Magnetic Interactions, the Renormalization Group and Color Superconductivity in High Density QCD

TL;DR

This paper studies how magnetic interactions influence the renormalization group flow of pairing interactions in high density QCD, deriving gauge-invariant equations and analyzing the superconducting gap including higher angular momentum states.

Contribution

It provides a gauge-invariant derivation of RG equations considering magnetic effects and Landau damping, and confirms the form of the superconducting gap at high density.

Findings

Derived the RG equations with magnetic interactions and Landau damping.

Confirmed the superconducting gap formula including higher angular momentum condensates.

Showed rotational invariance remains unbroken at asymptotically high density.

Abstract

We investigate the effect of long range magnetic interactions on the renormalization group (RG) evolution of local Cooper pairing interactions near the 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. We obtain the Landau pole $\Delta \sim \mu g^{-5} \exp(- \frac{3 \pi^2}{\sqrt{2} g})$, although the structure of our equations differs from previous results. We also investigate the gap equation, including condensates of higher angular momentum. We show that rotational invariance is unbroken at asymptotically high density, and verify that $\Delta$ is the correct value of the gap when higher modes are included in the analysis.