  We study the Feshbach resonance of spin-1/2 particles in the presence of a
uniform synthetic non-Abelian gauge field that produces spin orbit coupling
along with constant spin potentials. We develop a renormalizable quantum field
theory that includes the closed channel boson which engenders the Feshbach
resonance, in the presence of the gauge field. By a study of the scattering of
two particles in the presence of the gauge field, we show that the Feshbach
magnetic field, where the apparent low energy scattering length diverges,
depends on the conserved centre of mass momentum of the two particles. For high
symmetry gauge fields, such as the one which produces an isotropic Rashba spin
orbit coupling, we show that the system supports two bound states over a regime
of magnetic fields for a negative background scattering length and resonance
width comparable to the energy scale of the spin orbit coupling. We discuss the
consequences of these findings for the many body setting, and point out that a
broad resonance (width larger than spin orbit coupling energy scale) is most
favourable for the realization of the rashbon condensate.
