Gauge invariance and amplitudes of two-photon processes

TL;DR

This paper introduces a gauge-based method for deriving two-photon process amplitudes that simplifies numerical calculations and is applicable to various particle interactions, including polarized cases, enhancing event generator accuracy.

Contribution

A new gauge approach for calculating two-photon amplitudes that reduces numerical cancellations and extends to polarized particles, improving computational efficiency.

Findings

Amplitudes have no strong numerical cancellations.

Method successfully applied to multiple two-photon processes.

Extended to polarized particle interactions.

Abstract

A method to derive the convenient representations for many two-photon amplitudes is suggested. It is based on the use of the gauge in which the photon propagator has only space components. The amplitudes obtained have no any strong numerical cancellations and, therefore, are very convenient for numerical evaluations. Our approach is illustrated by the consideration of the processes $e^+e^-\to e^+e^-e^+e^-$, $e^+e^-\rightarrow e^+e^-\mu^+\mu^-$, and $e^+e^-\to \mu^+\mu^-\pi^+\pi^-$. The method is extended on the case of polarized particles. The amplitudes obtained in this approach have been employed for extension of the event generator developed by F.A. Berends, P.H. Daverveldt, and R. Kleiss.