A New QMC Model

1. A New QMC Model Ru-Keng Su Fudan University 2009.11 Hefei

2. Outline • Introduction and motivation • QMDD model and QMDTD model • A new QMC model • IQMDD+σmesons • IQMDD+σ+ωmesons • IQMDD+σ+ω+ρmesons • Conclusions

3. I. Introduction: QMC model • Explicitly include meson degree of freedom --- Quark Meson Coupling (QMC) Model • Consists of Non-overlapping Nucleon Bags Bounding by self-consistent Exchange of Meson in MFA MIT bag ρ σ u, d ω u, d

4. Two Shortcomings of QMC Model • It is a permanent quark confinement model because the MIT bag boundary condition cannot be destroyed by temperature and density. It cannot describe the quark deconfinement phase transition. • It is difficult to do nuclear many-body calculation beyond mean field approximation (MFA) by means of QMC model, because we cannot find the free propagators of quarks and mesons easily.

5. MIT Bags and QMC Model • Change MIT bag to Non-topological soliton model (F-L model) • Give up MIT bag boundary to extend the interactions of quarks and mesons to the whole space free propagators of quarks and mesons

6. Quark mass density- and/or temperature-dependent model Quark confinement: De-confinement phase transition: II. QMDD and QMDTD models Y. Zhang and R. K. Su, Phys. Rev. C 65, 035202 (2002); Y. Zhang and R. K. Su, Phys. Rev. C 67, 015202 (2003); C. Wu, W. L. Qian and R. K. Su, Phys. Rev. C 72, 035205 (2005); H. Mao, R. K. Su and W. Q. Zhao, Phys. Rev. C 74, 055204 (2006).

7. Shortcomings of QMDD Model • It is still an ideal quark gas model. No interactions exist between quarks except a confinement ansatz. • It still cannot explain the quark deconfinement phase transition and give us a correct phase diagram.

8. QMDTD R. K. Su et al. Euro. Phys. Lett 56 (2001) 361

9. QMDTD R. K. Su et al. PRC 65 (2002) 035202, PRC 67 (2003) 015202

10. Shortcomings of QMDTD model • QMDTD is an ideal gas model • The B(T) in QMDTD is input • To overcome these shortcomings, we add mesons

11. III. A new QMC model 1. IQMDD+σmesons The hamiltonian density of IQMDD is: C.Wu, W.L.Qian and R.K.Su, CPL22,1866(2005); C.Wu, W.L.Qian and R.K.Su, PRC72,035205(2005);

13. Quark density Sigma Field

14. Some properties of nucleon is calculated. We found that present model is successful in describing the nucleon.

15. IQMDD model at finite temperature H.Mao, R.K. SU and W.Q.Zhao, PRC74,055204(2006)

18. 2. IQMDD+σ+ωmesons • the Lagrangian density of the IQMDD model

19. The effective mass of nucleon

20. The density of states is given by Y. Zhang, W. L. Qian, S. Q. Ying, and R. K. Su, J. Phys. G 27, 2241 (2001)

21. Saturation Properties of Nuclear Matter The energy density of nuclear matter is The pressure of nuclear matter is

23. Saturation curve Pressure curve

24. Numerical Result

26. Boundary Conditions of Quark Field and Sigma Field Using Green’s function method to obtain omega field

27. Finite Temperature effective Potential

29. Parameter Choosing • T=0K • B=174MeVfm-3; • mω=783MeV; mσ=509MeV; • f=gσ=5.45; g=gω=3.37; • MN=539MeV; • b=-8400MeV

37. Conclusion for IQMDD+σ+ωmesons • IQMDD model not only can describe the saturation properties of nuclear matter, but also can explain the quark deconfinement phase transition successfully. • Tc=127MeV • Omega field is important

38. 3. IQMDD+σ+ω+ρmesons • Lagrangian density

39. C. Wu and R. K. Su, Jour. of Phys. G 36, 095101 (2009)

43. IV. Conclusion • The new QMC model is also a successful model to describe the properties of nuclear matter and nucleon MIT bag →Friegberg-Lee soliton bag mq → mq(ρq ) (quark mass density dependent) Including u, d, σ,ω,ρfreedoms

44. The results of our new QMC model locate in the regions between the values given by QHD-II model and QMC model

45. Future Work • Extend thus model to include the s quark and hyperons • Using this model to do the nuclear manybody calculation beyond mean field

46. Thank You!