Thermodynamics of the parity-doublet model: Symmetric nuclear matter and the chiral transition

We present a detailed discussion of the thermodynamics of the parity-doublet nucleon-meson model within a mean-field theory, at finite temperature and baryon-chemical potential, with special emphasis on the chiral transition at large baryon densities and vanishing temperature. We consider isospin-symmetric matter. We systematically compare the parity-doublet model to a related singlet model obtained by disregarding the chiral partner of the nucleon. After studying the ground state properties of nuclear matter, the nuclear liquid-gas transition, and the density modifications of the nucleon sigma term which govern the low-density regime, we give new insight into the underlying mechanisms of the zero-temperature chiral transition occurring at several times the nuclear saturation density. We show that the chiral transition is driven by a kind of symmetry energy that tends to equilibrate the populations of opposite parity baryons. This symmetry energy dictates the composition of matter at large baryon densities, once the phase space for the appearance of the negative-parity partner is opened. We furthermore highlight the characteristic role, within the thermodynamics, of the chiral-invariant mass of the parity-doublet model. We include the chiral limit into all of our discussions in order to provide a complete picture of the chiral transition.