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Published in Hadrons, Nuclei and Applications, World Scientific, Singapore, Proc.of the Conference Bologna2000. Structure of the Nucleus at the Dawn of the Century, G. Bonsignori, M. Bruno, A. Ventura, D. Vretenar Editors, pag. 319.
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We study the medium modifications of the spectral functions as well as production cross-sections of the strange vector mesons ($phi$, $K^*$ and $bar {K^*}$) in isospin asymmetric strange hadronic matter. These are obtained from the in-medium masses of the open strange mesons and the decay widths $phi rightarrow Kbar K$, $K^* rightarrow Kpi$ and $bar {K^*} rightarrow {bar K}pi$ in the hadronic medium. The decay widths are computed using a field theoretic model of composite hadrons with quark/antiquark constituents, from the matrix element of the light quark-antiquark pair creation term of the free Dirac Hamiltonian between the initial and final states. The matrix element is multiplied with a coupling strength parameter for the light quark-antiquark pair creation, which is fitted to the observed vacuum decay width of the decay process. There are observed to be substantial modifications of the spectral functions as well as production cross-sections of these vector mesons due to isospin asymmetry as well as strangeness of the hadronic medum at high densities. These studies should have observable consequences, e.g. in the yield of the hidden and open strange mesons arising from the isospin asymmetric high energy heavy ion collisions at the Compressed baryonic matter (CBM) experiments at the future facility at GSI.
The equilibrium between the so-called 2SC and CFL phases of strange quark matter at high densities is investigated in the framework of a simple schematic model of the NJL type. Equal densities are assumed for quarks $u,d$ and $s$. The 2SC phase is here described by a color-flavor symmetric state, in which the quark numbers are independent of the color-flavor combination. In the CFL phase the quark numbers depend on the color-flavor combination, that is, the number of quarks associated with the color-flavor combinations $ur,dg,sb$ is different from the number of quarks associated with the color flavor combinations $ug,ub,dr,db,sr,sg$. We find that the 2SC phase is stable for a chemical potential $mu$ below $mu_c=0.505$ GeV, while the CFL phase is stable above, the equilibrium pressure being $P_c=0.003$ GeV$^4$. We have used a 3-momentum regularizing cutoff $Lambda=0.8$ GeV, which is somewhat larger than is usual in NJL type models. This should be adequate if the relevant chemical potential does not exceed 0.6 GeV.
We present sets of equation of state (EOS) of nuclear matter including hyperons using an SU_f(3) extended relativistic mean field (RMF) model with a wide coverage of density, temperature, and charge fraction for numerical simulations of core collapse supernovae. Coupling constants of Sigma and Xi hyperons with the sigma meson are determined to fit the hyperon potential depths in nuclear matter, U_Sigma(rho_0) ~ +30 MeV and U_Xi(rho_0) ~ -15 MeV, which are suggested from recent analyses of hyperon production reactions. At low densities, the EOS of uniform matter is connected with the EOS by Shen et al., in which formation of finite nuclei is included in the Thomas-Fermi approximation. In the present EOS, the maximum mass of neutron stars decreases from 2.17 M_sun (Ne mu) to 1.63 M_sun (NYe mu) when hyperons are included. In a spherical, adiabatic collapse of a 15$M_odot$ star by the hydrodynamics without neutrino transfer, hyperon effects are found to be small, since the temperature and density do not reach the region of hyperon mixture, where the hyperon fraction is above 1 % (T > 40 MeV or rho_B > 0.4 fm^{-3}).
Bulk and single-particle properties of hot hyperonic matter are studied within the Brueckner-Hartree-Fock approximation extended to finite temperature. The bare interaction in the nucleon sector is the Argonne V18 potential supplemented with an effective three-body force to reproduce the saturating properties of nuclear matter. The modern Nijmegen NSC97e potential is employed for the hyperon-nucleon and hyperon-hyperon interactions. The effect of the temperature on the in-medium effective interaction is found to be, in general, very small and the single-particle potentials differ by at most 25% for temperatures in the range from 0 to 60 MeV. The bulk properties of infinite matter of baryons, either nuclear isospin symmetric or a beta-stable composition which includes a non-zero fraction of hyperons, are obtained. It is found that the presence of hyperons can modify the thermodynamical properties of the system in a non-negligible way.
Neutrino propagation in protoneutron stars requires the knowledge of the composition as well as the dynamical response function of dense hadronic matter. Matter at very high densities is probably composed of other particles than nucleons and little is known on the Fermi liquid properties of hadronic multicomponent systems. We will discuss the effects that the presence of $Lambda$ hyperons might have on the response and, in particular, on its influence on the thermodynamical stability of the system and the mean free path of neutrinos in dense matter.
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