1. Dibaryons with heavy quarks
Hongxia Huang & Jialun Ping
Nanjing Normal University
Fan Wang
Nanjing University
Strangeness Nuclear Physics
December 12nd – 14th, 2014, ChangSha, China

2. Outline
Introduction
Quark models and calculation methods
Possible H-like dibaryon states: cc and bb
Nc and Nb systems
Summary

3. Dibaryons: H, d*, di-Ω, NΩ, ……
Introduction
exotic states
Dibaryons: H, d*, di-Ω, NΩ, ……
Pentaquarks: Θ+ , Ξ-- , ……
Charmonium-like states: X(3872), Y(3940), Z(3900), Z(4430),……
Plausible molecular baryons: cD, cD, DN, DsN, ……
Dibaryons with heavy quarks: cc, cc, c c,
Nc, Nc, Ncc, NΩc, ……

4. Phenomenological models of two approaches: On the hadron level:
Theoretical methods
Lattice QCD
QCD sum rule
Phenomenological models of two approaches:
On the hadron level:
One-boson-exchange (OBE) model,
One-pion-exchange (OPE) model
......
On the quark level:
Isgur quark model , Chiral quark model,
Quark delocalization color screening model

5. Is the H dibaryon  a bound state?
First proposed by R. L. Jaffe
PRL 38, 195, 1977
Revived by Lattice QCD calculations of different collaborations:
NPLQCD, PRL 106, , 2011
HALQCD, PRL 106, , 2011
Reexamined in a chiral constituent quark model
PRC 85, , 2012
Is the H-like dibaryon cc a bound state?
Answers of two hadron level models
No in One-boson-exchange model PRD 84, , 2011
Yes in One-pion-exchange model PLB 704, 547, 2011
What about the quark level study of the cc system?

6. Quark Models and calculation method
Quark delocalization color screening model (QDCSM)
QDCSM was developed by Nanjing-Los Alamos collaboration in1990s aimed to multi-quark study (PRL 69, 2901, 1992)
Two new ingredients (based on quark cluster model configuration):
quark delocalization (orbital excitation)
color screening (color structure)
Apply to baryon-baryon interaction and dibaryons
NN, N , NΩ, …
deuteron success！ d*

7. NΩ is a very narrow dibaryon resonance in D-wave  scattering.
PRC 83 (2011)
HALQCD Collaboration, arXiv:
RHIC-STAR Collaboration
In QDCSM, d* is a dibaryon resonance in NN scattering.
PRC 79 (2009)
PRL 102 (2009) PRL 106 (2011)
PRL 112 (2014)
WASA-at-COSY Collaboration

8. CERN Courier

10. (1) Resonating group method (RGM)
Calculation method
(1) Resonating group method (RGM)
In RGM, the multi-quark wave function is approximated by the cluster wave function,
The internal motions of clusters are frozen and the relative motion wave function satisfies the following RGM equation

11. RGM equation
where

12. (2) Kohn-Hulthen-Kato(KHK) variational method

14. Possible H-like dibaryon states: cc , b b
PRC 89 ,035201,2014
The individual S-wave cc is unbound. A bound state is obtained for the cc system by channel-coupling.

15. The effects of tensor force are much smaller compared with that
of the central force.

16. Compare with the hadron level calculation (PLB 704, 547,2011)
Channel coupling (tensor force) is important.

17. Similar to H dibaryon:  system (PRC 69, 065207,2004)

18. bb system

19. Nc and Nb systems
PRC 87 ,034002,2013

20. The effective potentials
S-wave channels: attractive
D-wave channels: repulsive

21. Bound states
The individual Nc is unbound.
There is no any Nc bound state in the present channel-coupling calculation.
The tensor force is not important as the one on the hadron level calculation (PRD85,014015,2012)

22. Resonance states

23. Nb system

24. Summary
1. It is possible to form an H-like dibaryon state in the cc system.
2. There exists a Nc resonance state in the Nc D-wave scattering phase shifts.
3. The results of the bb and Nb systems are similar to those of the cc and
Nc systems,respectively.
4. The role of the central force is much more important than the tensor force in our
quark level calculation, while in the calculation on the hadron level, the tensor
force is shown to be important. Further investigation should be done to
understand the difference between these two approaches. It will help us to
understand whether the quark-hadron is equivalent or not.

25. Thank you!