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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). Parallel Session : Meson-Nucleon Systems 3. Interplay of antikaons with hyperons in nuclei and in neutron stars.

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Interplay of antikaons with hyperons in nuclei and in neutron stars

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  1. 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.)

  2. 1. Introduction Multi-strangeness system in hadronic matter In neutron-stars hyperonic matter Strange matter （u, d, s quark matter ) (Λ, Σ, Ξ, ・・・ in the ground state) Kaon condensation ・Coexistence of antikaons and hyperons Softening of EOS Toward unified description based on the same Kaon-baryon(B), B-B interaction model. In nuclei Kaonic nuclei [ Y.Akaishi and T.Yamazaki, Phys.Rev. C65 (2002) 044005. ] relativistic mean-field theory (RMF) +coupled with effective chiral Lagrangian Multi-Antikaonic Nuclei [T. Muto, T. Maruyama and T. Tatsumi, Phys. Rev. C79, 035207 (2009). ] ・Coexistence of antikaons and hyperons : difficult [T. Muto, T. Maruyama and T. Tatsumi, Genshikaku Kenkyu 57 Supplement 3, 230(2013).]

  3. 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.

  4. 2. Outline of the model Mesons: 2-1. Baryon-Baryon interaction B = 2-2. interactions Nonlinear chiral effective Lagrangian [ D. B. Kaplan and A. E. Nelson, Phys. Lett. B 175 (1986) 57. ] (nonlinear representation) Meson fields (K± ) Condensate assumption (K- mesons are condensed in the lowest energy state) Meson decay const.

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

  6. 2-3. Choice of parameters --- NN interaction --- gross features of normal nuclei and nuclear matter ・saturation properties of nuclear matter ・binding energy of nuclei and proton-mixing ratio ・density distributions of p and n (ρ0 =0.153 fm−３) --- vector meson couplings for Y --- SU(6) symmetry --- scalar meson couplings for Y --- repulsive case

  7. --- 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)

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

  9. 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

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

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

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

  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. 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 and 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 attraction Finite effects of nuclei

  17. 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 - baryon interaction at high densities are needed. (1) ambiguity of S-wave K-Baryon interactions content in the nucleon is small. Scalar int.: UK >> - 80 MeV ( ΣKN ~ 150 MeV ) (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. ]

  18. 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

  19. - Baryon interactions in K- field equation K- field equation S-wave vector int. S-wave scalar int. Chiral symmetry repulsion for Σ-andΞ-hyperons Vector interaction between K- mesons andhyperons (Σ-andΞ-) works repulsively as far as > 0 , unfavorable for coexistence.

  20. 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 .

  21. 4-2. Density distributions UK= − 180 MeV (extremely attractive) Ground state

  22. 5-3. Comparison with kaon condensation in neutron stars Finite system formed in laboratory Antikaons do not receive much attraction Finite effects of nuclei > μΛ　ー　μp ωK- Chemical equilibrium for strong processes hard to satisfy Antikaons receive much attraction dense infinite matter In neutron stars chemical equilibrium for weak processes K- chemical potential : ωK- = = O(mπ) for high densities

  23. Outlook Searching for multi-strangeness nuclei in experiments Search for fragments in Heavy-ion collisions M(PSR J1614-2230) =1.97 ± 0.04 M Stiffness of EOS at high density Many-body forces Baryon-baryon sector (cf : RMF extended to BMM, MMM type diagrams) [K. Tsubakihara and A. Ohnishi, arXiv:1211.7208.]

  24. 3-4 Strangeness fraction

  25. 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 KEK, J-PARC [ M. Iwasaki et al. T. Suzuki et al., Phys. Rev. C76, 068202(2007).] ・4He (K- stopped, p), 4He (K- stopped, n) KEK, BNL [ T. Kishimoto et al., Prog. Theor. Phys. 118 (2007), 181. ] ・In flight (K-, N) 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,・・・) interactions in matter Kaon condensation in neutron stars

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