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13th International Conference on Meson-Nucleon Physics and the Structure of the
Nucleon
(Pontificia Universita della Santa Croce, Rome, Sep.30 – Oct.4, 2013)
Parallel Session : Meson-Nucleon Systems 3
Interplay of antikaons with hyperons
in nuclei and in neutron stars
Takumi Muto (Chiba Inst. Tech.)
collaborators : Toshiki Maruyama (JAEA)
Toshitaka Tatsumi (Kyoto Univ.)
1. Introduction
Multi-strangeness system in hadronic matter
In neutron-stars
hyperonic matter
(Λ, Σ, Ξ, ・・・
in the ground state)
Strange matter
Kaon condensation
（u, d, s quark matter )
・Coexistence of antikaons and hyperons
Softening of EOS
In nuclei
Kaonic nuclei
Toward unified description based on the same
Kaon-baryon(B), B-B interaction model.
[ Y.Akaishi and T.Yamazaki, Phys.Rev. C65 (2002) 044005. ]
Multi-Antikaonic Nuclei
relativistic mean-field theory (RMF)
+coupled with effective chiral Lagrangian
[T. Muto, T. Maruyama and T. Tatsumi, Phys. Rev. C79, 035207 (2009). ]
・Coexistence of antikaons [T. Muto, T. Maruyama and T. Tatsumi,
Genshikaku Kenkyu 57 Supplement 3, 230(2013).]
and hyperons : difficult
We consider interplay between antikaons and hyperons
within the RMF framework
coupled with the effective chiral Lagrangian:
A possible existence of antikaonic nuclear bound states
with hyperon-mixing for finite nuclei
Appearance of hyperons and onset of kaon condensation
in β-equilibrated infinite matter (neutron stars)
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.
2. Outline of the model
2-1. Baryon-Baryon interaction
Mesons:
B=
2-2. K - N,K - K interactions Nonlinear chiral effective Lagrangian
[ D. B. Kaplan and A. E. Nelson, Phys. Lett. B 175 (1986) 57. ]
Meson fields (K± ) (nonlinear representation)
Condensate assumption
(K- mesons are condensed
in the lowest energy state)
Meson decay const.
Kaonic part of the Lagrangian density
S-wave scalar int.
S-wave vector int.
kaon fields (K± ) (nonlinear representation)
(scalar)
RMF
(vector)
(scalar)
(vector)
2-3. Choice of parameters
--- NN interaction --- 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 --repulsive case
--- vector meson couplings for Kaon --quark and isospin counting rule
SU(6) symmetry
--- scalar meson couplings for Kaon --K- optical potential depth :
at ρ0 in symmetric nuclear matter
UK- = (− 180 〜 − 80 ) MeV
Decay of f0(975)
3. Coexistence of antikaons and hyperons in finite nuclei
[ Initial target nucleus ]
A = N + Z : mass number
Z: the number of proton
|S|: the number of the embedded K-
3-1. Outline
ー
Multi-K Nuclei
p
r
Assume : Spherical symmetry
Local density approximation for baryons
K[ Strangeness conservation ]
K- meson
hyperon
[ Charge conservation ]
proton
neutron
[ Baryon number conservation ]
3-2. Thermodynamic potential
as
Chemical equilibrium
for strong processes
Take into account of nonmesonic processes,
in addition to mesonic process,
Coexistence condition of antikaons with hyperons in finite nuclei
4 Numerical results
For finite nuclei (
)
1. density distributions
2. Stability of multi-strangeness
nuclei
4 Numerical results
A=15, Z=8 (
)
4-1. density distributions
| UK | < 180 MeV
Ground state : Multi-hypernuclei
Central density 

 

No K- meson is bound.
4-2. Stability of multi-strangeness nuclei
Total energy
Energy difference per unit of strangeness
from normal nuclei ( |S| = 0 )
| UK | < 180 MeV
For |S| >3
Strong decay of
multi-hypernuclei
to
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
6 Summary and outlook
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 K - B and K - K interactions.
Finite nuclei
For moderate | UK- | (< 180 MeV), the ground state is given by
multi-hypernuclei without bound K- mesons.
Ξ- -mixing becomes dominant for large|S|.
Antikaons do not receive much K - B attraction
Finite effects of nuclei
Neutron stars
Effects of kaon condensates on EOS
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.
The soft EOS cannot support massive stars (~ 2 M).
Strong repulsion between baryons and
suppression of attractive K - baryon interaction
at high densities are needed.
