High $Q^2$ electron-proton elastic scattering at the future Electron-Ion Collider

Unpolarized electron-proton elastic scattering cross-section measurements at high $Q^2$ allow for improved extractions of the proton electromagnetic form factors as well as provide constraints on possible hard two-photon exchange effects. We present a detailed study of the feasibility of making these high $Q^2$ e-p elastic measurements at the future Electron-Ion Collider (EIC). The results show that e-p elastic cross sections can be obtained in the momentum transfer range of $6~(GeV/c)^2 < Q^2 < 40~(GeV/c)^2$, which would be the highest-ever $Q^2$ values measured. These data will all be at virtual photon polarizations close to unity, $\epsilon \sim 1$.