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 Λ?=?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.