Topological Susceptibility in the Superconductive Phases of Quantum Chromodynamics: a Dyson-Schwinger Perspective

TL;DR

This paper investigates the topological susceptibility in high-density superconductive phases of QCD using Dyson-Schwinger equations, providing insights into non-perturbative effects and implications for axion physics.

Contribution

It introduces a Dyson-Schwinger framework within High-Density Effective Theory to compute topological susceptibility in superconductive QCD phases, incorporating non-perturbative gluon propagators and $U(1)_A$ breaking.

Findings

Computed topological susceptibility in dense QCD phases.

Analyzed effects of non-perturbative gluon propagators.

Discussed implications for axion mass in superdense matter.

Abstract

We test non-perturbative gluon propagators recently studied in the literature, by computing the topological susceptibility, $\chi$, of the superconductive phases of Quantum Chromodynamics at high density. We formulate the problem within the High-Density Effective Theory, and use the 2-particle irreducible formalism to compute the effective potential of the dense phases. We focus on superconductive phases with two and three massless flavors. Within this formalism, we write a Dyson-Schwinger equation in the rainbow approximation for the anomalous part of the quark propagator in the superconductive phases, in which the non-perturbative gluon propagator plays its role. We complete the model by adding a $U(1)_A$-breaking term whose coupling is fixed perturbatively at large quark chemical potential. We then use the effective potential to compute $\chi$ in the superconductive phases. We finally discuss implications of the results for the axion mass in superdense phases of Quantum Chromodynamics.