Two-loop QED corrections to the scattering of four massive leptons

TL;DR

This paper computes two-loop quantum electrodynamics corrections for four massive leptons scattering, revealing elliptic integrals and geometric structures to improve analytical and numerical understanding of Bhabha and Møller scattering.

Contribution

It introduces the first analytical computation of elliptic Feynman integrals for this process, uncovering the underlying elliptic geometry and providing practical series expansions.

Findings

Derived explicit elliptic integral expressions for two-loop corrections

Uncovered elliptic geometric structures in the scattering amplitude

Provided compact series expansions for relevant kinematic regions

Abstract

We study two-loop corrections to the scattering amplitude of four massive leptons in quantum electrodynamics. These amplitudes involve previously unknown elliptic Feynman integrals, which we compute analytically using the differential equation method. In doing so, we uncover the details of the elliptic geometry underlying this scattering amplitude and show how to exploit its properties to obtain compact, easy-to-evaluate series expansions that describe the scattering of four massive leptons in QED in the kinematical regions relevant for Bhabha and M{\o}ller scattering processes.