Kaon-baryon coupling schemes and ! kaon condensation in hyperonic - PDF document

International Symposium on Neutron Star Matter (NSMAT 2016) （ Aoba Science Hall, Graduate School of Science, Tohoku Univ., Sendai, Japan) [ November 21 (Mon) -24 (Thu) 2016] �������������������������������������������������������������������������������� Parallel Session A � Kaon-baryon coupling schemes and ! kaon condensation in hyperonic matter ! Takumi Muto (Chiba Inst. Tech.) ! collaborators : Toshiki Maruyama (JAEA) ! Toshitaka Tatsumi (Kyoto Univ.) � 1. Introduction � Multi-strangeness system in neutron stars � ( Λ , Σ, Ξ, ・・・ in the ground state) ! Hyperon-mixed matter � Kaon condensation � (BEC of antikaons) � ・ Rapid cooling of neutron stars � ・ Softening of EOS � Coexistence of kaon condensation Hyperon puzzle ! and hyperons [(Y+K) phase] ? � (crisis) � Observations � [ P. Demorest, T.Pennucci, S. Ransom, ! M. Roberts and J.W.T.Hessels, ! M (PSR J1614-2230) = 1.97 ± 0.04 M ! ! Nature 467 (2010) 1081.] � [J. Antoniadis et al., ! M (PSR J0348+0432) = ( 2.01 ± 0.04) M ! ! Science 340, 6131 (2013).] � For hyperon-mixed matter � universal YNN, YYN, YYY repulsions � � [ S. Nishizaki, Y. Yamamoto and T. Takatsuka, Prog. Theor. Phys. 108 (2002) 703. ] � Stiffening the EOS at high densities �

For kaon condensates � ・ (Anti) kaons are free from Pauli effects � ー� - Ambiguity of S-wave K-B interaction. - � Two coupling schemes for nonlinear Kaon field and-Baryons � 1. Contact Interaction � 2. Meson-Exchange interaction � Effective Chiral Lagrangian � Applied to ! c.f. [H. Fujii, T. Maruyama, ! medium effect � Multi Antikaonic Nuclei � T. Muto, T.Tatsumi, ! [T. Muto, T. Maruyama and T. Tatsumi, ! Nucl. Phys. A 597 (1996), 645.] � Phys. Rev. C79, 035207 (2009). ] � -We consider dependence of (Y+K) phase (onset density, EOS) ! on K-Baryon coupling schemes within the RMF --- � 2-1. Baryon-Baryon interaction ! 2. Outline of the model � Baryons: � Mesons: ! Relativistic mean-field theory � parameters � --- NN interaction --- ! gross features of normal nuclei and nuclear matter � ( ρ 0 =0.153 fm − 3 ) � ・ saturation properties of nuclear matter ! =6.38 � ・ binding energy of nuclei and proton-mixing ratio ! ・ density distributions of p and n ! =8.71 � =4.26 � --- vector meson couplings for Y --- SU(6) symmetry !

--- σ meson couplings for Y --- ! Hyperon potentials deduced ! from hypernuclear experiments � ( analysis of Λ single-particle orbitals ) � ・ (K - , π ± ) at BNL ! T =3/2 state: strongly repulsive � [ J. Dabrowski, Phys. Rev. C60 (1999), 025205. ] ! ・ ( π - , K + ) at KEK ! 23.5 MeV 80.4 MeV [ H. Noumi et al., , ! Phys. Rev. Lett. 89 (2002), 072301; ibid 90(2003), 049902(E). ] ! � analysis of Σ - atoms : repulsive [ C. J. Batty, E. Friedman, A. Gal, ! Phys. Rep. 287 (1997), 385. ] ! repulsive case ! [c.f., K. Nakazawa et al., E373 exp. ! [ T. Fukuda et al., Phys. Rev. C58 (1998), 1306., ! PTEP 2015,033D02 (2015).] � P. Khaustov et al., Phys. Rev. C61 (2000), 054603. ] ! --- σ * meson couplings for Y --- ! Nagara event : Δ B ΛΛ （ 6 ΛΛ He) ! 1.0 MeV →�� 2-2 interactions ! K − B , K − K [ D. B. Kaplan and A. E. Nelson, ! SU(3) L × SU(3) R chiral effective Lagrangian ! Phys. Lett. B 175 (1986) 57. ] ! Baryons ! Ψ ! (p, n, ! Λ , Ξ - , Σ - ) ! Vector current ! Meson fields ( K ± ) ! Axial-vector current ! ( ) ! Classical K - field ! Meson decay constant ! μ K : kaon chemical potential �

