The Transition Temperature to the Superconducting Phase of QCD at High Baryon Density

TL;DR

This paper derives the leading-order perturbative expression for the transition temperature to the color superconducting phase of QCD at high baryon density, including angular momentum effects.

Contribution

It provides a perturbative derivation of the pre-exponential factor for the transition temperature, extending analysis to higher angular momentum pairings.

Findings

Derived the transition temperature's pre-exponential factor to leading order in g.

Compared transition temperature with zero temperature gap.

Extended analysis to higher angular momentum pairings.

Abstract

Recent interest in the study of color superconductivity has focused on the regime of high baryon density where perturbative QCD may be employed. Based on the dominant one-gluon-exchange interaction, both the transition temperature and zero temperature gap have been determined to leading order in the coupling, g. While the leading non-BCS behavior, $T_C\sim\mu g^{-5}e^{-\kappa/g}$, is easily obtained, the pre-exponential factor has proved more difficult to evaluate. Focusing on the transition temperature, we present a perturbative derivation of this factor, exact to leading order in g. This approach is first motivated by the study of a toy model and involves working to second order in the perturbative expansion. We compare this result to the zero temperature gap. Additionally, we extend the analysis to the case of higher angular momentum for longitudinal and transverse quark pairing.