Universal features of high-energy scattering of Laguerre-Gaussian states

TL;DR

This paper analyzes how Laguerre-Gaussian vortex states affect high-energy scattering, revealing universal kinematic features dependent on impact parameter and transverse momentum, with implications for experimental physics.

Contribution

It provides a systematic re-analysis of vortex-state scattering focusing on impact parameter effects and universal features of the differential cross section.

Findings

Non-zero impact parameter $b$ influences $P_ op$-dependent effects.

Universal kinematic features arise from LG wave packet shape.

Impact parameter can serve as a probe of vortex states.

Abstract

Vortex states of photons, electrons, and other particles are wave packets that carry intrinsic orbital angular momentum (OAM) and exhibit other features unavailable for plane waves. Collisions of high-energy vortex states can become a promising tool for nuclear and particle physics, once experimental challenges are overcome. An extensive literature exists on scattering processes involving vortex states; however, most works rely on assumptions that will be challenging to achieve in experiment. In this work, we initiate a systematic re-analysis of vortex-state scattering processes using paraxial Laguerre-Gaussian (LG) wave packets colliding at a non-zero impact parameter $b$. Since the total final transverse momentum $P_\perp$ is no longer fixed, we focus on how the differential cross section depends on $P_\perp$. We emphasize that non-trivial $P_\perp$-dependent features can originate either from the shape of the LG wave packets or from the dynamics of the scattering process under interest. Here, we focus on the former source and explore in detail these universal kinematic features, while the study of process-specific modifications, along with the novel insights they may bring, is delegated to a future work. Interestingly, the non-zero impact parameter $b$ plays a key role in many $P_\perp$-dependent effects, making it a useful probe of vortex states, not a nuisance factor as often assumed.