A New QMC Model Ru-Keng Su Fudan University Hefei

Outline I. Introduction and motivation II. QMDD model and QMDTD model III. A new QMC model 1. IQMDD+σmesons 2. IQMDD+σ+ωmesons 3. IQMDD+σ+ω+ρmesons IV. Conclusions

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 u, d σ ω ρ

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.

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

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

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.

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

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

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

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

Quark density Sigma Field

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

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

 the Lagrangian density of the IQMDD model 2. IQMDD+σ+ωmesons

The effective mass of nucleon

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)

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

Saturation curve Pressure curve

Numerical Result KR0R0 QMC N/A IQMDD with σ, ω mesons

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

Finite Temperature effective Potential

Parameter Choosing  T=0K B=174MeVfm -3 ; m ω =783MeV; m σ =509MeV; f=g σ =5.45; g=g ω =3.37; M N =539MeV; b=-8400MeV

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.  T c =127MeV  Omega field is important

3. IQMDD+σ+ω+ρmesons  Lagrangian density

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

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 m q → m q (ρ q ) (quark mass density dependent) Including u, d, σ,ω,ρfreedoms

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

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