  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 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
$1/(m \alpha a_s) \ll -1$ 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
$1/(m \alpha a_s) > 0$ region, all of the higher-loop contributions are of
similar order.
