Reexamination of phenomenological two-photon exchange corrections to the proton form factors and e+-p scattering

We extract the two-photon exchange (TPE) contributions to electron--proton elastic scattering using two parametrizations and compare the results to different phenomenological extractions and direct calculations of the TPE effects. We find that many of the extractions give similar results, and highlight the common assumptions and the impact of not including such assumptions. We provide a simple parametrization of the TPE contribution to the unpolarized cross section, along with an estimate of the fit uncertainties and the uncertainties associated with the assumptions made in the extraction. We look at the contributions as extracted from various e--p elastic scattering observables, and make predictions for ratio $R^{e^{+} e^{-}}$ of positron-proton to electron-proton elastic scattering cross sections.