Chiral, parity-doublet, effective-Lagrangian mean-field theories for nuclear and astrophysical phenomenology

TL;DR

This paper reviews chiral-parity effective Lagrangian models that describe baryons with parity doubling, highlighting their ability to unify descriptions of hadronic matter from vacuum to dense astrophysical environments.

Contribution

It summarizes the structure, mean-field formulation, and recent constraints of parity-doublet Lagrangians, emphasizing their implications for dense matter and neutron-star physics.

Findings

Parity-doublet models accommodate finite baryon masses with a chirally-invariant mass term.

Recent phenomenological and lattice data constrain the chirally-invariant mass parameter.

Parity doubling influences the equation-of-state and cooling mechanisms of neutron stars.

Abstract

Chiral-parity (parity-doublet) effective Lagrangian models provide a compact and symmetry-consistent framework for describing baryons and their negative-parity partners in terms of linearly-realized chiral symmetry. Unlike the conventional, linear, sigma model; the parity-doublet approach accommodates a chirally-invariant mass term, $m_0$, allowing finite baryon-masses even when the chiral condensate melts. This feature enables a unified treatment of hadronic matter across vacuum, nuclear and dense astrophysical regimes. This compact review summarizes the key structures of parity-doublet Lagrangians; outlines the mean-field formulation for nuclear and stellar matter; and highlights recent phenomenological and lattice constraints on the chirally-invariant mass. Emphasis is placed on mirror versus na\"ive chiral assignments; the role of vector interactions in achieving nuclear saturation; and the implications of parity doubling for the equation-of-state of dense matter and neutron-star cooling. The review concludes with current theoretical challenges and perspectives for extending these models beyond the mean-field approximation.