Renormalization-Group Invariant Parity-Doublet Model for Nuclear and Neutron-Star Matter

TL;DR

This paper develops a renormalization-group invariant mean-field approach for the Parity-Doublet Model, analyzing chiral symmetry restoration in nuclear and neutron-star matter with a focus on vacuum fluctuations.

Contribution

It introduces a multiplicatively renormalizable, explicitly invariant mean-field method for the PDM, emphasizing the role of baryonic vacuum fluctuations in chiral symmetry restoration.

Findings

Vacuum fluctuations significantly influence chiral condensate evolution.

The approach provides a consistent framework for thermodynamics of nuclear matter.

Chiral symmetry restoration occurs at high densities and temperatures relevant for neutron stars.

Abstract

The Parity-Doublet Model (PDM) is a chirally invariant effective theory for strong-interaction matter involving nucleons and their opposite-parity partners in a parity-doubling framework. We introduce a multiplicatively renormalizable mean-field approach to include the baryonic vacuum contributions to the resulting grand-canonical potential in an explicitly renormalization-group invariant form. As an application, we evaluate the pertinent thermodynamics of two-flavor symmetric and asymmetric nuclear matter, focusing on the restoration of spontaneously broken chiral symmetry at baryon densities and temperatures relevant for the astrophysics of neutron stars. Special attention is paid to the effect of the baryonic vacuum fluctuations on the evolution of chiral condensate with baryon density and temperature for specific choices of the chirally invariant baryon mass $m_0$ to demonstrate the importance of consistently including these vacuum fluctuations in the PDM.