  Two-photon exchange and the larger class of hadronic box diagrams are
difficult to calculate without a large degree of model-dependence. At the same
time, these processes are significant radiative corrections in parity-violating
electron scattering, in neutron decay, and may even be responsible for the
proton's form factor ratio discrepancy. New kinds of experimental data are
needed to help constrain models and guide future box-diagram calculations. The
target-normal single spin asymmetry, $A_n$, formed with an unpolarized beam
scattering from a target that is polarized normal to the scattering plane, is
sensitive to the imaginary part of the two-photon exchange amplitude, and can
provide a valuable constraint. A measurement with both electrons and positrons
can reduce sources of experimental error, and distinguish between the effects
of two-photon exchange and those of time-reversal symmetry violation. This
article describes a proposed experiment in Hall A, using the new Super Big-Bite
Spectrometer that can cover a momentum transfer range in the critical zone of
uncertainty between where hadronic calculations and those based on partonic
degrees of freedom are expected to be accurate.
