Chiral Restoration of Nucleons in Neutron Star Matter: Studies Based on a Parity Doublet Model

Abstract

We review the chiral variant and invariant components of nucleon masses and the consequence of their existence on the chiral restoration in extreme conditions, particularly in neutron star matter. We consider a model of linear realization of chiral symmetry with the nucleon parity doublet structure that permits the chiral invariant mass, m0, for positive and negative parity nucleons. The nuclear matter is constructed with the parity doublet nucleon model coupled to scalar fields σ, vector fields (ω,ρ), and mesons with strangeness through the U(1)A anomaly. In models with a large m0, the nucleon mass is insensitive to the medium, and the nuclear saturation properties can be reproduced without demanding strong couplings of the nucleons to the scalar fields σ and vector fields ω. We confront the resulting nuclear equations of state with nuclear constraints and neutron star observations and delineate the chiral invariant mass and effective interactions. To further examine the nuclear equations of state beyond the saturation density, we supplement quark models to set the boundary conditions from the high-density side. The quark models are constrained by the two-solar-mass conditions, and such constraints are transferred to nuclear models through the causality and thermodynamic stability conditions. We also calculate various condensates and the matter composition from nuclear to quark matter in a unified matter by constructing a generating functional that interpolates the nuclear and quark matter with external fields. Two types of chiral restoration are discussed: one due to the positive scalar charges of nucleons and the other triggered by the evolution of the Dirac sea. We found that the U(1)A anomaly softens equations of state from low to high density.

A Brief Overview of the Special Issue “Symmetry and Ultradense Matter in Compact Stars”

“…This process involves no bona fide Ginzburg-Landau-Wilsonian-type phase transitions. Nonetheless, driven by the sliding dilaton condensate as density increases, the skyrmionquantum-Hall unification [6] exposes [8] the presence of the U A (1) scalar meson η , which is considered to figure at high density associated with the baryonic parity doublet symmetry [9]. Parity-doublet symmetry, argued to be playing an important role in chiral symmetry restoration, could be an emergent symmetry [4], rather than intrinsic in QCD, playing a crucial role in leading to the pseudo-conformal model of compact stars with a sound speed of v 2 s /c 2 ≈ 1/3 [7].…”

“…Now, QCD sum-rules address on-shell properties of hadrons in medium and, hence, involve the issue of how the "mass parameters" of EFT Lagrangians figuring in many-body nuclear interactions can be related to the on-shell quantities. The issue of the chiral-invariant nucleon mass m 0 , whether emergent or intrinsic in QCD [9], could be studied in this approach. This class of issues has been a thorny one in nuclear physics for a long time, and it still remains as such in interpreting experiments in terms of vacuum-dependent quantities, e.g., in heavy-ion collisions.…”