Scale symmetry and composition of compact star matter

TL;DR

This paper investigates dense compact star matter using a skyrmion crystal approach with chiral effective theory, revealing scale symmetry breaking effects and conformal limits that influence the equation of state without indicating quark matter onset.

Contribution

It introduces a comprehensive skyrmion crystal model including scalar and vector mesons, constrains anomalous dimensions, and explores the implications of scale symmetry and conformal limits in dense matter.

Findings

Speed of sound approaches 1/3 at high density

Polytropic index near 1, consistent with conformal limits

Conformal limits do not signal quark matter onset

Abstract

The dense compact star matter is studied by using the skyrmion crystal approach. The chiral effective theory used includes the lightest scalar meson, the lowest-lying vector mesons as well as pions. Consistency with the vector manifestation and the dilaton limit fixed point at high density constrains the anomalous dimension of the gluon field $1.0 \lesssim |\gamma_{G^2}| \lesssim 2.0$ and leads to the significance of the scale symmetry breaking in the intrinsic parity-odd part of the effective theory. The speed of sound $v_s^2 \simeq 1/3$ and the polytropic index $\gamma \simeq 1$ -- both satisfy the conformal limits -- after the dilaton limit fixed point at high density but the matter is still in the hadronic phase. This means that neither the conformal speed of sound nor the smallness of the polytropic index can be used as a criterion of the onset of quark matter. These conclusions are significant for constructing the equation of state of nuclear matter.