Non-forward scattering of twisted particles

Twisted photons (i.e. photons carrying non-zero orbital angular momentum) are well-known in optics. Recently, it was suggested to use Compton backscattering off an ultra-relativistic electron beam to boost optical twisted photons into the high energy range. However, only the case of strictly forward/backward scattering has been studied so far. Here, we consider generic kinematic features of processes in which a twisted particle scatters with non-zero transverse momentum transfer.