Color superconductivity and charge neutrality in Yukawa theory

It is generally believed that when Cooper pairing occurs between two different species of fermions, their Fermi surfaces become locked together so that the resultant state remains 'neutral', with equal number densities of the two species, even when subjected to a chemical potential that couples to the difference in number densities. This belief is based on mean-field calculations in models with a zero-range interaction, where the anomalous self-energy is independent of energy and momentum. Following up on an early report of a deviation from neutrality in a Dyson-Schwinger calculation of color-flavor-locked quark matter, we investigate the neutrality of a two-species condensate using a Yukawa model which has a finite-range interaction. In a mean field calculation we obtain the full energy-momentum dependence of the self energy and find that the energy dependence leads to a population imbalance in the Cooper-paired phase when it is stressed by a species-dependent chemical potential. This gives some support to the suggestion that the color-flavor-locked phase of quark matter might not be an insulator.