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Cooper Pair's Magnetic Moment in MCFL Color Superconductivity

We investigate the effect of the alignment of the magnetic moments of Cooper pairs of charged quarks that form at high density in three-flavor quark matter. The high density phase of this matter in the presence of a magnetic field is known to be the Magnetic Color-Flavor-Locked (MCFL) phase of color superconductivity. We derive the Fierz identities of the theory and show how the explicit breaking of the rotational symmetry by the uniform magnetic field field opens new channels of interactions and allows the formation of a new diquark condensate. The new order parameter is a spin-1 diquark condensate proportional to the component in the field direction of the average magnetic moment of the pairs of charged quarks. In the region of large fields, the new condensate's magnitude becomes comparable to the larger of the two scalar gaps. Since there is no solution of the gap equations with nonzero scalar gaps and zero value of this magnetic moment condensate, its presence in the MCFL phase is unavoidable. This is consistent with the fact that the extra condensate does not break any symmetry that has not already been broken by the known MCFL gaps. The spin-1 condensate enhances the condensation energy of pairs formed by charged quarks and the magnetization of the system. We discuss the possible consequences of the new order parameter on the issue of the chromomagnetic instability that appears in color superconductivity at moderate density.