The OLYMPUS collaboration has recently performed a precise measurement of the positron-proton to electron-proton elastic scattering cross section ratio, $R_{2\gamma}$, over a wide range of the virtual photon polarization, $0.456<\epsilon<0.978$. This provides a direct measure of hard two-photon exchange in elastic lepton-proton scattering widely thought to explain the discrepancy observed between polarized and unpolarized measurements of the proton form factor ratio, $\mu_p G^{p}_{E}/G^{p}_{M}$. The OLYMPUS results are significantly lower than theoretical calculations that explain the observed discrepancy in terms of two-photon exchange but are in good agreement with predictions based on phenomenological fits to the available form factor data.

The motivation for measuring hard two-photon exchange is presented followed by a description of the OLYMPUS experiment and analysis. The important role of soft two-photon contributions from radiative corrections for the analysis is highlighted. Then, the OLYMPUS results are presented and compared with various theoretical calculations. Finally, a comparison between the OLYMPUS and two analogous modern experiments with one of the latest theoretical model is shown.