Chiral-parity (parity-doublet) effective Lagrangian models provide a symmetry-consistent and economical framework for describing baryons and their negative-parity partners within a linearly realized chiral symmetry. In contrast to the conventional linear sigma model, the parity-doublet formulation admits a chirally invariant mass term, m 0 , which allows baryons to retain finite masses; even as the chiral condensate vanishes. Within this setup, hadronic matter can be treated consistently across vacuum, nuclear and dense astrophysical environments. This review presents a focused synthesis of the essential structures of parity-doublet Lagrangians; outlines their mean-field implementation for nuclear and stellar matter; and discusses recent phenomenological and lattice constraints on the chirally invariant mass. Particular attention is given to mirror versus naïve 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 is concluded by highlighting open theoretical challenges and possible directions for extending these models beyond the mean-field approximation.
Ayon Mukherjee (2026) studied this question.