  A future gamma factory at CERN or accelerator-based gamma sources elsewhere
can include the possibility of energetic twisted photons, which are photons
with a structured wave front that can allow a pre-defined large angular
momentum along the beam direction. Twisted photons are potentially a new tool
in hadronic physics, and we consider here one possibility, namely the
photoproduction of $\Delta$(1232) baryons using twisted photons. We show that
particular polarization amplitudes isolate the smaller partial wave amplitudes
and they are measurable without interference from the terms that are otherwise
dominant.
