Perturbative nature of color superconductivity

Abstract

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 ${T}_{C}\ensuremath{\sim}\ensuremath{\mu}{g}^{\ensuremath{-}5}{e}^{\ensuremath{-}\ensuremath{\kappa}/g},$ 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.