  We consider pairing in a dilute system of Fermions with a short-range
interaction. While the theory is ill-defined for a contact interaction, the BCS
equations can be solved in the leading order of low-energy effective field
theory. The integrals are evaluated with the dimensional regularization
technique, giving analytic formulas relating the pairing gap, the density, and
the energy density to the two-particle scattering length.
