We present new precision measurements of the elastic electron-proton scattering cross section for momentum transfer ($Q^2$) up to $15.75(\mathrm{GeV}/c{)}^2$. 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 or 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 $8(\mathrm{GeV}/c{)}^2$ 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 $Q^2$.

• Received 22 March 2021
• Revised 6 November 2021
• Accepted 31 January 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.102002