On the two-boson exchange corrections to parity-violating elastic electron-proton scattering

The details of the calculation of the two-boson exchange effects in the parity-violating elastic $ep$ scattering within a simple hadronic model, including both the nucleon and $\Delta(1232)$-resonance intermediate states, are presented. We examine the sensitivity of our results with respect to choice of form factors. We emphasize the importance to use correct relations relating N to $\Delta$ and $\Delta$ to N transition vertex functions. The $N\Delta$ Coulomb quadrupole transition is found to play important role at higher $Q^2\geq 3.0$ GeV$^2$. We also elucidate the relation between our results and the well-known result on the $\gamma ZE$ effect given by Marciano and Sirlin (MS). The effect of the nucleon contribution $\delta_N$ to parity-asymmetry $A_{PV}$, is found to be in general, larger than the corresponding $\Delta$ contribution $\delta_\Delta$ except at extreme forward angles. The corrections to the extracted values of the strange form factors $G^{s}_{E}+\beta G^{s}_{M}$ from the HAPPEX, A4, and G0 data are also presented. The total TBE corrections to the extracted values of $G^{s}_{E}+\beta G^{s}_{M}$ in recent experiments of HAPPEX G0, and A4 are, depending on kinematics, found to be small except in a few cases where they range from -20.6% to $48.3$.