Electron scattering is a powerful tool for studying hadron and nuclear structure. In particular, one‑photon (OPE) and two‑photon exchange (TPE) mechanisms play an important role in the scattering of electrons on nuclei. The OPE mechanism is the dominant interaction, while the TPE is a small but sometimes critical contribution. In terms of the state of the art, the OPE has been well measured and is well understood but the TPE is not.
A simple but extremely powerful tool that experimentalists can use to refine our knowledge of the TPE mechanism is “single-proton knockout” which, as the name implies, involves knocking one and only one proton out of a target nucleus without interacting with the rest of the nucleus or creating new particles. Single-proton knockout is used to study the momentum distributions of protons in the nucleus. To make precision measurements of these distributions, the elastic electron-proton interaction must be well understood. This means having a precise knowledge of the proton electromagnetic form factors which encode the spatial distribution of charge and magnetization of the proton and, ultimately, determine the e-p elastic scattering cross section .
With the completion of the 12-GeV upgrade at JLab, a new generation of precision nuclear structure measurements have been performed that are capable of exploring new kinematic regions. JLab E12-07-108 was one of the first experiments after the completion of the upgrade, and the experiment made an extensive set of precision elastic e-p scattering measurements for momentum transfers from 2 to 16 GeV2. These data provide an improved understanding of the proton form factors and electromagnetic structure, the input needed for new proton knockout measurements, and strong experimental constraints on the impact of higher-order two-photon exchange (TPE) corrections in high-energy electron scattering. See Figure 1.
To effectively extract the elusive TPE contributions from other effects in the data, the team examined the impact of improved radiative corrections that go beyond the OPE. They found that these improved procedures reduced the discrepancy associated with TPE corrections in prior measurements by one-third but still require TPE contributions with a 4% angular dependence for Q2 from 6 to 16 GeV2 . See Figure 2.
 “Review of two-photon exchange in electron scattering,” J. Arrington, P. G. Blunden, W. Melnitchouk, Prog. Part. Nucl. Phys. 66 (2011) 782
 “Form factors and two-photon exchange in high-energy elastic electron-proton scattering,” M. E. Christy, et al., Phys. Rev. Lett. 128 (2022) 102002.