High precision measurements of the proton elastic electromagnetic form factors and their ratio at $Q^2$ = 0.50, 2.64, 3.20, and 4.10 GeV$^2$

The advent of high-intensity, high-polarization electron beams led to significantly improved measurements of the ratio of the proton's charge to electric form factors, GEp/GMp. However, high-$Q^2$ measurements yielded significant disagreement with extractions based on unpolarized scattering, raising questions about the reliability of the measurements and consistency of the techniques. Jefferson Lab experiment E01-001 was designed to provide a high-precision extraction of GEp/GMp from unpolarized cross section measurements using a modified version of the Rosenbluth technique to allow for a more precise comparison with polarization data. Conventional Rosenbluth separations detect the scattered electron which requires comparisons of measurements with very different detected electron energy and rate for electrons at different angles. Our Super-Rosenbluth measurement detected the struck proton, rather than the scattered electron, to extract the cross section. This yielded a fixed momentum for the detected particle and dramatically reduced cross section variation, reducing rate- and momentum-dependent corrections and uncertainties. We measure the cross section vs angle with high relative precision, allowing for extremely precise extractions of GEp/GMp at $Q^2$ = 2.64, 3.20, and 4.10 GeV$^2$. Our results are consistent with traditional extractions but with much smaller corrections and systematic uncertainties, comparable to the uncertainties from polarization measurements. Our data confirm the discrepancy between Rosenbluth and polarization extractions of the proton form factor ratio using an improved Rosenbluth extraction that yields smaller and less-correlated uncertainties than typical of previous Rosenbluth extractions. We compare our results to calculations of two-photon exchange effects and find that the observed discrepancy can be relatively well explained by such effects.