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

We revisit the question of the contributions of two-photon exchange with $\mathrm{\Delta }(1232)$ excitation to the electron-proton scattering in a hadronic model. Three improvements over the previous calculations are made, namely, correct vertex function for $\gamma N\to \mathrm{\Delta }$, realistic $\gamma N\Delta$ form factors, and coupling constants. The discrepancy between the values of $R\equiv {\mu }_p{G}_E\mathrm{/}{G}_M$ extracted from Rosenbluth technique and polarization transfer method can be reasonably accounted for if the data of Andivahis {\it et al.} \cite{Andivahis94} are analyzed. However, substantial discrepancy remains if the data of Qattan {\it et al.} \cite{Qattan05} 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.