  Thanks to progress in optics in the past two decades, it is possible to
create photons carrying well-defined non-zero orbital angular momentum (OAM).
Boosting these photons into high-energy range preserving their OAM seems
feasible. Intermediate energy electrons with OAM have also been produced
recently. One can, therefore, view OAM as a new degree of freedom in
high-energy collisions and ask what novel insights into particles' structure
and interactions it can bring. Here we discuss generic features of scattering
processes involving particles with OAM in the initial state. We show that they
make it possible to perform a Fourier analysis of a plane wave cross section
with respect to the azimuthal angles of the initial particles, and to probe the
autocorrelation function of the amplitude, a quantity inaccessible in plane
wave collisions.
