Angular Momentum Mixing in Single Flavor Color Superconductivity with Transverse Pairing

TL;DR

This paper investigates angular momentum mixing in single flavor color superconductivity with transverse pairing, showing that mixing slightly lowers free energy but the spherical state remains most stable.

Contribution

It demonstrates that angular momentum mixing occurs in single flavor CSC with transverse pairing and that the spherical CSL state remains energetically favored.

Findings

Angular momentum mixing lowers free energy slightly.

Most stable state remains spherical CSL.

Mixing does not significantly alter the pairing state stability.

Abstract

Because of the equal strength of the pairing potential mediated by one-gluon exchange for all partial waves to the leading order QCD running coupling constant and the nonlinearity of the gap equation, the non-spherical pairing in single flavor color superconductivity(CSC) can not be restricted in a single non-s-wave channel and the mixing among different angular momenta will occur. In this paper, we examine the angular momentum mixing in single flavor CSC with transverse pairing, in which the pairing quarks have opposite helicity. We find that the free energy of all non-spherical pairing states are lowered by angular momentum mixing compared with that contain p-wave only. But the amount of the free energy drop is numerically small. Consequently the most stable pairing state that respect the time reversal invariance remains the spherical CSL.