  Photons carrying non-zero orbital angular momentum (twisted photons) are
well-known in optics. Recently, it was suggested to use Compton backscattering
to boost optical twisted photons to high energies. Twisted electrons in the
intermediate energy range have also been produced recently. Thus, collisions
involving energetic twisted particles seem to be feasible and represent a new
tool in high-energy physics. Here we discuss some generic features of
scattering processes involving twisted particles in the initial and/or final
state. In order to avoid additional complications arising from non-trivial
polarization states, we focus here on scalar fields only. We show that
processes involving twisted particles allow one to perform a Fourier analysis
of the plane wave cross section with respect to the azimuthal angles of the
initial particles. In addition, using twisted states one can probe the
autocorrelation function of the amplitude, which is inaccessible in the plane
wave collisions. Finally, we discuss prospects for experimental study of these
effects.
