Department of Physics, Sungkyunkwan University
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Transcript of Department of Physics, Sungkyunkwan University
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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
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• 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
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Introduction
~150
T(MeV)
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Quark-meson coupling (QMC) model
• QMC Lagrangian in mean field approximation
σ, ω
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σ meson field :
ω meson field :
• Meson fields in QMC model• Meson fields in QMC model
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Bag energy of a baryon
Effective mass of a baryon
• Effective mass of a baryon• Effective mass of a baryon
MQMC model
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+ in symmetry nuclear matter
+ (1540 MeV) : uudds
• Effective mass of + • Effective mass of +
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The effective mass of Θ+ in nuclear matter
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• Decay of + in medium• Decay of + in medium
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• Chemical potential of K, N, + in medium• Chemical potential of K, N, + in medium
Chemical potential of +
Chemical potential of K and N
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Comparison between and K + N
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The effective mass of + in naïve quark model.
The possibility of decay of + in medium.
SummariesSummaries
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Hadron masses in neutron stars
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• Scaled effective Lagrangian• Scaled effective Lagrangian
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Pressure
Energy density
• Energy density .vs. pressure • Energy density .vs. pressure
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• Equation of state• Equation of state
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• Mass of neutron star
• Tolman-Oppenheimer-Volkoff equation
• Mass-radius relation of neutron star • Mass-radius relation of neutron star
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The mass-radius relation of neutron star
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• 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
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• Exotic phenomena in Neutron star
Kaon condensation in neutron star with hyperons
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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
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Strange tribaryons S0(3115) and S+(3140)
Very strong attraction
between K- and nucleons KEK PS-E471
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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
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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
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Effective mass of a baryon
Bag energy of a baryon
Effective mass of a baryon
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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
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Meson fields on kaon condensation
σ meson :
σ* meson :
ω meson :
φ meson :
ρ meson :
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Three conditions in neutron stars
• Chemical equilibrium :
μK = μe
• Charge neutrality : - n K = 0
• Baryon number conservation :
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Dispersion relation for s-wave condensation for K- (us)
Chemical potential
Baryon energy
Chemical potential of baryons and kaon
μK = ωK
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Coupling constants
Quark counting rule and SU(6) symmetry
gσK : free parameter
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• Relative populations in neutron star
• Results• Results
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Relative populations in neutron star
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Relative populations in neutron star
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Relative populations in neutron star
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Relative populations in neutron star
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Equation of state(Energy density vs. Pressure)
Pressure
Energy density
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Equations of state
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Mass-radius relation of neutron star
• Mass of neutron star
• Tolman-Oppenheimer-Volkoff equation
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The mass-radius relation of neutron star
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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