Color superconducting matter in a magnetic field

TL;DR

This paper studies how strong magnetic fields influence the pairing gaps in three-flavor quark matter, revealing oscillatory behaviors and significant deviations in gap structures that could impact magnetar physics.

Contribution

It introduces a detailed analysis of magnetic field effects on color superconducting gaps, including oscillatory behavior and the impact of neutrality conditions, which was not previously explored.

Findings

Gap parameters exhibit de Haas-van Alphen oscillations with magnetic field strength.

Neutrality conditions significantly alter the gap structure at high magnetic fields.

Strong magnetic fields in magnetars can cause notable deviations in quark pairing gaps.

Abstract

We investigate the effect of a magnetic field on cold dense three-flavor quark matter using an effective model with four-Fermi interactions with electric and color neutrality taken into account. The gap parameters Delta_1, Delta_2, and Delta_3 representing respectively the predominant pairing between down and strange (d-s) quarks, strange and up (s-u) quarks, and up and down (u-d) quarks, show the de Haas-van Alphen effect, i.e. oscillatory behavior as a function of the modified magnetic field B that can penetrate the color superconducting medium. Without applying electric and color neutrality we find Delta_2 \approx Delta_3 >> Delta_1 for 2 e B / mu_q^2, where e is the modified electromagnetic coupling constant and mu_q is one third of the baryon chemical potential. Because the average Fermi surface for each pairing is affected by taking into account neutrality, the gap structure changes drastically in this case; we find Delta_1 >> Delta_2 \approx Delta_3 for 2 e B > mu_q^2. We point out that the magnetic fields as strong as presumably existing inside magnetars might induce significant deviations from the gap structure Delta_1 \approx Delta_2 \approx Delta_3 at zero magnetic field.