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Two-flavor color superconductivity at finite temperature, chemical potential and in the presence of strong magnetic fields

Utilizing an extended two-flavor Nambu-Jona Lasinio (NJL) model, we review some of the effects of external magnetic fields on two-flavor color superconducting phase (2SC) at moderate baryon densities in the QCD phase diagram. The effective action of the extended NJL model consists of two mass gaps as functions of three intensive quantities, the temperature, the quark chemical potential and the external magnetic field. The nonzero values of the mass gaps, chiral and diquark condensates, induce spontaneous chiral and color symmetry breaking, respectively, and as a result two different phases of quark matter appear. We find the transition curves between these phases as well as the critical points in the QCD phase diagram in terms of the intensive quantities. Imposing a constant strong magnetic field on these two phases, we show that the mass gaps increase with the magnetic field and the symmetry breaking region in the QCD phase diagram expands even to the larger values of temperature and quark chemical potential. This phenomenon is a consequence of the magnetic catalysis of dynamical symmetry breaking, which is proven before.