Color Superconductivity and Confinement in the Chromodielectric Model

We derive an effective Lagrangian for pairing in nonlinear chromodielectric models (CDM), in leading order. The effective pairing coupling depends explicitly on the confinement field, χ, of the CDM. The self-consistent gap equations are constructed and solved for one example. For a quartic χ potential used in the calculations, in the chiral solution, obtained for large values of the confining field and very low quarks masses, the quarks do not pair. The chiral breaking solution, where χ is small and the quarks are massive, does show pairing. We show that the vector channel of the gap is much weaker than the scalar one. At small densities the gap increases dramatically and the corresponding quark matter collapses. However this occurs for densities where our approximation is no longer valid since pairing energy becomes of the order of magnitude of the sum of the kinetic and potential energies.