Speed of sound and trace anomaly in a unified treatment of the two-color diquark superfluid, the pion-condensed high-isospin matter, and the 2SC quark matter

TL;DR

This paper investigates the speed of sound and trace anomaly in various high-density QCD phases using a unified perturbative approach, revealing how gap effects influence these quantities and their potential peaks at intermediate densities.

Contribution

It provides a unified perturbative framework to analyze the speed of sound and trace anomaly across multiple high-density QCD phases, highlighting the role of gap energy and instanton effects.

Findings

Gap effects can increase the speed of sound when |/| dominates.

Trace anomaly is generally reduced and often negative at high density.

Instanton-induced interactions further enhance the speed of sound in certain phases.

Abstract

In a unified perturbative treatment from the high-density side, we compute the speed of sound and the trace anomaly as functions of the chemical potential $\mu$ for the two-color diquark superfluid, the pion-condensed high-isospin matter, and the 2SC quark matter. We find that the corrections induced by the gap energy $\Delta$ involve nontrivial interplay between the dimensionless magnitude $|\Delta/\mu|$ and the derivative $|\partial\Delta/\partial\mu|$. Even though the gap equation has a common structure for these phases of our interest, different numerical constants cause drastic changes in the speed of sound corrections. As long as $|\Delta/\mu|$ is dominant over the derivative, the gap effects increase the speed of sound, which is consistent with the expected behavior of exhibiting a peak at intermediate density. We then discuss the trace anomaly which is pushed down generally by the gap effects and turns out to be negative widely in the high density regime. For demonstration of non-perturbative enhancement, we take account of the instanton-induced interaction. We confirm a further increase in the speed of sound for the two-color diquark superfluid and the pion-condensed high-isospin matter, while the speed of sound for the 2SC quark matter deviates far below the conformal limit due to the derivative contribution.