1. 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

2. Multi-strangeness system in hadronic matter 1. 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.

3. 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)

4. 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

5. kaon fields ( K ± ) (nonlinear representation) (scalar) (vector) RMF (scalar)(vector) S-wave scalar int. S-wave vector int. Kaonic part of the Lagrangian density

6. ・ 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 ( ρ 0 =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

7. --- scalar meson couplings for Kaon --- at ρ 0 in symmetric nuclear matter Decay of f 0 (975) quark and isospin counting rule --- vector meson couplings for Kaon --- U K - = (− 180 〜 − 80 ) MeV K - optical potential depth : SU(6) symmetry

8. |S|: the number of the embedded K - Assume : Spherical symmetry A = N + Z : mass number Z: the number of proton Multi-K Nuclei p K-K- r ー 3. Coexistence of antikaons and hyperons in finite nuclei Local density approximation for baryons K - meson hyperon proton neutron [ Charge conservation ] [ Baryon number conservation ] [ Strangeness conservation ] [ Initial target nucleus ] 3-1. Outline

9. 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

10. 4 Numerical results 1. density distributions For finite nuclei ( ) 2.Stability of multi-strangeness nuclei

11. 4 Numerical results | U K | < 180 MeVA=15, Z=8 ( ) No K - meson is bound. 4-1. density distributions Ground state : Central density        Multi-hypernuclei

12. Total energy Energy difference per unit of strangeness from normal nuclei ( |S| = 0 ) Strong decay of multi-hypernuclei to For |S| >3 | U K | < 180 MeV 4-2. Stability of multi-strangeness nuclei

13. 5. Onset of kaon condensation in β-equilibrated matter (Neutron stars) chemical equilibrium for weak processes Onset of K - condensates

14. 5-1 Onset of kaon condensation in hyperon matter Appearance of antikaons with hyperons in finite nuclei

15. 5-2 EOS in β-equilibrated matter Energy/particle Particle fractions

16. 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 | U K - | (< 180 MeV), the ground state is given by multi-hypernuclei without bound K - mesons. 6 Summary and outlook Finite effects of nuclei Antikaons do not receive much attraction Finite nuclei

17. Effects of kaon condensates on EOS Neutron 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 and suppression of attractive - baryon interaction at 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 U K >> - 80 MeV ( Σ KN ~ 150 MeV )

18. (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).]

20. 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

21. The number density of K- mesons < 0 for X 0 << 0. The presence of K - condensates (θ) leads to a negative contribution to vector mean fields (ω 0, R 0, φ 0 ). < 0 Vector mean fields Scalar mean fields Coulomb field Equations of motion for meson fields

22. U K = − 180 MeV Ground state 4-2. Density distributions (extremely attractive)

23. 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-ωK- Finite effects of nuclei > μ Λ ー μ p hard to satisfy In neutron stars K - chemical potential : = O ( m π ) for high densities ω K- = dense infinite matter Antikaons do not receive much attraction Antikaons receive much attraction

24. 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 

25. 3-4 Strangeness fraction

26. 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 ・ 4 He (K - stopped, p), 4 He (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 matterKaon condensation in neutron stars kaonic nuclei search at J-PARC (K - pp, K - NNN, ・・・ )