1202.0872 (Lang Yu et al.)

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

Lang Yu, Igor A. Shovkovy

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
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.

View original: http://arxiv.org/abs/1202.0872