Neutron Star Matter with In-Medium Meson Mass C. H. Hyun, M. H Kim, - - PowerPoint PPT Presentation

Neutron Star Matter with In-Medium Meson Mass

• C. H. Hyun, M. H Kim, S. W. Hong

Sungkyunkwan University

• B. K. Jennings

TRIUMF

Origin of Matter and Evolution of the Galaxies, November 17 – 19, 2003, RIKEN, Wako, Japan

Outline

• 1. Introduction
• 2. Models
• 3. Results for neutron star matter
• 4. Summary

OMEG03 I

1 Introduction ⋆ Possible indication of hadron mass decrease in nuclear medium

Theory

– Brown-Rho (BR) scaling (Brown and Rho, PRL66 (1991) 2720) m∗

N

mN ≈ m∗

σ

mσ ≈ m∗

ω

mω ≈ m∗

ρ

mρ . (1) – QCD-sum rule (Hatsuda and Lee, PRC46 (1992) R34) m∗ρ mρ ≈ m∗

ω

mω ≃ 0.82. (2) – Quark-meson-coupling model (Saito, Tsushima and Thomas, PRC55 (1997) 4050) m∗

N

mN ≃ 0.79, m∗

ρ

mρ ≈ m∗

ω

mω ≃ 0.83. (3)

OMEG03 II

Experiment : Dilepton decay of ρ- and ω- mesons

– KEK-PS E325 (Ozawa et al., PRL86 (2001) 5019) – CERES/NA45 Collab. (Adamov´ a et al., PRL 91 (2003) 042301) ⋆ Contraints of symmetric nuclear matter at saturation density

EB = 16MeV at ρ0 = 0.17 fm−3 m∗

N = (0.7 ∼ 0.8)mN

K = 200 ∼ 300MeV asym = 32.5MeV

⋆ Neutron star (NS) : Narrow mass zone (Thorsett and Chakrabarty, ApJ. 512 (1999) 288) MNS = (1.0 ∼ 1.6)M⊙ (4) ⋆ Question : Can the properties of NS be affected by meson-mass changes in matter? Constant meson mass vs Density-dependent meson mass

OMEG03 III

2 Models ⋆ Models with constant meson mass (1) Walecka model (QHD) LMF

QHD = L0 + U(¯

σ), L0 = ¯ ψN

• iγµ∂µ − m∗

N − gωN γ0 ¯

ω0 − 1 2 gρN γ0 ¯ b03 τ3

• ψN − 1

2m2

σ ¯

σ2 + 1 2m2

ω ¯

ω2

0 + 1

2m2

ρ ¯

b2

03,

m∗

N = mN − gσN ¯

σ, U(¯ σ) = 1 3mN b (gσN ¯ σ)3 + 1 4c (gσN ¯ σ)4. – ¯ σ, ¯ ω0, ¯ b03 : Mean field equation of motion – gσN, gωN, b, c : From EB, ρ0, m∗

N, K

– gρN : From asym

OMEG03 IV

(2) Modified Quark-meson coupling model (MQMC) (X. Jin and B. K. Jennings, PRC54 (1996) 1427) LMF

MQMC = ¯

ψq[iγµ∂µ − (m0

q − gq σ ¯

σ) − gq

ω γ0 ¯

ω0 − 1 2gq

ρ γ0 ¯

b03 τ3 − B] × θV (R − r)ψq −1 2m2

σ ¯

σ2 + 1 2m2

ω ¯

ω2

0 + 1

2m2

ρ ¯

b2

03,

m∗

N =

• EN

bag

2 − 3 x2

q

R2, EN

bag = 3Ωq

R − ZN R + 4 3πR3B, Ωq =

• x2

q + R2m∗2 q ,

(m∗

q = m0 q − gq σ¯

σ), B = B0

• 1 − gB

σ

4 δ ¯ σ mN δ – B0, ZN : From mN = 939 MeV at R = 0.6 fm – gq

σ, gq ω, gB σ , δ : From EB, ρ0, m∗ N, K

– gq

ρ : From asym

OMEG03 V

⋆ Models with density-dependent meson mass (1) BR-scaled effective chiral Lagrangian (QHD-BR) (C. Song et al., PRC56 (1997) 2244) L = L0(mσ → m∗

σ, mV → m∗ V , gV N → g∗ V N), (V = ω, ρ)

m∗

N = M ∗ N − gσN ¯

σ, M ∗

N

mN = m∗

σ

mσ = m∗

V

mV =

• 1 + y ρ

ρ0 −1 , g∗

V N

gV N =

• 1 + z ρ

ρ0 −1 – gσN, gωN, y, z : From EB, ρ0, m∗

N, K

(2) MQMC with scaled meson mass (SMQMC) L = LMF

MQMC(mσ → m∗ σ, mV → m∗ V )

– More parameters than the number of contraints : y fitted to BR-scaling law

OMEG03 VI

(3) MQMC with meson bag (MQMC-MB) L = LMF

MQMC(mV → m∗ V ),

m∗

V =

• EV

bag

2 − 2 x2

q

R2, EV

bag = 2Ωq

R − ZV R + 4 3π R3 B – ZV : From mV (770 MeV for ρ-meson and 783 MeV for ω-meson) ⋆ Properties at the saturation Constant meson mass Density dependent meson mass QHD MQMC QHD-BR SMQMC MQMC-MB m∗

N/mN

0.77 0.78 0.67 0.76 0.85 m∗

V /mV

1.0 1.0 0.78 0.78 0.86 K (MeV) 311 286 265 592 324

OMEG03 VII

3 Results for neutron star matter ⋆ Equation of state (EoS)

100 200 300 400 500 600 700 0 100 300 500 700 P (MeV/fm3) ε (MeV/fm3) QHD QHD-BR 100 200 300 400 500 600 700 0 100 300 500 700 ε (MeV/fm3) MQMC SMQMC MQMC-MB

Stiffer equation of state → Larger maximum mass of NS

OMEG03 VIII

Why is the EoS so stiff?

P ≃ −Pσ + Pω + Pρ + PN, Pσ = 1 2m∗2

σ ¯

σ2, Pω = 1 2m∗2

ω ¯

ω2

0,

Pρ = 1 2m∗2

ρ ¯

b2

30,

PN = 1 3π2

• N=n,p

kN k4

• k2 + m∗2

N

dk.

50 100 150 200 250 1 2 3 4 P (MeV/fm3) ρ/ρ0 QHD PN Pσ Pω Pρ 50 100 150 200 250 1 2 3 4 ρ/ρ0 QHD-BR PN Pσ Pω Pρ

OMEG03 IX

⋆ Particle fraction : ρi/ρ (i = n, p, e, µ)

0.001 0.01 0.1 1 0 0.5 1 1.5 2 2.5 3 3.5 4 Particle Fraction ρ/ρ0 QHD n p e µ 0.001 0.01 0.1 1 0 0.5 1 1.5 2 2.5 3 3.5 4 QHD-BR n p e µ 0.001 0.01 0.1 1 0 0.5 1 1.5 2 2.5 3 3.5 4 MQMC n p e µ 0.001 0.01 0.1 1 0 0.5 1 1.5 2 2.5 3 3.5 4 SMQMC n p e µ 0.001 0.01 0.1 1 0 0.5 1 1.5 2 2.5 3 3.5 4 MQMC-MB n p e µ

OMEG03 X

4 Summary ⋆ The effect of density-dependent meson mass on the properties of NS matter was investigated. ⋆ EoS is sensitive to the behavior of meson mass. ⋆ Hyperon degrees of freedom need to be included. ⋆ Many possibilities are still wide open.