Single-branch theory of ultracold Fermi gases with artificial Rashba spin-orbit coupling

We consider interacting ultracold fermions subject to Rashba spin-orbit coupling. We construct a single-branch interacting theory for the Fermi gas when the system is dilute enough so that the positive helicity branch is not occupied at all in the non-interacting ground state. We show that the theory is renormalizable in perturbation theory and therefore yields a model of polarized fermions that avoids a multi-channel treatment of the problem. Our results open the path towards a much more straightforward approach to the many-body physics of cold atoms subject to artificial vector potentials.