  The effects of multi-photon-exchange and other higher-order QED corrections
on elastic electron-proton scattering have been a subject of high experimental
and theoretical interest since the polarization transfer measurements of the
proton electromagnetic form factor ratio $G_E^p/G_M^p$ at large momentum
transfer $Q^2$ conclusively established the strong decrease of this ratio with
$Q^2$ for $Q^2 \gtrsim 1$ GeV$^2$. This result is incompatible with previous
extractions of this quantity from cross section measurements using the
Rosenbluth Separation technique. Much experimental attention has been focused
on extracting the two-photon exchange (TPE) effect through the unpolarized
$e^+p/e^-p$ cross section ratio, but polarization transfer in polarized elastic
scattering can also reveal evidence of hard two-photon exchange. Furthermore,
it has a different sensitivity to the generalized TPE form factors, meaning
that measurements provide new information that cannot be gleaned from
unpolarized scattering alone. Both $\epsilon$-dependence of polarization
transfer at fixed $Q^2$, and deviations between electron-proton and
positron-proton scattering are key signatures of hard TPE. A polarized positron
beam at Jefferson Lab would present a unique opportunity to make the first
measurement of positron polarization transfer, and comparison with
electron-scattering data would place valuable constraints on hard TPE. Here, we
propose a measurement program in Hall A that combines the Super BigBite
Spectrometer for measuring recoil proton polarization, with a non-magnetic
calorimetric detector for triggering on elastically scattered positrons. Though
the reduced beam current of the positron beam will restrict the kinematic
reach, this measurement will have very small systematic uncertainties, making
it a clean probe of TPE.
