Two-boson exchange corrections to parity-violating elastic electron-proton scattering

Abstract

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