Directional dependence of color superconducting gap in two-flavor QCD in a magnetic field

TL;DR

This paper investigates how a magnetic field influences the directional dependence of the color superconducting gap in two-flavor dense quark matter, revealing anisotropic effects in the gap function at high densities.

Contribution

It demonstrates that magnetic fields induce a directional dependence in the superconducting gap in two-flavor QCD, with the gap size varying based on the quasiparticle momentum orientation relative to the magnetic field.

Findings

Gap function becomes anisotropic with magnetic field

Maximum gap occurs for momenta perpendicular to the field

Weak magnetic fields justify the approximations for stellar conditions

Abstract

We study the effect of a magnetic field on the pairing dynamics in two-flavor color superconducting dense quark matter. The study is performed in the weakly coupled regime of QCD at asymptotically high density, using the framework of the Schwinger-Dyson equation in the improved rainbow approximation. We show that the superconducting gap function develops a directional dependence in momentum space. Quasiparticles with momenta perpendicular to the direction of the magnetic field have the largest gaps, while quasiparticles with momenta parallel to the field have the smallest gaps. We argue that the directional dependence is a consequence of a long-range interaction in QCD. The quantitative measure of the ellipticity of the gap function is determined by a dimensionless ratio, proportional to the square of the magnetic field and inversely proportional to the fourth power of the quark chemical potential. For magnetic fields in stars, $B\lesssim 10^{18} G$, the corresponding ratio is estimated to be less than about $10^{-2}$, justifying the use of the weak magnetic field limit in all stellar applications.