D0 D0

near mass shell kmvq

10

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)

530

448 ?

413 349348

0- 0+ 1- 1+

137144

xxx? 396xxx 345

B(5279)

B(57xx)?

B*(5325)

B1(5721)

Bs(5366)

Bs(58xx)?

Bs*(5415)

Bs1(5830)

4646

11

2. Multiquarks with one heavy quark

1. Some introduction with diquarks

2. Possible multiquark states

12

Babar: DSJ(2317) 0+

Puzzle in Constituent Quark Model(2400) 1. D0 K+ (2358) threshold effect

2. Chiral partner of (0- 1-)

3. Tetraquark

X(3872) G<10 MeV , Y(4260),

Z(4430) G<50 y’p

Z(4051),Z(4248) cc1p

Zb(10610), Zb(10650) Up

molecule ?

D0 D* D1

1864 2007 2420

D0+D* D*+D* D+D1 D1+D*

3872 4014 4284 4427

B0 B* B1

5279.5 5325.1 5721

B0+B* B*+B* B+B1 B1+B*

10604.6 10650.2 11000.5 11046.1

Belle

Recent highlights on Multi-quark hadrons –heavy quark sector

13

Normal meson

Tetraquark Molecule

Geometri-cal config-

uration

Flavor quantum number

ud ud ud

u uud

ud

uu

ud

Navara, Nielsen, SHLee Phys Rept (11)

Normal meson, Tetraquark and Molecule

14

Color spin interaction (De Rujula, Georgi, Glashow..)

q1 q2 q4

Diquark vs. quark-antiquark configurations

Color Spin Flavor D

Q-Q 3bar 0 3bar -2

1 6 2/3

6 0 6 1

1 3bar -1/3

Color Spin Flavor D

Q-Qbar 1 0 1,8 -4

1 1,8 4/3

8 0 1,8 1/2

1 1,8 -1/6

q2

jj

aj

aiji ss

Diquark attracation vs quark-antiquark

2121

1

mmssCB

q3q1

q2

3131

1

mmssCM

BM CC 3

15

Recently observed states with hidden heavy quark Yasui

Most probably molecular state NOT tetraquark

jj

aj

aiji

jig ss

mmH 1q3q1

c c

q3

q1 c

c

q3q1

cc

q3q1

c c

p p

p

D D* D1

D*

X(3872)

Z(4430)

16

Diquark attracation vs quark-antiquark

2121

1

mmssCB

q3q1

q2

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

Type of diquark and its q-q binding

S=C=0 (ud) A

S=-1, ms=5/3mu (us) 3/5 A (ds) 3/5 A

C=1, mc=5mu (uc) 1/5 A (dc) 1/5 A (sc) 3/25 A

MeV 1454

3A

2

u

B

m

C

3131

1

mmssCM

BM CC 3

23 3 make mm

Multiquark configuration –Yasui, Ko, Liu, Lee (08,09)

q3

17

1+ u d c c u dc c 0- 1-)cc(udT1cc

22 4

1

4

3

c

B

u

B

m

C

m

C

cu

M

cu

M

mm

C

mm

C

4

1

4

3

- Binding against decay = - 79.3 MeV

• A picture of Lc (K.Kim, D. Jido, SHL)

u d c

4

32u

B

m

C

Tetra-quark

• A Tetraquark

18

u d

0+

) Oka (M. repulsion Instanton MeV 29Binding H

u s

d s

u d

s

u d

s

H di-baryon

su

B

u

B

mm

C

m

C

4

32

4

32

22 4

3

4

3

u

B

u

B

m

C

m

C

Di-baryon (conf 1) – (qq)(qq)(qq)

19

u d

0+

MeV 92Binding H c

u s

Hc di-baryon

u c

u d

u

u

c

s

Hc di-baryon P Xc

cu

B

su

B

u

B

mm

C

mm

C

m

C

4

3

4

3

4

32

su

B

u

B

mm

C

m

C

4

3

4

32

Kpp

ppK

c

c

)(

)( (udusuc)H 0c

mc 132

Di-baryon (conf 2) – (qq)(qq)(qQ)

20

3. Quarkonium

21

..),(

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

......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

22

q2 process expansion parameter

example

0 Photo-production of open charm

m2J/ y

> 0 Bound state properties

Formalism by Peskin (79)

J/y dissociation: NLOJ/y mass shift: LO

-Q2 < 0 QCD sum rules for heavy quarks

Predicted mhc <mJ/y 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

23

n

nQCDn

nnn

FG

qxqm

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

mgmgmg

mgmgg

c

c

c

c

=

42 1 ,

1 , mg

tmg

apm

Separation scale

24

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(9

128E

maxx

xdx

amJ

Attractive for ground state

Separation scale

For small T modify matrix el-ement

25

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

• Due to the sudden change of condensate near Tc

<a/p B2

>T

<a/p E2 >T

G0

G2

• Abrupt changes for mass and width near Tc

(GeV)/Jm

26

NN

NN

N

mxdxxGmG

mGm

0.9 ),(2

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

Op Op

22

000

• Linear density approximation

• Condensate at finite density

n.m.0

000 0.061-1

9

8

GmGG N

Tc

2

0

2

5

2 0.7 ..

GGGmn

• At r = 5 x r n.m.

167.0 2.0

167.0 2.0

2

2

s

s

B

E

9.02

sG

Operators in at finite density and hadronic phase

27

• 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

28

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

Time

Space

Space

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

W(S-S) = 1- <a/p 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)

<a/p B2

>T

<a/p E2 >T

29

SU(3) Gauge Boyd (1996)

2+1 HotQCD (2012)

Behavior near Tc

30

rr

rrV s )(

3

4)(

)(GeV 2

small

r

b decdec /)0()( TTTT

dec/TT

T/Tc

sString Tension: QCD order pa-rameter

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

31

Chiral sym-metry break-

ing

Confinement

JPARCOne heavy

quark

Two heavy quark

Heavy quark

Analytic approaches

Lattice calculation

32

1. Hadrons with one heavy quark (D, …) in medium can give new insight into chiral symmetry restoration

a) nuclear target ? Heavy ion at JPAR

b) Lattice calculation

Summary

2. Molecules are interesting. Flavor exotic multiquark states will exist in the heavy sector

a) From B decay

b) From JPARC

3. Quarkonium in medium will give new insights into confinement prob-lem

33

S=C=0 (ud) -A

S=-1, ms=5/3mu (us) -3/5 A (ds) -3/5 A

C=1, mc=5mu (uc) -1/5 A (dc) -1/5 A (sc) -3/25 A

MeV 1454

3A

2

u

B

m

C

u d

A- A-

1/2+

s

MeV 487MeV '

468A5

4Binding

u d

L=1

u d s

u

d

A- A5

9-

MeV 46823

)1670()1520(2 2*]2/1[

*]2/3[

I

LL2 contribution

- 500 MeV

in Five body quark model by Hiyama, Hosaka et al (06)

Q+

P K

Q+ (Jaffe Wilczek) in a naïve quark model

Multiquark configuration –Yasui, Ko, Liu, Lee (08,09)