Color superconductivity in weak coupling

We derive perturbatively the gap equations for a color-superconducting condensate with total spin $J=0\mathrm{}$ in dense QCD. At zero temperature, we confirm the results of Son for the dependence of the condensate on the coupling constant, and compute the prefactor to leading logarithmic accuracy. At nonzero temperature, we find that to leading order in weak coupling, the temperature dependence of the condensate is identical to that in BCS-like theories. The condensates for total spin $J=1\mathrm{}$ are classified; to leading logarithmic accuracy these condensates are of the same order as those of spin $J=0.\mathrm{}$