Color neutral two-flavor superconducting phase of cold and dense quark matter in the presence of constant magnetic fields

The color neutral two-flavor superconducting 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 (chi SB) mass gap sigma(B), a color superconducting (CSC) mass gap Delta(B) and a color chemical potential mu(8) is introduced in the presence of a rotated U(1) magnetic field (B) over tilde. 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 chemical potential. The structure of the chi SB and CSC phases is also presented in the mu(c)-(e) over tildeB plane, and the effect of mu(8) on the phase structure of the model is explored. As it turns out, whereas the transition from the chi SB to CSC phase is of first order, nonvanishing mu(8) affects essentially the second order phase transition from CSC to the normal phase.