Sigma Condensed Nuclear Matter in the Extended Linear Sigma Model

We apply the linear sigma model to nuclear matter with finite nuclear density. Although the linear sigma model has no repulsive interaction, we introduce vector meson contributions to satisfy the saturation property of the nuclear matter. We also consider a nucleon mass term, scalar meson mass terms, and a sigma meson-chiral loop interaction, which are not chiral invariant, in addition to chiral-invariant higher-power chiral loop terms. The bulk properties of the nuclear matter are estimated on the assumption of sigma meson condensation. The parameters introduced in this model are determined such that the energy per nucleon of the system realizes its minimum at the normal nuclear density, ρ B =0 .19 /fm 3 (the Fermi momentum pF = 278. 5M eV/c), with the value −15.75 MeV, and the incompressibility is given by K ∼ 200 MeV. With these parameter values, the effective pion mass squared is often negative at low densities. A negative pion mass squared implies the existence of a pion classical field. Here, we do not consider the pion condensed state, and therefore we seek parameter values that result in a positive pion mass squared at normal density.