BCS Theory of Hadronic Matter at High Densities

The equilibrium between the so-called 2SC and CFL phases of strange quark matter at high densities is investigated in the framework of a simple schematic model of the NJL type. Equal densities are assumed for quarks u, d and s. The 2SC phase is here described by a color-flavor symmetric state, in which the quark numbers are independent of the color-flavor combination. In the CFL phase the quark numbers depend on the color-flavor combination, that is, the number of quarks associated with the color-flavor combinations ur, dg, sb is different from the number of quarks associated with the color flavor combinations ug, ub, dr, db, sr, sg. We find that the 2SC phase is stable for a chemical potential μ below μ_c = 0.505 GeV, while the CFL phase is stable above, the equilibrium pressure being P_c = 0.003 GeV⁴. We have used a 3-momentum regularizing cutoff Delta = 0.8 GeV, which is somewhat larger than is usual in NJL type models. This should be adequate if the relevant chemical potential does not exceed 0.6 GeV.