Color neutral 2SC phase of cold and dense quark matter in the presence of constant magnetic fields

Abstract: The color neutral two-flavor superconducting (2SC) phase of cold and dense quark matter is studied in the presence of constant magnetic fields and at moderate baryon densities. In the first part of the paper, a two-flavor effective Nambu--Jona-Lasinio model consisting of a chiral symmetry breaking mass gap sigma_{B}, a color superconducting mass gap Delta_{B} and a color neutrality coefficient mu_{8} is introduced in the presence of a rotated U(1) magnetic field B. To study the phenomenon of magnetic catalysis in the presence of strong magnetic fields, the gap equations corresponding to sigma_{B} and Delta_{B}, as well as mu_{8} are solved in the lowest Landau level approximation. In the second part of the paper, a detailed numerical analysis is performed to explore the effect of any arbitrary magnetic field on the above mass gaps and the color neutrality coefficient. The structure of the chiral symmetry breaking and color superconducting phases is also presented in the mu_{c}-B plane, and the effect of the color neutrality coefficient mu_{8} on the phase structure of the model is explored. As it turns out, whereas the transition from the chiral symmetry breaking to color superconducting phase is of first order, nonvanishing mu_{8} affects essentially the second order phase transition from color superconducting to the normal phase.