  A framework for computing the superfluid gap in an effective field theory
(EFT) of fermions interacting via momentum-independent contact forces is
developed. The leading universal corrections in the EFT are one-loop in-medium
effects at the Fermi surface, and reproduce the well-known
Gor'kov-Melik-Barkhudarov result. The complete subleading universal corrections
are presented here, and include one-loop effects away from the Fermi surface,
two-loop in-medium effects, as well as modifications to the fermion propagator.
Together, these effects are found to reduce the gap at low densities.
Applications to neutron superfluidity in neutron stars are also discussed.
