Non-perturbative couplings and color superconductivity

Abstract

Quark matter at sufficiently high density exhibits color superconductivity, due to attractive gluonic interactions. At lower densities of order Λ QCD 3, it has been proposed that instanton generated vertices may play an important role in the Cooper pair formation. We study the renormalization group flow to the Fermi surface of the full set of couplings generated by gluonic and instanton interactions. In earlier work we showed that if the gluonic interactions dominate at the matching scale, their running determines the scale of the Cooper pair formation Δ. Here we consider all possibilities, including the one in which the instanton interactions dominate all others at the matching scale. In the latter case we find that a number of additional induced couplings (including the gluonic ones) reach their Landau poles almost simultaneously with the instanton vertex. Presumably all contribute to the Cooper pair formation. The most important consequence of including all the couplings is a large increase in the gap size Δ.