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

- The 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• Meson fields in QMC model

Bag energy of a baryon

Effective mass of a baryon

• Effective mass of a baryon• Effective mass of a baryon

MQMC model

+ in symmetry nuclear matter

+ (1540 MeV) : uudds

• Effective mass of + • Effective mass of +

The effective mass of Θ+ in nuclear matter

• Decay of + in medium• Decay of + in medium

• Chemical potential of K, N, + 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 naïve quark model.

The possibility of decay of + in medium.

SummariesSummaries

Hadron masses in neutron stars

• Scaled effective Lagrangian• Scaled effective Lagrangian

Pressure

Energy density

• Energy density .vs. pressure • Energy density .vs. pressure

• Equation of state• Equation of state

• Mass of neutron star

• Tolman-Oppenheimer-Volkoff equation

• Mass-radius relation of neutron star • 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.

SummariesSummaries

• The observed compact stars

MJ0751+1807 = (2.2 0.2) M,

M4U1700-37 = (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 V0+iW0 = -50 – i 60 MeV

Deep optical potential V0+iW0 = -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

Strange tribaryons S0(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* (f0=975 MeV) and vector φ (=1020 MeV)

• Theory - the extended QMC model• 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+, Σ0, Σ-, Ξ0, 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 :

UK (ρ0) = - gσK σ (ρ0) – gωK ω (ρ0)

|UK (ρ0)| = 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 :

μK = μe

• 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

μK = ωK

Coupling constants

Quark counting rule and SU(6) symmetry

gσK : free parameter

• Relative populations in neutron star

• Results• Results

Relative populations in neutron star

Relative populations in neutron star

Relative populations in neutron star

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 UK increases, the EoS becomes softer at low densities, while becomes stiffer at high densities. Deep potential The light and small neutron stars

SummariesSummaries

2. The possibility of very deep optical potential (phases)

- shallow : nuclear- hyperonic -Kaonic+hyperonic phase - deep : nuclear – kaonic – kaonic+hyperonic phase