Helicity amplitudes for the small--angle process e^-e^{\pm}\to e^-\gamma\gamma + e^{\pm} with both photons along one direction and its cross channel

TL;DR

This paper derives comprehensive analytic expressions for helicity amplitudes in small-angle double bremsstrahlung during electron scattering, focusing on configurations where both photons are aligned with the electron, aiding precise theoretical and computational analyses.

Contribution

It provides the first complete set of helicity amplitudes for the process with arbitrary helicities, including cross-channel reactions, with approximations valid for high energies and small angles.

Findings

Analytic expressions for 64 helicity amplitudes are obtained.

The amplitudes are accurate up to terms of order m^2/E_j^2, heta_j^2, and heta_j m/E_j.

The study includes various kinematic limits for the helicity amplitudes.

Abstract

We study the small--angle double bremsstrahlung in $e^-e^\pm$ scattering for a jet kinematics where both photons move along the electron direction. This region gives the main contribution to the cross section. We present analytic expressions for all 64 amplitudes with arbitrary helicity states of the initial and final leptons and the produced photons convenient for analytic and numerical studies. The accuracy of the obtained amplitudes is given omitting only terms of the order of m^2/E_j^2, \theta_j^2 and \theta_j m/E_j. The helicity amplitudes for the cross channel \gamma e^\pm \to \gamma e^+e^- + e^\pm are given. Several limits for the helicity amplitudes of hard or soft final particles are considered.