$\Delta(1232)$ Resonance Contribution to Two-Photon Exchange in Electron-Proton Scattering Revisited

We revisit the question of the contributions of the two-photon exchange with \(\Delta (1232)\) excitation to the electron-proton scattering in a hadronic model. Three improvements over the previous calculations are made, namely, correct vertex function for \( \gamma N\rightarrow\Delta\), realistic \( \gamma N\Delta\) form factors, and coupling constants. The discrepancy between the values of \( R\equiv \mu_{p} G_{E}/G_{M}\) extracted from Rosenbluth technique and polarization transfer method can be reasonably accounted for if the data of Andivahis et al. (Phys. Rev. D 50, 5491 (1994)) are analyzed. However, substantial discrepancy remains if the data of Qattan et al. (nucl-ex/0610006) are used. For the ratio \( R^{\pm}\) between \( e^{\pm} p\) scatterings, our predictions appear to be in satisfactory agreement with the preliminary data from VEPP-3. The agreement between our model predictions and the recent measurements on single spin asymmetry, transverse and longitudinal recoil proton polarizations ranges from good to poor.