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

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 ?

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.

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-

Some insights from for Multiquark configurations in a schematic quark model

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

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

quark antiquark in Meson p 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 =

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

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, ?

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

Stable Multiquark configurations in a schematic diquark model

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

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

Result:

Result- cont Constituent diquark mass

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

Tetra-quark – hadronic weak decay modes 1+  0- 1- u d c c u c d c

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, 082001 (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)

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

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

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

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

Production ratios for predicted Multiquarks Qc production at RHIC and LHC Qc/D > 0.74 x 10 -4 Qc/Ds > 0.23 x 10 -3 Hc production at RHIC and LHC Hc/D > 0.8 x 10 -4 Hc/Ds > 0.25 x 10 -3 Tcc production Tcc/D > 0.34 x 10 -4 RHIC > 0.8 x 10 -4 LHC

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

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

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