Irreducible tensor basis and general Fierz relations for Bhabha scattering like amplitudes

TL;DR

This paper develops an irreducible tensor basis for Bhabha scattering amplitudes, simplifying calculations and enabling off-shell analysis, while also deriving Fierz relations between different channels.

Contribution

It introduces a new tensor basis for Bhabha scattering amplitudes based on Lorentz symmetry, facilitating amplitude calculations and off-shell applications.

Findings

Basis simplifies amplitude contraction calculations

Fierz relations connect s- and t-channel bases

Applied to compute tree-level Bhabha scattering amplitude

Abstract

We construct an irreducible s- and t-channel tensor basis for Bhabha scattering like amplitudes based on the properties of the underlying Lorentz symmetry in four space-time dimensions. In the given basis the calculation of amplitude contractions like the amplitude square reduces to the contraction of their corresponding coefficient tensors. Further the basis retains the full amplitude information and thus can be applied in off-shell cases. The general Fierz transformations which relate the s- and t-channel basis with each other are obtained. As an example for application we use the basis to calculate the tree-level Bhabha scattering amplitude.