The Two-Photon-Exchange and \gamma Z-Exchange Corrections to parity-Violating Elastic Electron-Proton Scattering

Leading electroweak corrections play an important role in precision measurements of the strange form factors. We calculate the two-photon-exchange (TPE) and $\gamma Z$-exchange corrections to the parity-violating asymmetry of the elastic electron-proton scattering in a simple hadronic model including the finite size of the proton. We find both can reach a few percent and are comparable in size with the current experimental measurements of strange-quark effects in the proton neutral weak current. The effect of $\gamma Z$-exchange is in general larger than that of TPE, especially at low momentum transfer $Q^2\le 1 GeV^2$. Their combined effects on the values of $G^s_E+\beta G^s_M$ extracted in recent experiments can be as large as -40% in certain kinematics.