Vortex states of photons, electrons, and other particles are wave packets that carry intrinsic orbital angular momentum 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 amount of 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 reanalysis of vortex-state scattering processes using paraxial Laguerre-Gaussian (LG) wave packets colliding at a nonzero impact parameter $b$. Since the total final transverse momentum ${\mathbf{P}}_{\perp }$ is no longer fixed, we focus on how the differential cross section depends on ${\mathbf{P}}_{\perp }$. We emphasize that nontrivial ${\mathbf{P}}_{\perp }$-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 nonzero impact parameter $b$ plays a key role in many ${\mathbf{P}}_{\perp }$-dependent effects, making it a useful probe of vortex states, not a nuisance factor as often assumed.

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• Electron & positron scattering
• Electrons
• Angular momentum
• Lepton colliders