High precision measurements of the proton elastic electromagnetic form factors and their ratio at Q² = 0.50, 2.64, 3.20, and 4.10 GeV²

Background: 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, G_Ep/G_Mp. However, high-Q² measurements of this ratio yielded significant disagreement with extractions based on unpolarized scattering measurements, raising questions about the reliability of the measurements and consistency of the techniques. Purpose: Jefferson Lab experiment E01-001 was designed to provide a high precision extraction of G_Ep/G_Mp from unpolarized cross-section measurements using a modified version of the Rosenbluth separation technique to allow for a more precise comparison with polarization data. Method: Rosenbluth separations involve precise measurements of the angular dependence of the elastic e-p cross section at fixed momentum transfer, Q². Conventional Rosenbluth separations detect the scattered electron, requiring the 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 elastic e-p cross section. This yielded a fixed momentum for the detected particle and dramatically reduced variation of the cross section with angle, significantly reducing rate- and momentum-dependent corrections and uncertainties. Results: We measure the cross section vs angle with high relative precision, allowing for extremely high precision extractions of G_Ep/G_Mp at Q² = 2.64, 3.20, and 4.10 GeV². Our results are consistent with traditional Rosenbluth extractions, but with much smaller corrections and systematic uncertainties, comparable to the uncertainties from polarization measurements. Conclusions: 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 those 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.