Scattering of Twisted Particles: Extension to Wave Packets and orbital helicity

High-energy photons and other particles carrying non-zero orbital angular momentum (OAM) emerge as a new tool in high-energy physics. Recently, it was suggested to generate high-energy photons with non-zero OAM (twisted photons) by the Compton backscattering of laser twisted photons on relativistic electron beams. Twisted electrons in the intermediate energy range have also been demostrated experimentally; twisted protons and other particles can in principle be created in a similar way. Collisions of energetic twisted states can offer a new look at particle properties and interactions. A theoretical description of twisted particle scattering developed previously treated them as pure Bessel states and ran into difficulty when describing the OAM of the final twisted particle at non-zero scattering angles. Here we develop further this formalism by incorporating two additional important features. First, we treat the initial OAM state as a wave packet of a finite transverse size rather than a pure Bessel state. This realistic assumption allows us to resolve the existing controversy between two theoretical analyses for non-forward scattering. Second, we describe the final twisted particle in terms of the orbital helicity --- the OAM projection on its average direction of propagation rather than on the fixed reaction axis. Using this formalism, we determine to what extent the twisted state is transferred from the initial to final OAM particle in a generic scattering kinematics. As a particular application, we prove that in the Compton backscattering the orbital helicity of the final photon stays close to the OAM projection of the initial photon.