Thermodynamics of the parity-doublet model: Asymmetric and neutron matter

We consider isospin-asymmetric matter in the parity-doublet model within an extended mean-field calculation, increasing continuously the neutron excess all the way to pure neutron matter. We compute the liquid-gas and the chiral phase transitions occurring at zero to moderate temperatures, but put special emphasis on the phase structure of matter at zero temperature and large baryon densities. The calculation of the free energy involves the solution of gap equations. This is achieved by transforming these gap equations into ordinary differential equations that control the flow with increasing baryon density of various physical quantities: the isoscalar condensate, the densities of protons and neutrons, as well as those of their respective chiral partners. In this formulation, the initial conditions for the differential equations determine the entire phase structure. It is further demonstrated that the threshold for the onset of the population of the chiral partners is exclusively determined by the fermionic parameters, most notably by the chiral-invariant mass of the nucleon. We underline the role of a parity symmetry energy in driving the equilibration of the nucleons and their parity partners across the chiral transition. We provide a detailed analysis of the changes in the matter properties as one varies the neutron excess, including a special discussion of the chiral limit, and we compare systematically the parity-doublet model to its corresponding singlet model, where the chiral partner of the nucleon is neglected. Finally, we focus on neutron matter and compute the equation of state and the speed of sound. The results are confronted to those of other calculations as well as to recent Bayesian analyses of neutron-star observations.