Two-photon-exchange effects in the electro-excitation of the $\Delta$ resonance

Abstract

We evaluate the two-photon exchange contribution to the $eN\to e\Delta (1232)\to e\pi N$ process at large momentum transfer with the aim of a precision study of the ratios of electric quadrupole (E2) and Coulomb quadrupole (C2) to the magnetic dipole (M1) ${\gamma }^{\ast }N\Delta$ 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.

Comments: 4 pages, 4 figures