K-B coupling schemes � S wave scalar int. � Contact K-B interaction � Meson-exchange (ME) � Nonlinear K - field � Scalar mean fields � Nonlinear σ self-interaction potential : � Contact K-B interaction � Meson-exchange (ME) � S wave vector int. � Nonlinear K - field � Vector mean fields �

3. Results � 3-1 Lowest kaon energy ω in hyperonic matter # and onset density of kaon condensation � ω ：� Pole of kaon propagator � Meson-Exchange � without ! dU/d σ � 3-3 EOS in β -equilibrated matter ! Energy per particle � ( Σ KN ~ 280 MeV ! for Contact Int. � for <N |N> ~ 0 ) � ss chemical equilibrium ! for weak processes !

Gravitational Mass –Radius relatiosn � observation � 4. Summary � σ self-interaction potential � K- B Meson-Exchange int. � ・ d U /d σ from nonlinear scalar self-int.potential : repulsive � universal ! result ? � c.f. [P.J.Ellis, R.Knorren and M.Prakash, Phys. Rev. C52(1995), 3470.] � Push up the onset density of kaon condensation � ・ K- ω , ρ , φ meson coupling terms in the E.O.M.of vector mean-fields ! ー� weaken the K-B vector attraction in the K-condensed phase. ! (Y+K) phase is unlikely ! (Recent Lattie QCD) � for � U K ~ − 75MeV � ( Σ KN ~ 280 MeV ) � ss content in the nucleon is small. � [R. D. Young, A. W. Thomas, ! K- B Contact int. � Nucl. Phys. A844(2010) 266c.] � (Y+K) phase is likely to occur even for � U K ~ − 75MeV � ( Σ KN ~ 280 MeV ) � , leading to softening the EOS steadily. �

5. Discussion � Effects leading to stiff EOS of (Y+K) phase at high density � (1) Baryon-baryon sector � (i) Phenomenological universal YNN, YYN, YYY repulsions � ��� [ S. Nishizaki, Y. Yamamoto and T. Takatsuka, ! Prog. Theor.Phys. 108 (2002) 703. ] � [R. Tamagaki, Prog. Theor. Phys. 119 (2008), 965. ] : String-Junction model � (cf : RMF extended to BMM, MMM type diagrams) � [K. Tsubakihara and A. Ohnishi, Nucl. Phys. A 914 (2013), 438; arXiv:1211.7208.] � (ii) 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).] � Suppression of hyperons ? � (2) Finite-size effects of baryons in Hadron phase � ・ Excluded volume effect of baryons � Stiffening the EOS ! of hadron phase � ・ limitation of hadron picture � ! and necessity of cross over between hadron and quark phases � Repulsive ! core � Hadron picture � = 1.0 fm -3 � for r 0 = 0.5 fm � quark phase � core radius: r 0 � Hadron phase � Crossover � ρ C � Future issues � ・ Properties of kaon-condensates in hadronic phase and quark phase � ・ connecting hadron phase and quark phase →� ! taking into account of Crossover region ! c.f. [ K. Masuda, T. Hatsuda, T. Takatsuka, Astrophys. J. Lett. 764, 12 (2013).] �

Preliminary result : EOS of kaon-condensated phase ! with excluded-volume effect � We must refit the parameters ! to reproduce saturation properties ! of nuclear matter within ! the excluded-volume formalism . �