Color-Superconducting Gap in the Presence of a Magnetic Field

We explore the effects of an external magnetic field in the structure and magnitude of the diquark condensate in a three massless quark flavor color superconductor. It is shown that the long-range component $\widetilde{B}$ of the external magnetic field that penetrates the color-flavor locked (CFL) phase modifies its gap structure, producing a new phase of lower symmetry. Our analysis is performed within an NJL effective field theory with four-fermion interactions, inspired by one-gluon exchange. Using Ritus' method, we compute the quark propagators in the presence of a background magnetic field, and derive the gap equations for arbitrary values of the field. An analytical solution is found for strong magnetic fields. A main outcome of our study is that the $\widetilde{B}$ field tends to strengthen the gaps that get contributions from pairs of $\widetilde{Q}$-charged quarks. These gaps are enhanced through the field-dependent density of states of the $\widetilde{Q}$-charged quarks on the Fermi surface. Our considerations are relevant for the study of highly magnetized compact stars.