NNLO QED corrections and inelastic two-photon exchange in elastic lepton-proton scattering with McMule

Abstract

We supplement McMule, a Monte Carlo framework that provides QED corrections up to next-to-next-to-leading order (NNLO) in the fine structure constant $\alpha$, with the inelastic two-photon exchange (TPE) contribution, based on the data-driven dispersive calculation of Tomalak, Pasquini and Vanderhaeghen, which we extend to the $Q^2\to 0$ limit that enables applications in the low-$Q^2$ region relevant for upcoming low-energy experiments. We present results for two experimental settings: the future MAGIX@MESA experiment and the ISR@MAMI measurement. For MAGIX@MESA kinematics, the inelastic TPE is small, comparable to the proton-side NLO corrections and subdominant to both the leptonic radiative corrections and the full NNLO QED corrections once a 1 MeV photon-energy cut is applied. For the ISR@MAMI kinematics, NNLO QED corrections modify the radiative tail below the elastic peak at the 10% level.

10 pages, 5 figures, accepted in the proceedings of the International Workshop on Low Energy Electron Positron Physics at Jefferson Lab (LEEPP2026), Jefferson Lab, 23-27 March 2026