Spin physics is an intricate and fascinating chapter in HEP phenomenology. It seems inevitable that, in order to probe spin-parity properties of hadrons and their interactions, one needs either to collide polarized initial particles or to study non-trivial angular distributions in exclusive processes. I will argue that it is possible to probe spin- and parity-dependent observables in inclusive processes with unpolarized particles — provided, they are prepared in a "twisted" state, that is, a non-plane-wave state equipped with a non-zero orbital angular momentum with respect to its propagation direction.

This new degree of freedom offers access to quantities which are inaccessible with the usual plane wave collisions. Although this proposal cannot be checked at existing accelerators, these novel opportunities represent a compelling scientific case to justify a dedicated work on instrumentation development.