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

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.