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

Abstract

We study the potential of the axion, a, of Quantum Chromodynamics, in the two-flavor colorsuperconducting 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 Uð1ÞA symmetry: the latter is responsible of the coupling of axions to quarks. We introduce two quark condensates, hL and hR, describing condensation for left-handed and right-handed quarks respectively; we then study the loci of the minima of the thermodynamic potential, Ω, in the (hL; hR) plane, noticing how the instanton-induced interaction favors condensation in the scalar channel when the θ angle, θ ¼ a=fa, vanishes. Increasing θ we find a phase transition where the scalar condensate rotates into a pseudoscalar one. We present an analytical result for the topological susceptibility, χ, 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 ma is related to the full topological susceptibility via χ = m_a^2 f_a^2; hence our result for χ gives an analytical result form_a in the superconductive phase of high-density Quantum Chromodynamics.