1. Department of Physics, Sungkyunkwan University C. Y. Ryu, C. H. Hyun, and S. W. Hong Application of the Quark-meson coupling model to dense nuclear matter 2005 KPS Meeting Chon Buk University

2. Introduction - T he quark-meson coupling (QMC) model Results and summaries Application  + in nuclear matter Hadron masses in neutron stars kaon condensation in neutron stars with hyperons Outline

3. Introduction ~150 T (MeV)

4. Quark-meson coupling (QMC) model QMC Lagrangian in mean field approximation σ, ω

5. σ meson field : ω meson field : Meson fields in QMC model

6. Bag energy of a baryon Effective mass of a baryon MQMC model

7.  + in symmetry nuclear matter  + (1540 MeV) : uudds Effective mass of  +

8. The effective mass of Θ + in nuclear matter

9. Decay of  + in medium

10. Chemical potential of K, N,  + in medium Chemical potential of  + Chemical potential of K and N

11. Comparison between   and  K +  N

12. The effective mass of  + in na ï ve quark model. The possibility of decay of  + in medium. Summaries

13. Hadron masses in neutron stars

14. Scaled effective Lagrangian

15. Pressure Energy density Energy density.vs. pressure

16. Equation of state

17. Mass of neutron star Tolman-Oppenheimer-Volkoff equation Mass-radius relation of neutron star

18. The mass-radius relation of neutron star

19. Scaled effecive Lagrangian The maximum mass and radius of neutron star increase. Summaries The observed compact stars MJ0751+1807 = (2.2  0.2) M , M4U1700-37 = (2.44  0.2) M 

20. Exotic phenomena in Neutron star Kaon condensation in neutron star with hyperons

21. J. Schaffner-Bielich, V. Koch & M. Effenberger, Nucl. Phys. A669 (2000) 153. A. Ramos & E. Oset, Nucl. Phys. A671 (2000) 481. A. Cieply, E. Friedman, A. Gal & J. Mares, Nucl. Phys. A696 (2001) 173. Shallow optical potential V 0 +iW 0 = -50 – i 60 MeV Deep optical potential V 0 +iW 0 = -120 – i 10 MeV Y. Akaishi & T. Yamazaki, Phys. Rev. C65 (2002) 044005. N. Kaiser, P.B. Siegel & W. Weise, Nucl. Phys. A594 (1995) 325. K - optical potential

22. Strange tribaryons S 0 (3115) and S + (3140) Very strong attraction between K - and nucleons KEK PS-E471

23. Quark-meson coupling (QMC) model : MIT bag model + σ – ω - ρ mesons OZI rule : s-quark doesn ’ t interact with u(d)-quark assume only s-s quarks interaction : strange meson fields, scalar σ * (f 0 =975 MeV) and vector φ (=1020 MeV) Theory - the extended QMC model

24. The extended QMC model for baryon octet σ – ω – ρ (only u(d) quark) + σ* – φ (only s quark) Lagrangian density for baryon octet B = p, n, Λ, Σ +, Σ 0, Σ -, Ξ 0, Ξ - l = e, μ

25. Effective mass of a baryon Bag energy of a baryon Effective mass of a baryon

26. K - in neutron star matter with hyperons Kaon Lagrangian : U K (ρ 0 ) = - g σK σ (ρ 0 ) – g ωK ω (ρ 0 ) |U K (ρ 0 )| = 80, 100, 120 and 140 MeV Effective mass of a kaon : Real part of optical potential at the saturation density

27. Meson fields on kaon condensation σ meson : σ * meson : ω meson : φ meson : ρ meson :

28. Three conditions in neutron stars Chemical equilibrium : μ K = μ e Charge neutrality : - n K = 0 Baryon number conservation :

29. Dispersion relation for s-wave condensation for K - (us) Chemical potential Baryon energy Chemical potential of baryons and kaon μ K = ω K

30. Coupling constants Quark counting rule and SU(6) symmetry g σK : free parameter

31. Relative populations in neutron star Results

32. Relative populations in neutron star

36. Equation of state (Energy density vs. Pressure) Pressure Energy density

37. Equations of state

38. Mass-radius relation of neutron star Mass of neutron star Tolman-Oppenheimer-Volkoff equation

39. The mass-radius relation of neutron star

40. 1.The populations of particles and the EoS are very sensitive to the values of optical potential. The values have to be fixed by experiments. 3. As U K increases, the EoS becomes softer at low densities, while becomes stiffer at high densities. Deep potential  The light and small neutron stars Summaries 2. The possibility of very deep optical potential (phases) - shallow : nuclear- hyperonic -Kaonic+hyperonic phase - deep : nuclear – kaonic – kaonic+hyperonic phase