Nonlinear photon trident versus double Compton scattering and resummation of one-step terms

TL;DR

This paper analyzes the nonlinear photon trident process, compares it to double Compton scattering, and introduces novel resummation techniques involving Meijer-G functions for accurate expansion at various regimes.

Contribution

It presents a detailed comparison between photon trident and double Compton scattering and introduces new resummation methods for one-step terms using Meijer-G functions.

Findings

Resummation methods effectively handle small- and large-$hi$ expansions.

New resummations require few terms for high precision.

Photon trident process closely resembles double Compton scattering.

Abstract

We study the photon trident process, where an initial photon turns into an electron-positron pair and a final photon under a nonlinear interaction with a strong plane-wave background field. We show that this process is very similar to double Compton scattering, where an electron interacts with the background field and emits two photons. We also show how the one-step terms can be obtained by resumming the small- and large-$\chi$ expansions. We consider a couple of different resummation methods, and also propose new resummations (involving Meijer-G functions) which have the correct type of expansions at both small and large $\chi$. These new resummations require relatively few terms to give good precision.