On the perturbative nature of color superconductivity

We study color superconductivity, which is a possible phase of high density QCD. We present a systematic derivation of the transition temperature, T_C, through study of the di-quark proper vertex obtained from the QCD Lagrangian. With this approach, we confirm the dependence of T_C on the coupling g, namely $T_C\sim\mu g^{-5}e^{-C/g}$, that has been obtained from one-gluon exchange. From a systematic examination of the perturbative expansion of the vertex to O(g^4), we find an additional leading order contribution to the prefactor of the exponential.