A chiral lagrangian with Broken Scale: testing the restoration of symmetries in astrophysics and in the laboratory

TL;DR

This paper develops a chiral Lagrangian model incorporating broken scale invariance to explore symmetry restoration in high-density and high-temperature matter, with implications for astrophysics and laboratory experiments.

Contribution

It introduces a phase diagram for chiral and scale symmetry restoration using a scalar dilaton field, highlighting the conditions under which these symmetries are restored or broken.

Findings

Chiral symmetry is restored at high temperatures but remains broken at low temperatures.

Scale invariance is more easily restored at low baryon densities.

The model predicts significant softening of matter at high densities, affecting neutron star properties and gravitational wave signals.

Abstract

We study matter at high density and temperature using a chiral lagrangian in which the breaking of scale invariance is regulated by the value of a scalar field, called dilaton \cite{Heide:1993yz,Carter:1995zi,Carter:1996rf,Carter:1997fn}. We provide a phase diagram describing the restoration of chiral and scale symmetries. We show that chiral symmetry is restored at large temperatures, but at low temperatures it remains broken at all densities. We also show that scale invariance is more easily restored at low rather than large baryon densities. The masses of vector mesons scale with the value of the dilaton and their values initially slightly decrease with the density but then they increase again for densities larger than $\sim 3 \rho_0$. The pion mass increases continuously with the density and at $\rho_0$ and T=0 its value is $\sim$ 30 MeV larger than in the vacuum. We show that the model is compatible with the bounds stemming from astrophysics, as e.g. the one associated with the maximum mass of a neutron star. The most striking feature of the model is a very significant softening at large densities, which manifests also as a strong reduction of the adiabatic index. While the softening has probably no consequence for Supernova explosion via the direct mechanism, it could modify the signal in gravitational waves associated with the merging of two neutron stars.