Improved extraction of two-photon exchange amplitudes from elastic electron-proton scattering cross section data up to Q2=5.20 (GeV/ c)2

In this work, we improve on and extend to low- and high-Q2 values the extractions of the two-photon-exchange (TPE) amplitudes and the ratio Pl/PlBorn(ϵ,Q2) using world data on electron-proton elastic scattering cross section σR(ϵ,Q2) with an emphasis on data covering the high-momentum region, up to Q2=5.20(GeV/c)2, to better constrain the TPE amplitudes in this region. We provide a new parametrization of the TPE amplitudes, along with an estimate of the fit uncertainties. We compare the results to several previous phenomenological extractions and hadronic TPE predictions. We use the new parametrization of the TPE amplitudes to extract the ratio Pl/PlBorn(ϵ,Q2), and then compare the results to previous extractions, several theoretical calculations, and direct measurements at Q2=2.50(GeV/c)2.