1

Theoretical aspects of exotic hadrons

Su Houng Lee

1. Few words on hadronic molecule candidates

2. Few words on diquarks and heavy Multiquark States

3. Summary of disucssions

2

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) , Y(4260),

Z(4430) ’

Z(4051),Z(4248) c1

Must contain cc ?

molecule ?

Recent Highlights in Hadron Physics – Heavy quark sector

D0 D* D1

1864 2007 2420

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

3871 4014 4284 4427

3

Scalar tetraquark (Jaffe 76)

Search for H dibaryon Search for + pentaquark

Previous Work on Multiquark hadrons - Light quark sector

(1405) (Jido, Sekihara..)

N K +

4

New perspectives on hadron physics from RHIC

particle H f0 a0 Ds0 X(3872) (1405)

correlation K+ K- D0 K+ D0 D0* P K-

large number of c , b quark production

Vertex detector: weakly decaying exotics

Larger source size: A. Ohnishi ..

5

Some insights from for Multiquark configurations in a

schematic quark model

ji

jiji

H ssmm

C

,

.confining.Kinetic Mass

6

Color spin interaction

color spin interaction:

jj

aj

aiji

jijj

aj

aijig

ss

mmCssH

,

q1 q2 q4

Diquark configurations vs. quark-antiquark configurations

Color Spin Favor Q-Q 3bar 0 3bar -2

1 6 2/3

6 0 6 1

1 3bar -1/3

Color Spin Favor Q-Qbar 1 0 1,8 -4

1 1,8 4/3

8 0 1,8 1/2

1 1,8 -1/6

q2

Takeuchi

7

MeV 4700 MeV, 1500 MeV, 500 MeV, 300 bcsdu mmmmm

Diquark inside Baryons

u d u d

s

s

ji

jiji

B ssmm

C

,

.confining.Kinetic Mass

du

B

mm

C

4

3conf.Kinetic Mass c

su

B

du

B

mm

C

mm

C

4

1conf.Kinetic Mass c

Example

Mass diff M –MN M-M Mc-Mc Mb-Mb

Formula 290 MeV 77 MeV 154 MeV 180 MeV

Experiment 290 MeV 75 MeV 170 MeV 192 MeV

8

quark antiquark in Meson

d u d u

Works very well with 3x CB = CM = 635 mu2

u d d ux 3 =

Mass diff M –M MK*-MK MD*-MD MB*-MB

Formula 635 MeV 381 MeV 127 MeV 41 MeV

Experiment 635 MeV 397 MeV 137 MeV 46 MeV

ji

jiji

M ssmm

C

,

.confining.Kinetic Mass

9

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 480MeV 366A5

4Binding

u d

L=1

u d s

u

d

A- A5

9-

MeV 15.36623

)1405()1520(2 2*]2/1[

*]2/3[

I

LL2 contribution

- 500 MeV

in Full quark model by Hiyama, Hosaka et al

+ 1540 can not be a pentaquark state, if it exists ?

P K

+ in a naïve quark model

10

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- A5

3-

1/2+

d

MeV 254A4

7 w.r.t.Binding )1405(

s d u d u

s

d

A20

7- 3A-

1405 can not be a pentaquark state, ?

can (1405) be a 5 quark state

11

Di-bayron (Conf 1) – (qq) (qq) (qq)

u d

0+

repulsionInstanton MeV 29Binding H

u s

H di-baryon could be bound

unfortunately not found in so far

d s

u d

s

u d

s

H di-baryon

CFL Phase of color superconductivity ?

2SC Phase

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

12

Stable Multiquark configurations

in a schematic diquark model

ji

jiji

H ssmm

C

,

.confining.Kinetic Mass

13

Multiquark configuration: Yasui, Ko, Lee (EJP08,EJP09)

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

14

Diquark picture for , (with D. Jido , K. Kim)

Magnetic moment: = (ud)0 s , =(us)0d+(ds)0u

u d

s

QCD sum rule with diquark field

du

B

mm

C

4

3conf.Kinetic Mass c

su

B

du

B

mm

C

mm

C

4

1conf.Kinetic Mass c

222

4

1FsmDismDL sudud

2

296

1 , :parameters G

mm

su

B

du

B

su

B

mm

C

mm

C

mm

C

4

1

4

3

15

Result:

