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

TL;DR

Chiral-parity mean-field theories extend relativistic RMF models by incorporating a parity-doublet structure with a chirally invariant mass $m_{0}$, enabling finite baryon masses across the chiral transition. The framework distinguishes mirror and naïve chiral assignments, couples baryons to scalar and vector mesons, and employs a mean-field reduction to describe nuclear saturation, finite nuclei, and neutron-star matter, with $m_{0}$ acting as a key tuning parameter for the EoS. Lattice-QCD and experimental data support parity doubling near the chiral crossover and constrain $m_{0}$ around $\mathcal{O}(700\,\mathrm{MeV})$, while phenomenology shows a soft EoS at moderate densities that stiffens at higher densities and can accommodate $2\,M_\odot$ neutron stars. The approach provides a conceptual bridge between hadronic physics and QCD thermodynamics, but requires beyond-mean-field treatments, clearer parity-partner identifications, and tighter, multi-channel constraints to become a precision tool for dense matter.

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 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 concludes with current theoretical challenges and perspectives for extending these models beyond the mean-field approximation.

Figures (3)

• Figure 2.1: Masses of the positive- and negative-parity nucleons in the mirror and naïve assignments, as functions of the chiral condensate $\sigma_0$. Figure adapted from Ref. hosaka2003progress.
• Figure 3.1: Temperature dependence of the effective masses of the positive- and negative-parity nucleons in one of the parity-doublet mean-field models. The convergence of $m_{N_+}^*$ and $m_{N_-}^*$ at high $T$ reflects chiral restoration.
• Figure 3.2: Binding energy comparison: (a) binding energy $\left(E/A - m_N\right)$ as a function of normalised baryon density $\left(\rho_B/\rho_0\right)$ for one of the parity-doublet mean-field models; and (b) the corresponding standard RMF (NL3) result, adapted from Ref. Motohiro:2015taa. The parity-doublet EoS softens at moderate densities and stiffens at higher densities due to the density dependence of the effective masses $m_{N_\pm}^*$.