1. The Study of the Possible Phase Diagram of Deconfinement in FL Model
Faculty of Physics and electronic Technology,Hubei University,Wuhan
The Study of the Possible Phase Diagram of Deconfinement in FL Model
Shu Song†（舒崧）,Li Jia-rong*（李家荣）
† Faculty of Physics and Electronic Technology, Hubei University, Wuhan, China
*Institute of Particle Physics, Hua-Zhong Normal
University, Wuhan, China

2. Introduction
The field equations and effective potential in FL model
The discussions about the soliton solutions and the deconfinement
The study of the phase transition order
Summary

3. Introduction
An important discovery at the BNL Relativistic Heavy Ion Collider (RHIC) in recent years is the strongly interacting quark-gluon plasma (sQGP)
Shuryak has pointed out there should be lots of bound states especially for light and heavy bound states at Tc < T < 4Tc.
Recent researches use color Coulomb potential to describe the bound states which lead to sQGP.
However, in the present work, to obtain a simple and intuitive picture of sQGP, we will use a simple model to study the possible physical mechanism of the bound state in sQGP and the corresponding phase diagram of deconfinement.
E.V. Shuryak and I. Zahed, Phys.Rev.C70, (2004).

4. Friedberg-Lee soliton model (FL model)
The Lagrangian of the FL model,
ψ represents the quark field, and σ denotes the phenomenological scalar field which is introduced to describe the complicated nonperturbative features of QCD vacuum.
where,
R.Friedberg and T.D.Lee, Phys.Rev.D15,1694(1977);16,1096(1977).
T.D.Lee,Particle Physics and Introduction to Field Theory.

5. FL model at finite temperatures and finite densities
E.k. Wang, J.R. Li, L.S.Liu, PRD41(1990)2288
S.Gao, E.K. Wang, J.R. Li, PRD46(1992)3211
S.H. Deng, J.R. Li, PLB302(1993)279
H. Mao, M.J.Yao and W.Q.Zhao, PRC77(2008)065205

6. The field equations and effective potential in FL model
The field equations at mean field theory (MFT) approximation:
The thermal excitations and effective potential:

7. The discussions about the soliton solutions and the deconfinement
For the static and spherically symmetric soliton field,
The boundary conditions

8. At different temperatures and chemical potentials, the soliton equation could be solved under different configurations of
B is the bag constant which is defined as the energy difference between the two vacuums.
B is temperature and chemical potential dependent.
When B is zero, the deconfinement phase transition occurs.

9. Numerical Results
Effective potentials for different temperatures and chemical potentials
(A) For different temperatures and zero chemical potential.
(B) For different chemical potentials and fixed temperature.

10. The corresponding soliton solutions
(C) Soliton solutions for different temperatures and zero chemical potential.
(D) Soliton solutions for different chemical potentials and fixed temperature.

11. Physical Analysis
The deconfinement phase transition takes place when the two vacuums degenerate.
The soliton solutions before deconfinement describe the confinement of hadronic state.
The soliton solutions after deconfinement describe the bound state of quaks of sQGP.
The system becomes wQGP when the solitons disappear.

12. Phase Diagram
At MFT, the deconfinement phase transition is first order in the whole phase diagram.
The whole phase diagram has been divided into three phases: the hadronic phase, the sQGP and the wQGP.
Song Shu and Jia-rong Li, Phys. Rev. C 82 (2010)

13. The study of the phase transition order
First order
(MFT)

15. Analysis by Landau theory
thus：

16. phase diagram
2nd order
1st order

17. Summary
The deconfinement and soliton solutions in FL model have been thoroughly discussed. We indicate that the soliton solutions after deconfinement represent the bound states of quarks, which could possibly lead to the sQGP phase.
The phase transition order can only be first order in FL model at MFT. By Landau theory we show that only if the fluctuations counteract the cubic term in the thermodynamical potential could the second order phase transiton occur.
The dynamical calculations of the fluctuations in FL model beyond MFT is in progress…

18. 谢 谢! (Thanks)