Electron-to-Muon Forward Annihilation at High Energy

Abstract

We study the high-energy behavior of electron-to-muon annihilation in forward kinematics in QED with two massive lepton species. Using effective field theory renormalization group techniques we derive the all-order asymptotic behavior of the annihilation amplitude through the next-to-leading logarithmic approximation. Furthermore, we consider one- and two-loop fixed-order corrections to the forward-annihilation amplitude in the high-energy limit, which we compute up to power corrections. The goal of this paper is to elaborate on various technical details that we omitted in the original presentation of our results in arXiv:2510.04914.