Magnetic phases in three-flavor color superconductivity

The best natural candidates for the realization of color superconductivity are quark stars-not yet confirmed by observation-and the extremely dense cores of compact stars, many of which have very large magnetic fields. To reliably predict astrophysical signatures of color superconductivity, a better understanding of the role of the star's magnetic field in the color-superconducting phase that is realized in the core is required. This paper is an initial step in that direction. The field scales at which the different magnetic phases of a color superconductor with three quark flavors can be realized are investigated. Going from weak to strong fields, the system first undergoes a symmetry transmutation from a color-flavor-locked (CFL) phase to a magnetic-CFL (MCFL) phase, and then a phase transition from the MCFL phase to the paramagnetic-CFL (PCFL) phase. The low-energy effective theory for the excitations of the diquark condensate in the presence of a magnetic field is derived using a covariant representation that takes into account all the Lorentz structures contributing at low energy. The field-induced masses of the charged mesons and the threshold field at which the CFL -> MCFL symmetry transmutation occurs are obtained in the framework of this low-energy effective theory. The relevance of the different magnetic phases for the physics of compact stars is discussed.