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 ∼ µg −5 e −κ/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.

We explore the relation between the chromomagnetic instability of a homogeneous two flavor color superconductor and the LOFF state. We perturb the free energy of the 2SC by generating a small net momentum for the quark pair. We find that the imaginary Meissner mass of a particular gluon implies that the LOFF state is energetically favored. 1

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