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

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

Introduction ~150 T (MeV)

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

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

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

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

The effective mass of Θ + in nuclear matter

Decay of  + in medium

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

Comparison between   and  K +  N

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

Hadron masses in neutron stars

Scaled effective Lagrangian

Pressure Energy density Energy density.vs. pressure

Equation of state

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

The mass-radius relation of neutron star

Scaled effecive Lagrangian The maximum mass and radius of neutron star increase. Summaries The observed compact stars MJ = (2.2  0.2) M , M4U = (2.44  0.2) M 

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

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) N. Kaiser, P.B. Siegel & W. Weise, Nucl. Phys. A594 (1995) 325. K - optical potential

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

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

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

Effective mass of a baryon Bag energy of a baryon Effective mass of a baryon

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

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

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

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

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

Relative populations in neutron star Results

Relative populations in neutron star

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

Equations of state

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

The mass-radius relation of neutron star

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