(1) ambiguity of S-wave K-Baryon interactions
Scalar int.: UK >> - 80 MeV
( ΣKN ~ 150 MeV )
ss content in the nucleon is small.
(Recent Lattie QCD)
[R. D. Young, A. W. Thomas, Nucl. Phys. A844(2010)266c.]
・In flight (K-, N) KEK, BNL
deep K-nucleus potential, ~ −200 MeV (analysis of missing mass
spectra)
[ T. Kishimoto et al., Prog. Theor. Phys. 118 (2007), 181. ]
Stiffness of EOS at high density
Beyond mean-field approximation for baryon-baryon sector
(2) Many-body forces
(c.f. phenomenological universal YNN, YYN, YYY repulsions
[ S. Nishizaki, Y. Yamamotoand T. Takatsuka,
Prog. Theor.Phys. 108 (2002) 703. ] )
(cf : RMF extended to BMM, MMM type diagrams)
[K. Tsubakihara and A. Ohnishi, arXiv:1211.7208.]
(3) relativistic Hartree-Fock
Introduction of tensor coupling of vector mesons
Cf. for hyperonic matter,
[T. Miyatsu, T. Katayama, K. Saito, Phys. Lett.B709 242(2012).]
Connection to quark matter
(4) Relation between kaon condensation in hadronic matter
and that in quark matter
K- Baryon interactions in K- field equation
K- field equation
S-wave scalar int.
S-wave vector int.
Chiral symmetry
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.
Equations of motion for meson fields
Scalar mean fields
Vector mean fields
Coulomb field
The presence of K- condensates (θ) leads to a negative contribution
to vector mean fields (ω0, R0 , φ0 ) .
<0
The number density of K- mesons
< 0 for X0 << 0 .
4-2. Density distributions UK= − 180 MeV (extremely attractive)
Ground state
5-3. Comparison with kaon condensation in neutron stars
Finite system formed in laboratory
Antikaons do not receive much K - B attraction
ωK- > μΛ ー μp
Finite effects of nuclei
Chemical equilibrium for strong processes
hard to satisfy
In neutron stars Antikaons receive
much K - B attraction
chemical equilibrium for weak processes
K- chemical potential : ω =
K-
dense infinite matter
= O(mπ)
for high densities
Outlook
Searching for multi-strangeness nuclei in experiments
Search for fragments in Heavy-ion collisions
Stiffness of EOS at high density
Many-body forces
M(PSR J1614-2230)
= 1.97 ± 0.04 M
Baryon-baryon sector
(cf : RMF extended to BMM, MMM type diagrams)
[K. Tsubakihara and A. Ohnishi, arXiv:1211.7208.]
3-4 Strangeness fraction
Kaonic nuclei Highly dense and low temperature object
Theoretical prediction based on deep K- potential
[ Y.Akaishi and T.Yamazaki, Phys.Rev. C65 (2002) 044005. ]
kaonic nuclei by AMD [A. Dote, H. Horiuchi et al., Phys. Lett. B 590 (2004) 51;
Phys.Rev. C70 (2004) 044313. ]
Sharrow potential ~ 60 MeV in chiral unitary approach
Experimental searches
・ 4He (K- stopped, p), 4He (K- stopped, n) KEK, J-PARC [ M. Iwasaki et al.
T. Suzuki et al., Phys. Rev. C76, 068202(2007).]
[ T. Kishimoto et al., Prog. Theor. Phys. 118 (2007), 181. ]
・ In flight (K-, N) KEK, BNL
deep K-nucleus potential, ~200 MeV (analysis of missing mass spectra)
・ K- pp state
FINUDA [ M. Agnello et al., Phys. Rev. Lett. 94 (2005) 212303;
Phys. Lett. B654(2007), 80. ]
DISTO Collaboration [T. Yamazaki et al., arXiv: 1002.3526v1 [nucl-ex].]]
For review articles,
[A. Gal, R. S. Hayano (Eds.), Nucl. Phys. A804 (2008). ]
[E. Oset et al., arXiv: 0912.3145v1[nucl-th]. ]
[B. F. Gibson, K. Imai, T. Motoba, T. Nagae, A. Ohnishi (Eds.), proceedings of HYP-X,
Nucl. Phys. A835 (2010). ]
kaonic nuclei search at J-PARC (K- pp, K-NNN,・・・)
KN interactions in matter
Kaon condensation in neutron stars