Properties of the QCD axion in two-flavor color superconductive matter with massive quarks

We investigate the properties of QCD axion at low temperature and moderate density in the Nambu-Jona-Lasinio model with instanton induced interactions by simultaneously considering the scalar and pseudoscalar condensates in both quark-antiquark and diquark channels. We derive the analytical dispersion relations of quarks with four-type condensates at nonzero theta angle <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>θ</a:mi><a:mo>=</a:mo><a:mi>a</a:mi><a:mo>/</a:mo><a:msub><a:mrow><a:mi>f</a:mi></a:mrow><a:mrow><a:mi>a</a:mi></a:mrow></a:msub></a:mrow></a:math>. The axion mass, quartic self-coupling, and the axion potential are calculated in both the chiral symmetry breaking and two-flavor color superconducting phases. Using the commonly adopted model parameters, we find that, due to the emergence of color superconductivity, the chiral phase transition not only does not lead to a significant decrease in axion mass and self-coupling but rather results in an obvious enhancement of them. As a <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>θ</c:mi></c:math> function, the axion potential exhibits an approximate period of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>π</e:mi></e:math>, which is quite different from the case without considering the color superconductivity. The surface tension of axion domain wall is also calculated in the presence of color superconductivity.