Radiative corrections to elastic lepton-proton scattering with focus on two-photon-exchange diagrams

Lepton (electron and muon) scattering experiments are excellent tools to gain insight into the nucleon structure. Elastic electron-proton scattering probes the spatial distribution of charge and magnetization inside the proton, and comparing electron-proton and muon-proton scattering data tests lepton universality. The availability of a plethora of scattering data with increased precision and observed discrepancies such as the proton form factor puzzle and the proton radius puzzle motivated a renewed effort to improve the theoretical framework. Realizing that the one-photon-exchange approximation (OPE), i.e. the Born approximation, is not sufficient, radiative corrections in QED, especially the two-photon-exchange (TPE) diagrams, are under investigation. The TPE diagrams are of special interest among the radiative corrections, since they depend on the proton structure. In this work, we present a complete calculation of QED radiative corrections to elastic electron-proton and muon-proton scattering at next-to-leading order, taking into account loop-momentum-dependent form factors. In the discussion of their numerical impact on lepton-proton scattering cross sections, we pay special attention to the TPE diagrams and compare them with existing theoretical predictions and lepton-proton scattering data.