We examine the two-photon exchange contribution to the $eN\to e\Delta (1232)\to e\pi N$ process with the aim of a precision study of the ratios of electric quadrupole $(E2)$ and Coulomb quadrupole $(C2)$ to the magnetic dipole $(M1)$ ${\gamma }^{*}N\Delta$ transitions. We relate the two-photon exchange amplitude to the $N\to \Delta$ generalized parton distributions and obtain a quantitative estimate of the two-photon effects. The two-photon exchange corrections to the $C2/M1$ ratio depend strongly on whether this quantity is obtained from an interference cross section or from the Rosenbluth-type cross sections, in similarity with the elastic, $eN\to eN$, process.

• Received 6 September 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.012301