Interplay of antikaons with hyperons in nuclei and in neutron stars

Interplay of antikaons with hyperons in nuclei and in neutron stars

13th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (Pontificia Universita della Santa Croce, Rome, Sep.30 – Oct.4, 2013)

Takumi Muto (Chiba Inst. Tech.) collaborators : Toshiki Maruyama (JAEA) Toshitaka Tatsumi (Kyoto Univ.)

Parallel Session : Meson-Nucleon Systems 3

Multi-strangeness system in hadronic matter1. Introduction

Strange matter（ u, d, s quark matter )

hyperonic matter(Λ, Σ, Ξ, ・・・in the ground state)

Kaon condensation

・ Coexistence of antikaons and hyperons

In neutron-stars

Softening of EOS

Kaonic nuclei [ Y.Akaishi and T.Yamazaki, Phys.Rev. C65 (2002) 044005. ]

Multi-Antikaonic Nuclei

In nuclei

・ Coexistence of antikaons and hyperons : difficult

relativistic mean-field theory (RMF)+coupled with effective chiral Lagrangian

[T. Muto, T. Maruyama and T. Tatsumi, Phys. Rev. C79, 035207 (2009). ]

[T. Muto, T. Maruyama and T. Tatsumi, Genshikaku Kenkyu 57 Supplement 3, 230(2013).]

Toward unified description based on the same Kaon-baryon(B), B-B interaction model.

A possible existence of antikaonic nuclear bound states with hyperon-mixing for finite nuclei

Both K- mesons and hyperons are taken into account together in a unified way for both finite nuclei and neutron stars within the same framework.

We consider interplay between antikaons and hyperons within the RMF framework coupled with the effective chiral Lagrangian:

Appearance of hyperons and onset of kaon condensation in β-equilibrated infinite matter (neutron stars)

2-1. Baryon-Baryon interaction

[ D. B. Kaplan and A. E. Nelson, Phys. Lett. B 175 (1986) 57. ]

2-2. interactions Nonlinear chiral effective Lagrangian

Meson fields (K± ) (nonlinear representation)

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

Mesons:B =

Meson decay const.

2. Outline of the model

kaon fields (K± ) (nonlinear representation)

(scalar) (vector)

RMF

(scalar) (vector)

S-wave scalar int. S-wave vector int.

Kaonic part of the Lagrangian density

・ saturation properties of nuclear matter・ binding energy of nuclei and proton-mixing ratio・ density distributions of p and n

gross features of normal nuclei and nuclear matter

(ρ0 =0.153 fm− ３ )

2-3. Choice of parameters

--- NN interaction ---

--- vector meson couplings for Y --- SU(6) symmetry

--- scalar meson couplings for Y ---

repulsive case

--- scalar meson couplings for Kaon ---

at ρ0 in symmetric nuclear matter

Decay of f0(975)

quark and isospin counting rule

--- vector meson couplings for Kaon ---

UK- = (− 180 〜 − 80 ) MeV

K- optical potential depth :

SU(6) symmetry

|S|: the number of the embedded K-

Assume : Spherical symmetry

A = N + Z : mass number

Z: the number of protonMulti-K Nuclei

p

K-

r

ー

3. Coexistence of antikaons and hyperons in finite nuclei

Local density approximation for baryons

K- mesonhyperon

proton

neutron

[ Charge conservation ]

[ Baryon number conservation ]

[ Strangeness conservation ]

[ Initial target nucleus ]3-1. Outline

3-2. Thermodynamic potential

Chemical equilibrium for strong processes

as

Take into account of nonmesonic processes,

in addition to mesonic process,

Coexistence condition of antikaons with hyperons in finite nuclei

4 Numerical results

1. density distributions

For finite nuclei ( )

2. Stability of multi-strangeness nuclei

4 Numerical results

| UK | < 180 MeVA=15, Z=8 ( )No K- meson is bound.

4-1. density distributions

Ground state :

Central density ρρ

Multi-hypernuclei

Total energy Energy difference per unit of strangeness from normal nuclei ( |S| = 0 )

Strong decay of multi-hypernucleito

For |S| >3

| UK | < 180 MeV

4-2. Stability of multi-strangeness nuclei

5. Onset of kaon condensation in β-equilibrated matter (Neutron stars)

chemical equilibrium for weak processes

Onset of K- condensates

5-1 Onset of kaon condensation in hyperon matter

Appearance of antikaons with hyperons in finite nuclei

5-2 EOS in β-equilibrated matter

Energy/particle Particle fractions

We have considered a possible existence of kaonic bound nuclei with hyperon-mixing and kaon condensation in hyperonic matter In the same framework of the RMF coupled with nonlinear effective chiral Lagrangian for and interactions.

Ξ- -mixing becomes dominant for large|S|.

For moderate | UK- | (< 180 MeV), the ground state is given by multi-hypernuclei without bound K- mesons.

