σ and π meson properties and delocalization of the nucleon in a hot and dense nuclear medium

Abstract

The modifications of meson and baryon properties due to the presence of an external hot baryon medium are investigated in the Nambu-Jona-Lasinio (NJL) model. The corresponding meson sector is solved for a quark continuum at finite density and temperature. This results in modified values of the constituent quark mass (pion decay constant) and the pion and sigma masses. We find a second order chiral phase transition with a non-monotonic temperature-density phase diagram. The solitonic sector is approximated by the Gell-Mann-Lévi σ-model whose lagrangian is uniquely obtained in terms of the modified meson properties. The nucleon mass and the charge radii are evaluated by means of projection techniques. Similar to the chiral phase transition the critical curve in the phase diagram for delocalization of the nucleon (no solitonic solution) is non-monotonic. All meson and baryon properties studied show a non-monotonic temperature dependence at finite density. At medium densities of about (2–3) ϱ nm the baryonic phase exists only at intermediate temperatures.