We use the world's data on elastic electron-proton scattering and calculations of two-photon exchange effects to extract corrected values of the proton's electric and magnetic form factors over the full $Q^2$ range of the existing data. Our analysis combines the corrected Rosenbluth cross section and polarization transfer data, and is the first extraction of $G_E$ and $G_M$ including explicit two-photon exchange corrections and their associated uncertainties. In addition, we examine the angular dependence of the corrected cross sections to examine the possible nonlinearities of the cross section as a function of ɛ.

Two-photon exchange contributions to elastic electron-proton scattering cross sections are evaluated in a simple hadronic model including the finite size of the proton. The corrections are found to be small in magnitude, but with a strong angular dependence at fixed $Q^2$. This is significant for the Rosenbluth technique for determining the ratio of the electric and magnetic form factors of the proton at high $Q^2$, and partly reconciles the apparent discrepancy with the results of the polarization transfer technique.

A detailed study of two-photon exchange in unpolarized and polarized elastic electron-nucleon scattering is presented, taking particular account of nucleon finite size effects. Contributions from nucleon elastic intermediate states are found to have a strong angular dependence, which leads to a partial resolution of the discrepancy between the Rosenbluth and polarization transfer measurements of the proton electric to magnetic form factor ratio, $G_E/G_M$. The two-photon exchange contribution to the longitudinal polarization transfer $P_L$ is small, whereas the contribution to the transverse polarization transfer $P_T$ is enhanced at backward angles by several percent, increasing with $Q^2$. This gives rise to a small, $\lesssim 3\%$ suppression of $G_E/G_M$ obtained from the polarization transfer ratio $P_T/P_L$ at large $Q^2$. We also compare the two-photon exchange effects with data on the ratio of $e^{+}p$ to $e^{-}p$ cross sections, which is predicted to be enhanced at backward angles. Finally, we evaluate the corrections to the form factors of the neutron and estimate the elastic intermediate state contribution to the ${}^3\mathrm{He}$ form factors.

An extensive theoretical analysis of off-forward parton distributions (OFPDs) is presented. The OFPDs and the form factors of the quark energy-momentum tensor are estimated at a low energy scale using a bag model. Relations among the second moments of OFPDs, the form factors, and the fraction of the nucleon spin carried by quarks are discussed.