Promises and challenges of high-energy vortex states collisions

Vortex states of photons, electrons, and other particles are non--plane-wave solutions of the corresponding wave equation with helicoidal wave fronts. These states possess an intrinsic orbital angular momentum with respect to the average propagation direction, which represents a new degree of freedom, previously unexplored in particle or nuclear collisions. Vortex states of photons, electrons, neutrons, and neutral atoms have been experimentally produced, albeit at low energies, and are being intensively explored. Anticipating future experimental progress, one can ask what additional insights on nuclei and particles one can gain once collisions of high-energy vortex states become possible. This review describes the present-day landscape of physics opportunities, experimental progress and suggestions relevant to vortex states in high energy collisions. The aim is to familiarize the community with this emergent cross-disciplinary topic and to provide a sufficiently complete literature coverage, highlighting some results and calculational techniques.