(GeV) m

2296

1G

m

16

Result- cont (GeV) m

2296

1G

m

Constituent diquark mass

MeV 410)( udmMeV 600 to500)( usm

MeV 9024

3mm (us)

MeV 14524

3mm (ud)

spin color todue Attraction

su

du

usu

B

udu

B

mmm

C

mmm

C

17

Tetra-quark - configurations

u d d u u dd u0+

boundnot BM CC0- 0-

Binding against decay = (Mass of 2 Mesons) – (Mass of Tetraquark)

22 4

3

4

3

u

B

u

B

m

C

m

C

22 4

3

4

3

u

M

u

M

m

C

m

C

u d c b u dc b0+

MeV -21.25

T of Binding 0cb

0- 0-

bc

B

u

B

mm

C

m

C

4

3

4

32

bu

M

cu

M

mm

C

mm

C

4

3

4

3

18

Tetra-quark – hadronic weak decay modes

KKBD )( )bc(udT 000cb

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

19

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)

c

c

20

Pentaquarks (states with two diquarks )

u d

1/2-

Q

u s u d Q

s

u

Qs D

su

B

u

B

mm

C

m

C

4

3

4

32

Qu

M

u

B

mm

C

m

C

4

3

4

32

KDcs )( )c(udus 0

21

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

Di-bayron – general considerations

2

0+ 4

6

2

4

di-baryon B B

Conf-1

2

4

B B

Conf-2

22

Di-bayron (Conf 1) – (qq) (qq) (qq)

u d

0+

repulsioninstanton MeV 29Binding H

u s

H di-baryon could be bound

unfortunately not found so far

d s

u d

s

u d

s

H di-baryon

CFL like state

2SC like state

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

23

Di-baryon (Conf 2) – (qq) (qq) (qQ)

u d

0+

MeV 92Binding H c

u s

Hc di-baryon new prediction

could be found in heavy ion collision

u c

u d

u

u

c

s

Hc di-baryon P c

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

24

Tcc/D > 0.34 x 10 -4 RHIC

> 0.8 x 10 -4 LHC

c/D > 0.8 x 10 -4

Hc/Ds > 0.25 x 10 -3

Kpp

ppK

c

c

)(

)( (udusuc)H 0c

Production ratios for predicted Multiquarks

cDx

cDsx

c production at RHIC and LHC

Hc production at RHIC and LHC

Tcc production

25

2. Diquarks are unique features of QCD, Mutltiquark states will exits in Heavy sector, due to diquark structure Tcc (ud cc) bs (udusb), Hc(udusuc) real weak decay, small background in RHIC, LHC can be a very useful heavy exotic factory

If found, it will be the first flavor exotic ever,

will tell us about QCD, q-q interaction and dense matter great step forward in QCD

1. Particle correlation from HIC could be a nice way to measure hadronic interation and /or bound state information

3. Diquarks can enhance and/or shift pt dependence of /K, c/D production in HIC can be a signature of remnant property of sQGP

4. New Idea ??? For hadron physics in Heavy Ion collision

Summary of talk and discussions this week

particle H f0 a0 Ds0 X(3872) (1405)

correlation K+ K- D0 K+ D0 D0* P K-

26

color spin interaction: light scalar nonet

jj

aj

aiji

jijj

aj

aijig

ss

mmCssH

, q3q1

q2 q4

Diquark configurations

• Diquark basis 0,3;0,3 15.01,6;1,6 98.00,9F

• Q-antiQ basis

Scalar nonet |9,0+>

8888F VV 39.0VV, 33.0PP 43.0PP, 74.00,9

Color Spin Favor s-s

Q-Q 3bar 0 3bar -2

1 6 2/3

6 0 6 1

1 3bar -1/3

Color Spin Favor s-s

Q-Qbar 1 0 1,8 -4

1 1,8 4/3

8 0 1,8 1/2

1 1,8 -1/6

Tetraquark: Jaffe

27

Multiquark configuration: Mulders, Aerts, de Swart PRD80

color spin interaction: light scalar nonet

jj

aj

aiji ss

u d

u d u

u d u s

u d u s u

u d u s u s

32Q

13Q

34Q

35Q

16Q