Topological susceptibility in the superconductive phases of quantum chromodynamics: A Dyson-Schwinger perspective

We test nonperturbative gluon propagators recently studied in the literature, by computing the topological susceptibility, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>χ</a:mi></a:math>, of the superconductive phases of quantum chromodynamics at high density. We formulate the problem within the high-density effective theory, and use the two-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 nonperturbative gluon propagator plays its role. We complete the model by adding a <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>U</c:mi><c:mo stretchy="false">(</c:mo><c:mn>1</c:mn><c:msub><c:mo stretchy="false">)</c:mo><c:mi>A</c:mi></c:msub></c:math>-breaking term whose coupling is fixed perturbatively at large quark chemical potential. We then use the effective potential to compute <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>χ</g:mi></g:math> in the superconductive phases. We finally discuss implications of the results for the axion mass in superdense phases of quantum chromodynamics.