Atom-dimer and dimer-dimer scatterings in a spin-orbit-coupled Fermi gas

Using the diagrammatic approach, here we study how spin-orbit coupling (SOC) affects the fermion-dimer and dimer-dimer scattering lengths in the Born approximation, and we benchmark their accuracy with the higher-order approximations. We consider both isotropic and Rashba couplings in three dimensions and show that the Born approximation gives accurate results in the 1/(m alpha a(s)) << -1 limit, where m is the mass of the fermions, alpha is the strength of the SOC, and a(s) is the s-wave scattering length between fermions. This is because the higher-loop contributions form a perturbative series in the 1/(m alpha a(s)) < 0 region that is controlled by the smallness of the residue Z of the dimer propagator. In sharp contrast, since Z grows with the square root of the binding energy of the dimer in the 1/(m alpha(as)) > 0 region, all of the higher-loop contributions are of similar order.