Lepton-Pair Scattering With an Off-Shell and an On-Shell Photon at Two Loops in Massless QED

TL;DR

This paper computes two-loop scattering amplitudes involving a lepton pair and photons in massless QED, using advanced techniques to support high-precision predictions for future experiments.

Contribution

It provides the first complete two-loop amplitude calculations for lepton-photon scattering with off-shell and on-shell photons in massless QED, employing modern computational methods.

Findings

Amplitudes expressed in terms of special functions.

Reconstruction from numerical finite-field evaluations.

Supports N3LO predictions for electron-muon scattering.

Abstract

I present the computation of the two-loop amplitudes for the scattering of a lepton pair with an off-shell and an on-shell photon in massless QED. We apply modern techniques developed to tackle QCD amplitudes with many scales: we express the Feynman integrals in terms of a basis of special functions, and reconstruct the amplitudes from numerical finite-field evaluations. Our results complete the amplitude-level ingredients for the N3LO predictions of electron-muon scattering needed to meet the precision target of the future MUonE experiment.