KEK理論センター研究会「ストレンジネス核物理２０１０」(KEK 研究本館小林ホール, 2010.12.2-4)

K 中間子束縛状態におけるハイペロン混在の効果
千葉工大 武藤 巧
原子力機構 丸山 敏毅, 京大理巽 敏隆

1. Introduction

Multi-Antikaonic Nuclei (MKN) に対する hyperon -mixing effects

2. Formulation 2-1 Outline of Kaon-condensed hypernuclei
2-2 Relativistic Mean-Field (RMF) theory
3. Numerical results 3-1 density distributions
3-2 |S|-dependence of central density ρΒ(0)3-3 Stability of the multi-strangeness nuclei
4. 中性子星内部のK中間子凝縮との関係

5. Summary and outlook

1. Introduction Multi-strangeness system in hadronic matter
中性子星内部の高密度物質
hyperonic matter(Λ, Σ, Ξ, ・・・in the ground state)

Strange matter

Kaon condensation

実験で得られる高密度物質（u, d, s quark matter )Strangeness-conserving system[ Y. Akaishi and T.Yamazaki, Phys.Rev. C65 (2002) 044005. ][A. Dote, H. Horiuchi et al., Phys. Lett. B 590 (2004) 51;
Phys.Rev. C70 (2004) 044313. ](bound state of K- meson)

Kaonic nuclei|S| = 0, 1, 2, 3,・・Multi-Antikaonic Nuclei (MKN)
relativistic mean-field theory (RMF)[T. Muto, T. Maruyama and T. Tatsumi,
Phys. Rev. C79, 035207 (2009). ]・central region: high density ρB∼3.5 ρ0

Meson-exchange models (MEM)[ c.f. D. Gazda, E. Friedman,A. Gal, J. Mares,
Phys. Rev. C76, 055204 (2007);
Phys. Rev. C77, 045206 (2008). ]ストレンジネス数の増加によるＫ中間子ダイナミクスの変化
中性子星物質中でのＫ凝縮との関係

Multi-Antikaonic Nuclei (MKN) に対する hyperon -mixing effects(Coexistence of antikaons and hyperons)[ T. Muto, Phys. Rev. C 77 (2008) 015810; Nucl. Phys. A804 (2008) 322. ](in the liquid drop picture)・Considerable softening of the EOS
Nucleon-nucleon repulsion is avoided at high densities.
[c.f. S. Nishizaki, Y. Yamamoto, T. Takatsuka,
Prog. Theor. Phys.108(2002)703.]

due to hyperon-mixing

Kaon-baryon attractive interactions get stronger.

・ At high densities, stiffness of the EOS is recovered
due to repulsive interaction between baryons
A local energy minimum => highly dense self-bound object--- decaying only through weak processes[D. Gazda, E. Friedman, A. Gal, J. Mares, Phys. Rev. C 80, 035205 (2009).]

非一様密度分布など原子核の有限性を現実的に取り入れた枠組みが必要。
相対論的平均場理論 (ＲＭＦ)によるＫ凝縮ハイパー核の可能性の検討

2. Formulation 2-1 Outline of Kaon-condensed hypernucleiーMulti-K Nucleip
KK- mesonhyperonprotonr[ Initial target nucleus ]A = N + Z : mass number
Z: the number of proton|S|: the number of the embedded KAssume : Spherical symmetry
Local density approximation for baryons( p, n, Λ, Σ- )[ Strangeness conservation ][ Charge conservation ]neutron[ Baryon number conservation ]2-2 Relativistic Mean-Field (RMF) theory
N-N(N = p, n)

Y-N, Y-Y(Y = Λ, Σー)

σ* ~ -ss
φ ~ sγsNonlinear chiral effective Lagrangian[ D. B. Kaplan and A. E. Nelson,
interactions
K " N,K " K
Phys. Lett. B 175 (1986) 57. ]Meson fields (K± ) (nonlinear representation)!

Condensate assumption(K- mesons are condensed in the lowest energy state)

kaon fields (K± ) (nonlinear representation)(scalar)(scalar)(vector)

RMF

contact int.

meson exchange

(i)

(ii)

(vector)2-3 Equations of motion for meson fields
K- field equationーー・nonlinear K-K int.

(coherent state)2-4 Choice of parameters--- NN interaction --Reproduce gross features of normal nuclei and nuclear matter・saturation properties of nuclear matter (ρ0 =0.153 fm−３)
・binding energy of nuclei and proton-mixing ratio
・density distributions of p and n--- vector meson couplings for Y --- SU(6) symmetry--- scalar meson couplings for Y ---ハイパー核実験[ D. J. Millener, C. B. Dover and A. Gal,
Phys. Rev. C38 (1998), 22700. ]repulsive case[ J. Dabrowski, Phys. Rev. C60 (1999), 025205. ](K-, π ) at BNL, (π-, K+) at KEK

--- vector meson couplings for Kaon --quark and isospin counting rule--- scalar meson couplings for Kaon --at ρ0 in symmetric nuclear matter
UK= − 80 MeV (ΣKN ~ 330 MeV)

Decay of f0(975)

3. Numerical results

3-1 density distributions

A=15, Z=8 ()UK= - 80 MeV

preliminary

No K- meson is bound.
Without hyperon-mixing

With hyperon-mixing

Without hyperon-mixing

With hyperon-mixing

No K- meson is bound.

3-2 |S|-dependence of central density ρΒ(0)Central region
MKNの場合K- mesons と protons が強い引力で中心に引かれる。
ρΒ(0) ∼ 2.6 ρ0 for large ¦S¦

Multi-hypernucleiの場合

ρΒ(0) ∼ ρ0

3-3 Stability of the multi-strangeness nuclei
Total energy of the MKNBinding energy : ーStrong decay of the MKN

4. 中性子星内部のK中間子凝縮との関係
実験室系
ωK- = 400 ~ 450 MeV

原子核の有限性> μΛ ー μp

Chemical equilibrium for strong processes
満たしにくい無限系

中性子星内部
chemical equilibrium for weak processes

K- chemical potential : ω =K-< 0 for high densities

--- including Ξ- --Energy / baryon (ε / ρB )Particle fractionK+ condensate

K- density :free part<0K-B vector int.

5. Summary and outlook
相対論的平均場理論と K -B, K - K 相互作用に対する非線形
chiral Lagrangianの枠組みで, K- 中間子とハイペロンの共存した原子核の存在可能性を検討した。
!

! !

原子核の有限性のため, K- 中間子がバリオンから受ける引力が無限系（中性子星内部）の場合ほど大きくなく,K- の lowest energy が ωK- ~ 400 MeV よりも低くならない。
を通じて, 初めK- 中間子が担っていたストレンジネスがすべてハイペロン(Y)に吸収される。
中心核密度 ρΒ(0) ∼ ρ0Outlook
Role of hyperons (Y)・Ξ- -mixing の効果
・inelastic channel coupling effects (kaon decay width . . . )・Role of P-wave KNY interactions

Quasi-baryons

・Realistic framework beyond the local density approximation
for baryons