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. Recent Highlights in Hadron Physics – Heavy quark sector
Babar: DSJ(2317) 0+
Puzzle in Constituent Quark Model(2400)
D0 K+ (2358) threshold effect
Chiral partner of (0- 1-)
Tetraquark
molecule ? D0 D* D1
1864
2007
2420
D0+D*
D*+D*
D+D1
D1+D*
3871
4014
4284
4427
X(3872) , Y(4260),
Z(4430)  y’p
Z(4051),Z(4248) cc1p
Must contain cc ?

3. N S Previous Work on Multiquark hadrons - Light quark sector +
Scalar tetraquark (Jaffe 76)
L(1405) (Jido, Sekihara..) N S K + p
Search for H dibaryon
Search for Q+ pentaquark
The experimental observations completes the observation of scalar nonets, that posses the inverted mass spectrum and consequently the implicit multiquark nature of the scalar nonet.
Tetraquarks were introduced by Jaffe, as a natural extension of the bag model, and to explain the anomalously large scalar meson mass, which are naturally explained if one assumes a hidden ssbar quark.
The question of whether the scalar nonnet is a tetraquark is still an ongoing heated discussion.

4. New perspectives on hadron physics from RHIC
large number of c , b quark production
Vertex detector: weakly decaying exotics
Larger source size: A. Ohnishi ..
particle H
f0 a0
Ds0
X(3872)
L(1405)
correlation
L L
K+ K-
D0 K+
D0 D0*
P K-

5. Some insights from for Multiquark configurations in a schematic quark model

6. Color spin interaction
Diquark configurations vs. quark-antiquark configurations q1 q2 q2 q4
Color
Spin
Favor D
Q-Q
3bar -2 1 6
2/3
-1/3
There are several advantages in applying this formalism to heavy quark system.
Color
Spin
Favor D
Q-Qbar 1
1,8 -4
4/3 8
1/2
-1/6
Takeuchi

7. Diquark inside Baryons
Example u d u d s s
Mass diff
MD –MN
MS-ML
MSc-MLc
MSb-MLb
Formula
290 MeV
77 MeV
154 MeV
180 MeV
Experiment
75 MeV
170 MeV
192 MeV

8. quark antiquark in Mesonp r d u d u
Mass diff
Mr –Mp
MK*-MK
MD*-MD
MB*-MB
Formula
635 MeV
381 MeV
127 MeV
41 MeV
Experiment
397 MeV
137 MeV
46 MeV
Works very well with 3x CB = CM = 635 mu2 u d
x 3 =

9. Q+ in a naïve quark model
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
L=1 Q+ P K u d u d  u d s d
1/2+ u s
L2 contribution
- 500 MeV
in Full quark model by Hiyama, Hosaka et al
Q can not be a pentaquark state, if it exists ?

10. can L(1405) be a 5 quark state L S p  1/2+
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 L S p u d s d  u d u d
1/2+ s d
L 1405 can not be a pentaquark state, ?

11. Di-bayron (Conf 1) – (qq) (qq) (qq)
H di-baryon u d u d u d u s  0+
CFL
Phase of color superconductivity ?
2SC Phase s s d s
H di-baryon  could be bound
unfortunately not found in so far

12. Stable Multiquark configurations
in a schematic diquark model

13. Type of diquark and its q-q binding
Multiquark configuration: Yasui, Ko, Lee (EJP08,EJP09)
Diquark attracation vs quark-antiquark q1 q3 q2
diquark picture: Yasui, Ko, Liu, Lee,.. (EJP08,EJP09)
There are several advantages in applying this formalism to heavy quark system.
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

14. Diquark picture for L, S (with D. Jido , K. Kim)
Magnetic moment: L = (ud)0 s , S =(us)0d+(ds)0u u d s
QCD sum rule with diquark field

15. Result:

16. Result- cont
Constituent diquark mass

17. Tetra-quark - configurations
Binding against decay = (Mass of 2 Mesons) – (Mass of Tetraquark) 0+  0- 0- u d d u u d d u 0+  0- 0- u d c b u c d b

18. Tetra-quark – hadronic weak decay modes1+  0- 1- u d c c u c d c

19. e Tcc (3800) e+ Previous works on Tcc Can look for 1+ (Tcc)
Z. 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)
Can look for 1+ (Tcc)
Belle: PRL 98, (07)
e+ e-  J/y + X(3904)
 D D* e c c
Tcc (3800) c c e+
SHL, S Yasui, W Liu, C Ko (08)

20. Pentaquarks (states with two diquarks )
QQs L D u d u s  u d Q u
1/2- s Q

21. Di-bayron – general considerations
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
di-baryon B B 1 2 3 4 1 2 3 4 
Conf-1 0+ 5 6 5 6 B B 1 2 6 4
Conf-2 3 5

22. Di-bayron (Conf 1) – (qq) (qq) (qq)
H di-baryon u d u d u d u s  0+
CFL
like state
2SC like state s s d s
H di-baryon  could be bound
unfortunately not found so far

23. Di-baryon (Conf 2) – (qq) (qq) (qQ)
Hc di-baryon P Xc 0+ u d u s u d u s  u c u c
Hc di-baryon  new prediction
could be found in heavy ion collision

24. Production ratios for predicted Multiquarks
Qc production at RHIC and LHC
Qc/D > x 10 -4
Qc/Ds > x
Hc production at RHIC and LHC
Hc/D > x 10 -4
Hc/Ds > x
Tcc production
Tcc/D > 0.34 x RHIC
> 0.8 x LHC

25. Summary of talk and discussions this week
Particle correlation from HIC could be a nice way to measure hadronic interation and /or bound state information
particle H
f0 a0
Ds0
X(3872)
L(1405)
correlation
L L
K+ K-
D0 K+
D0 D0*
P K-
Diquarks are unique features of QCD, Mutltiquark states will exits in Heavy sector, due to diquark structure Tcc (ud cc) Qbs (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
Diquarks can enhance and/or shift pt dependence of L/K, Lc/D production in HIC  can be a signature of remnant property of sQGP
New Idea ???  For hadron physics in Heavy Ion collision

26. Tetraquark: Jaffe q1 q3 q2 q4
color spin interaction: light scalar nonet q1 q3 q2 q4
Diquark configurations
Color
Spin
Favor
s-s LL
Q-Q
3bar -2 1 6
2/3
-1/3
Color
Spin
Favor
s-s LL
Q-Qbar 1
1,8 -4
4/3 8
1/2
-1/6
There are several advantages in applying this formalism to heavy quark system.
Scalar nonet |9,0+>
Diquark basis
Q-antiQ basis

27. Multiquark configuration: Mulders, Aerts, de Swart PRD80
color spin interaction: light scalar nonet u d u d u u d u s
There are several advantages in applying this formalism to heavy quark system. u d u s u u d u s u s