Magnetic interactions, the renormalization group and color superconductivity in high density QCD

We investigate the effect of long range magnetic interactions on the renorm alization group (RG) evolution of local Cooper pairing interactions near th e Fermi surface in high density QCD. We use an explicit cut-off on momentum modes, with special emphasis on screening effects such as Landau damping, to derive the RG equations in a gauge invariant, weak coupling expansion. W e obtain the Landau pole Delta similar to mu g(-5)exp(-3 pi(2)/root 2 g), a lthough the structure of our equations differs from previous results. We al so investigate the gap equation, including condensates of higher angular mo mentum. We show that rotational invariance is unbroken at asymptotically hi gh density, and verify that Delta is the correct value of the gap when high er modes are included in the analysis. (C) 2000 Elsevier Science B.V. All r ights reserved.