Two photon exchange with nuclei from $e^{+}$/$e^{-}$ elastic cross section ratios

Hadronic box diagrams pose a significant source of radiative corrections to lepton scattering and $\beta$-decay measurements, yet their calculation remains highly model-dependent. Two-photon exchange is a box diagram generally relevant to most lepton scattering experiments, and is directly detectable via multiple observables. Single-spin asymmetries (SSA) are sensitive to the imaginary part of the TPE amplitude, while the ratio of $e^{+}$/$e^{-}$ elastic scattering cross sections is sensitive to the real part of the TPE amplitude. While SSA measurements have been reported for several complex nuclei, measurements of the $e^{+}$/$e^{-}$ ratio exist only for the proton. Proposed here is a measurement of the $e^{+}$/$e^{-}$ ratio on ${}^4$He, a feasible nuclear target for which the ratio's deviation from unity due to TPE is expected to be on order of 1-2%. Choosing a low Z nucleus minimizes Coulomb distortions, which could greatly overwhelm TPE for heavier nuclei. The proposed 19-day program, including measurements at three kinematic settings between 0.3 < Q${}^2$< 0.4 GeV${}^2$, would be made possible by the addition of a positron source at Jefferson Lab.