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Two-photon exchange corrections in elastic electron-proton scattering

We apply a subtracted dispersion relation (DR) formalism with the aim to improve predictions for the two-photon exchange (TPE) corrections to elastic electron-proton scattering observables at small momentum transfers. We study the formalism on the elastic TPE contribution in comparison with existing data for unpolarized cross sections. We extend the general formalism of TPE to elastic scattering with massive lepton and perform a numerical estimate of the muon-proton scattering at low momentum transfer in view of the upcoming muon-proton scattering experiment (MUSE). We study the influence of the double-virtual Compton scattering (VVCS) subtraction function on the unpolarized lepton-proton scattering cross-section. We show that the resulting TPE correction is negligible in the electron-proton scattering and smaller than planned uncertainties of the MUSE experiment for the subtraction functions evaluated in chiral perturbation theory.