6 Summary and outlook

Finite effects of nucleiAntikaons do not receive much attraction

Finite nuclei

Effects of kaon condensates on EOSNeutron stars

K- -baryon attractive interactions, especially, the S-wave scalar attractions lead to additional softening of the EOS as compared with the case of hyperonic matter.

Strong repulsion between baryons andsuppression of attractive - baryon interactionat high densities are needed.

(1) ambiguity of S-wave K-Baryon interactions

Scalar int.: content in the nucleon is small.

[R. D. Young, A. W. Thomas, Nucl. Phys. A844(2010)266c.]

The soft EOS cannot support massive stars (~ 2 M).

(Recent Lattie QCD)

・ In flight (K-, N)

[ T. Kishimoto et al., Prog. Theor. Phys. 118 (2007), 181. ]

deep K-nucleus potential, ~ −200 MeV (analysis of missing mass spectra)

KEK, BNL

UK >> - 80 MeV( ΣKN ~ 150 MeV )

(4) Relation between kaon condensation in hadronic matter and that in quark matter

　 (c.f. phenomenological universal YNN, YYN, YYY repulsions 　　　 [ S. Nishizaki, Y. Yamamotoand T. Takatsuka,

Prog. Theor.Phys. 108 (2002) 703. ] )

(2) Many-body forces

Stiffness of EOS at high density

(cf : RMF extended to BMM, MMM type diagrams) [K. Tsubakihara and A. Ohnishi, arXiv:1211.7208.]

Beyond mean-field approximation for baryon-baryon sector

(3) relativistic Hartree-Fock

Connection to quark matter

Introduction of tensor coupling of vector mesons

Cf. for hyperonic matter, [T. Miyatsu, T. Katayama, K. Saito, Phys. Lett.B709 242(2012).]

S-wave scalar int.S-wave vector int.

- Baryon interactions in K- field equation

repulsion for Σ- and Ξ- hyperons

Vector interaction between K- mesons and hyperons (Σ- and Ξ- ) works repulsively as far as > 0 , unfavorable for coexistence.

Chiral symmetry

K- field equation

The number density of K- mesons

< 0 for X0 << 0 .

The presence of K- condensates (θ) leads to a negative contribution to vector mean fields (ω0, R0 , φ0 ) . < 0

Vector mean fields

Scalar mean fields

Coulomb field

Equations of motion for meson fields

UK= − 180 MeV

Ground state

4-2. Density distributions (extremely attractive)

5-3. Comparison with kaon condensation in neutron stars

chemical equilibrium for weak processes

Chemical equilibrium for strong processes

Finite system formed in laboratory

ωK-

Finite effects of nuclei> μΛ 　ー　 μp

hard to satisfy

In neutron stars

K- chemical potential : = O(mπ) for high densities

ωK- =

dense infinite matter

Antikaons do not receive much attraction

Antikaons receive much attraction

Outlook

Many-body forces

Baryon-baryon sector

(cf : RMF extended to BMM, MMM type diagrams)

[K. Tsubakihara and A. Ohnishi, arXiv:1211.7208.]

Stiffness of EOS at high density

Searching for multi-strangeness nuclei in experiments

Search for fragments in Heavy-ion collisions

M(PSR J1614-2230) = 1.97 ± 0.04 M

3-4 Strangeness fraction

Kaonic nuclei

[A. Dote, H. Horiuchi et al., Phys. Lett. B 590 (2004) 51; Phys.Rev. C70 (2004) 044313. ]

kaonic nuclei by AMD

Highly dense and low temperature object

[ Y.Akaishi and T.Yamazaki, Phys.Rev. C65 (2002) 044005. ]Theoretical prediction based on deep K- potential

・ 4He (K- stopped, p), 4He (K- stopped, n)

・ In flight (K-,

N) ・ K- pp state

[A. Gal, R. S. Hayano (Eds.), Nucl. Phys. A804 (2008). ] For review articles,

[ T. Kishimoto et al., Prog. Theor. Phys. 118 (2007), 181. ]

KEK, J-PARC [ M. Iwasaki et al.T. Suzuki et al., Phys. Rev. C76, 068202(2007).]

deep K-nucleus potential, ~200 MeV (analysis of missing mass spectra)

[ M. Agnello et al., Phys. Rev. Lett. 94 (2005) 212303; Phys. Lett. B654(2007), 80. ]

Experimental searches

[E. Oset et al., arXiv: 0912.3145v1[nucl-th]. ]

Sharrow potential ~ 60 MeV in chiral unitary approach

FINUDA

[T. Yamazaki et al., arXiv: 1002.3526v1 [nucl-ex].]]DISTO Collaboration

KEK, BNL

[B. F. Gibson, K. Imai, T. Motoba, T. Nagae, A. Ohnishi (Eds.), proceedings of HYP-X, Nucl. Phys. A835 (2010). ]

interactions in matter Kaon condensation in neutron stars

kaonic nuclei search at J-PARC (K- pp, K-NNN, ・・・ )