Threshold effects in high-energy vortex state collisions

Collisions of particles prepared in non--plane-wave states with a non-trivial phase structure, such as vortex states carrying an adjustable orbital angular momentum (OAM), open novel opportunities in atomic, nuclear, and high-energy physics unavailable for traditional scattering experiments. Recently, it was argued that photoinduced processes such as $\gamma d \to pn$ and $\gamma p \to \Delta^+$ initiated by a high-energy vortex photon should display a remarkable threshold shift and a sizable cross section enhancement as the impact parameter $b$ of the target hadron with respect to the vortex photon axis goes to zero. In this work, we theoretically explore whether this effect exists within the quantum-field-theoretic treatment of the scattering process. We do not rely on the semiclassical assumption of pointlike, non-spreading target particle and, instead, consider the toy process of heavy particle pair production in collision of two light particles prepared as a Laguerre-Gaussian and a compact Gaussian wave packets, paying special attention to the threshold behavior of the cross section. We do observe threshold smearing due to non-monochromaticity of the wave packets, but we do not confirm the near-threshold enhancement. Instead we find an OAM-related dip at $b\to 0$ as compared with the two Gaussian wave packet collision.