Form Factors and Two-Photon Exchange in High-Energy Elastic Electron-Proton Scattering

We present new precision measurements of the elastic electron-proton scattering cross section for momentum transfer (Q${}^2$) up to 15.75~\gevsq. Combined with existing data, these provide an improved extraction of the proton magnetic form factor at high Q${}^2$ and double the range over which a longitudinal/transverse separation of the cross section can be performed. The difference between our results and polarization data agrees with that observed at lower Q${}^2$ and attributed to hard two-photon exchange (TPE) effects, extending to 8~(GeV/c)${}^2$ the range of Q${}^2$ for which a discrepancy is established at $>$95% confidence. We use the discrepancy to quantify the size of TPE contributions needed to explain the cross section at high Q${}^2$.