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.
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