Scattering of wave packets with phases

TL;DR

This paper develops a method to analyze $2\rightarrow N_f$ scattering involving wave packets with arbitrary phases, revealing quantum effects like impact parameter dependence and phase sensitivities absent in plane-wave approximations.

Contribution

It introduces a power series expansion approach for scattering with wave packets, capturing quantum effects and generalizing previous plane-wave results.

Findings

Cross section depends on impact parameter and phases.

Quantum features emerge in scattering beyond plane-wave approximation.

Method applies to vortex particles, Airy beams, and their generalizations.

Abstract

A general problem of $2\rightarrow N_f$ scattering is addressed with all the states being wave packets with arbitrary phases. Depending on these phases, one deals with coherent states in $(3+1)$ D, vortex particles with orbital angular momentum, the Airy beams, and their generalizations. A method is developed in which a number of events represents a functional of the Wigner functions of such states. Using width of a packet $\sigma_p/\langle p\rangle$ as a small parameter, the Wigner functions, the number of events, and a cross section are represented as power series in this parameter, the first non-vanishing corrections to their plane-wave expressions are derived, and generalizations for beams are made. Although in this regime the Wigner functions turn out to be everywhere positive, the cross section develops new specifically quantum features, inaccessible in the plane-wave approximation. Among them is dependence on an impact parameter between the beams, on phases of the incoming states, and on a phase of the scattering amplitude. A model-independent analysis of these effects is made. Two ways of measuring how a Coulomb phase and a hadronic one change with a transferred momentum $t$ are discussed.