1. QUARK MATTER SYMMETRY ENERGY AND QUARK STARS Peng-cheng Chu ( 初鹏程 ) (INPAC and Department of Physics, Shanghai Jiao Tong University. kyois@sjtu.edu.cn) Collaborators ： Lie-wen Chen (SJTU)

2. Outline Symmetry energy introduction in quark matter. Isospin density-dependent-quark-model. EOS in the Isospin DDQM of Beta-equilibrium strange quark matter Properties of compact star based on the Isospin DDQM. Summary and outlook. Main References: G.X.Peng,H.C.Chiang,J.J.Yang,L.Li. Phys.Rev.C 61 015201 F. Weber,Progress in Particle and Nuclear Physics 54 (2005) 193-288 G.X.Peng,A.Li,U.Lombardo Phys. Rev.C 77,065807 (2008) Thomas D.Cohen, R.J.Furnstahl, and David K.Griegel Phys.Rev.C 45 X.J.Wen, X.H.Zhong, G.X.Peng, P.N.Shen, P.Z.Ning Phys.Rev.C 72 015204

3. Motivation to learn Strange quark matter may be the ground state~

4. The loop diagram of my work Maybe 2 solar mass of a compact star The EoS of quarks The phenomenological models of quarks Constraints of QCD chiral symmetry Color confinement The symmetry energy of quarks

5. Symmetry energy of quark matter. In quark matter: The symmetry energy In hadron matter: [-3,3] [-1,1]

6. In symmetric quark matter, make And Then Symmetry energy of quark matter. So we deduce the non-interaction symmetry energy of quark matter Define the symmetry energy as We can get the non-interaction symmetry energy of quark matter

7. Symmetry energy of quark matter. So we choose the second and discuss the symmetry energy in 3 different models

8. Density-dependent-quark-model. Since bag model incorporate the bag constant,many ways of effective term can be introduced to meet the principle. Write the Hamiltonian density as: Use the effective mass to make the form like a non-interacting system: mq is the effective massG.X.Peng,H.C.Chiang,J.J.Yang,L.Li. Phys.Rev.C 61 015201 The two hamiltonian density must have the same eigenenergy then

9. Isospin density-dependent-quark-model. If we considered as an invariant interacting term for q=u,d or s Notice that: Hellmann-Feynman theorem Give a renormalization-group invariant about quark condensate. Thomas D.Cohen, R.J.Furnstahl, and David K.Griegel Phys.Rev.C 45 is used in sum-rules as –(225±25MeV)^3 for each flavor of quarks

10. Isospin density-dependent-quark-model. Isospin density-dependent-quark-model "+" for d quark, else for u quark For s quark, DI = 0. With this treatment and doing volume integral : We check the range of DI

11. Symmetry energy of quark matter. G.X.Peng,H.C.Chiang,J.J.Yang,L.Li. Phys.Rev.C 61 015201,1999 In Density-dependent-quark-model. Follow the postulate above,the symmetry energy is: The mass is effective mass

12. Symmetry energy of quark matter. The symmetric energy vs. baryon number density in CDDM(D^1/2=160Mev, ms=80Mev)

13. Symmetry energy of quark matter. The equivalent mass when we take the iso-spin dependence is: Then the symmetry energy under this isospin DDQM is: The mass is effective mass "+" for d quark, else for u quark. Where

14. Symmetry energy of quark matter When DI=0, CDDM and isospin DDQM has the same form

15. Symmetry energy of quark matter DI = 1.0 Isospin DDQM

16. Symmetry energy of quark matter The symmetry energy vs. baryon number density in Isospin DDQM

17. Symmetry energy in NJL model We can get the symmetry energy in NJL model Where i for u,d and s quarks. Λ=602.3MeV, G =1.835/602.3^2, K = 12.36/602.3^5

18. Symmetry energy in NJL model rhoQs = rhoB rhoQs = 0.

19. Thermodynamic treatment to EOS Now we calculate the EoS of beta equilibrium quark matter based on the isospin density dependent quark model. According to the thermodynamic treatment where Define Then the chemical potential is

20. Thermodynamic treatment to EOS Strange quark matter is considered as a mixture of u,d,s quarks and electrons. chemical equilibrium: Baryon density : Charge-neutrality: Solve this system of equation,we can get the elements of the EOS

21. Thermodynamic treatment to EOS And for d,s quark: To solve the equations, we make nB given Mev fm-3DI=0DI=0.3DI=1.0 Energy per baryon(min)919.980929.018929.466 Pressure (zero)-.2616080.923606E-02-.330257E-01 Energy per baryon’s minimum value and zero pressure plot appear at the same time

22. Thermodynamic treatment to EoS Now check DI’s effect in the EoS of quark matter When DI increases, the minimum of the lines increase too.

23. Thermodynamic treatment to EOS Compare the relationship between the Fermi momentum and chemical potential DI=0. DI=0.1DI=0.06. DI=0.02.

24. Thermodynamic treatment to EOS Compare the relationship between the quark fraction and rhoB

25. The properties of Quark star M/M ⊙

26. The properties of Quark star Set Ms0 as the parameter of the quark star while making DI=1.1 & D^1/2=147 MeV

27. Rotating Quark star

28. HADRON-QUARK PHASE TRANSITION HADRONIC PHASE: RMF Theory where the sum on B runs over the baryon octet :

29. HADRON-QUARK PHASE TRANSITION In the RMF model, the meson fields are treated as classical fields, and the field operators are replaced by their expectation values. Effective mass

30. HADRON-QUARK PHASE TRANSITION The coupling constants set TM1 to calculate. For neutron star matter consisting of a neutral mixture of baryons and leptons, the β equilibrium conditions without trapped neutrinos are given by

31. HADRON-QUARK PHASE TRANSITION Then we get the chemical potential of baryons and leptons The charge neutrality condition is given by Where

32. HADRON-QUARK PHASE TRANSITION At a given baryon density The total energy density and pressure of neutron star matter are written by

33. HADRON-QUARK PHASE TRANSITION Also the pressure is given as : Phase transition may occur in the core of massive neutron star.

34. HADRON-QUARK PHASE TRANSITION The two crucial equations: The energy density and the baryon density in the mixed phase are given by Solve the system of equations, we can get the phase transition diagram, which I haven’t done yet.

35. HADRON-QUARK PHASE TRANSITION Particle fraction vs Baryon number density

36. HYBRID STAR The mass-radius relation for the hybrid star & Quark star.

37. OTHER QUARK MODELS Quasi-particle bag model D&T-DQM NJL,PNJL,MIT,CFL,CDM …

38. Isospin DDQM at Finite temperature: EoS at Finite Temperature in Isospin DDQM X.J.Wen, X.H.Zhong, G.X.Peng, P.N.Shen, and P.Z.Ning Phys.Rev.C 72 015204,2005

39. Summary and outlook. 1.We extend the density-dependent-quark- mass(DDQM) model in which the confinement is modeled by the density- dependent quark masses to include the isospin dependence. 2.We make use of the model we provide to discuss the form of symmetry energy in quark matter. And we discuss the reason why people choose the symmetry parameter. 3.Based on the isospin dependent DDQM model,we study the symmetry energy of quark matter and the EoS of strange quark matter. And we give the symmetry energy in NJL model. 4. We give the quark star properties based on the Isospin DDQM and acquire a 2 solar mass quark star.

40. Get the mass-radius relation for strange stars and study the structure of strange stars with surface effect considered. We can use RMFT and Isospin DDQM to study the hadron-quark phase transition. I will study on the stuff about quark matter based on QCD right away.

41. INPAC