On the Perturbative Nature of Color Superconductivity

TL;DR

This paper systematically derives the transition temperature for color superconductivity in high density QCD from the fundamental Lagrangian, confirming its dependence on the coupling constant and analyzing perturbative contributions.

Contribution

It provides a detailed derivation of T_C from QCD, including the effects of one-loop corrections, extending previous approximations.

Findings

Confirmed T_C dependence on coupling g as $T_C \,\sim\, \mu g^{-5} e^{-\,\kappa/g}$

Identified an O(1) contribution to the prefactor from one-loop quark self energy

Found other radiative and two-gluon exchange contributions to be subleading

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 $T_C \sim \mu g^{-5} e^{-\kappa/g}$, 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.