Topological susceptibility and axion potential in two-flavor superconductive quark matter

TL;DR

This paper investigates the axion potential and topological susceptibility in two-flavor color superconducting quark matter using a Nambu-Jona-Lasinio-like model, revealing phase transitions and analytical expressions for axion properties at high density.

Contribution

It provides the first analytical calculation of the topological susceptibility and axion mass in the superconductive phase of dense QCD.

Findings

Topological susceptibility remains finite at finite temperature.

Axion mass is directly related to the topological susceptibility in the superconductive phase.

Phase transition involves rotation of scalar condensate into a pseudo-scalar one.

Abstract

We study the potential of the axion, $a$, of Quantum Chromodynamics, in the two-flavor color superconducting phase of cold and dense quark matter. We adopt a Nambu-Jona-Lasinio-like model. Our interaction contains two terms, one preserving and one breaking the $U(1)_A$ symmetry: the latter is responsible of the coupling of axions to quarks. We introduce two quark condensates, $h_L$ and $h_R$, describing condensation for left-handed and right-handed quarks respectively; we then study the loci of the minima of the thermodynamic potential, $\Omega$, in the $(h_L,h_R)$ plane, noticing how the instanton-induced interaction favors condensation in the scalar channel when the $\theta-$angle, $\theta=a/f_a$, vanishes. Increasing $\theta$ we find a phase transition where the scalar condensate rotates into a pseudo-scalar one. We present an analytical result for the topological susceptibility, $\chi$, in the superconductive phase, which stands both at zero and at finite temperature. Finally, we compute the axion mass and its self-coupling. In particular, the axion mass $m_a$ is related to the full topological susceptibility via $\chi=m_a^2 f_a^2$, hence our result for $\chi$ gives an analytical result for $m_a$ in the superconductive phase of high-density Quantum Chromodynamics.