Perturbative nature of color superconductivity

Color superconductivity is a possible phase of high density QCD. We present a systematic derivation of the transition temperature T-c from the QCD Lagrangian through study of the di-quark proper vertex. With this approach, we confirm the dependence of T-c on the coupling g, namely T(c)similar to mu g(-5)e(-kappa/g), previously obtained from the one-gluon exchange approximation in the superconducting phase. The diagrammatic approach we employ allows us to examine the perturbative expansion of the vertex and the propagators. We find an additional O(1) contribution to the prefactor of the exponential from the one-loop quark self energy and that the other one-loop radiative contributions and the two gluon exchange vertex contribution are subleading.