On gap equations and color-flavor locking in cold dense QCD with three massless flavors

The superconductivity in cold dense QCD with three massless flavors is analyzed in the framework of the Schwinger-Dyson equation. The set of two coupled gap equations for the color antitriplet, flavor antitriplet (3̄,3̄) and the color sextet, flavor sextet (6,6) order parameters is derived. It is shown that the antitriplet-antitriplet gives the dominant contribution to the color-flavor locked order parameter, while the sextet-sextet is small but nonzero.