Nonlinear trident pair production in an arbitrary plane wave: a focus on the properties of the transition amplitude

TL;DR

This paper analyzes nonlinear electron-positron pair production in arbitrary plane waves, focusing on the transition amplitude's properties, regularization, and the distinguishable two-step and one-step contributions, with implications for experimental measurements.

Contribution

It provides a regularized, gauge-invariant expression for the transition amplitude and distinguishes between two-step and one-step processes in nonlinear trident pair production.

Findings

Amplitude regularized and gauge-invariant

Two-step and one-step contributions identified

Potential for experimental measurement of one-step contribution

Abstract

The process of nonlinear electron-positron pair production by an electron colliding with an arbitrary plane wave electromagnetic field (nonlinear trident pair production) is studied analytically and numerically. Special emphasis is put on the properties of the transition amplitude. In fact, its original expression as resulting from applying the Wick's theorem turns out to be divergent and not to manifestly fulfill gauge invariance. By restoring the latter, the amplitude is regularized and investigated in different regimes. In particular, the amplitude is divided into a two-step and a one-step contributions, depending on the scaling dependence on the laser pulse duration. The corresponding contributions to the positron angular distribution spectra and the resulting interference terms are studied numerically emphasizing the possibility of measuring experimentally the contribution of the one-step contribution.