Accessing the Elastic Form-Factors of the $\Delta(1232)$ Using the Beam-Normal Asymmetry

Abstract

The beam-normal single-spin asymmetry, $B_n$, exists in the scattering of high energy electrons, polarized transverse to their direction of motion, from nuclear targets. To first order, this asymmetry is caused by the interference of the one-photon exchange amplitude with the imaginary part of the two-photon exchange amplitude. Measurements of $B_n$, for the production of a $\Delta(1232)$ resonance from a proton target, will soon become available from the Qweak experiment at Jefferson Lab and the A4 experiment at Mainz. The imaginary part of two-photon exchange allows only intermediate states that are on-shell, including the $\Delta$ itself. Therefore such data is sensitive to $\gamma\Delta\Delta$, the elastic form-factors of the $\Delta$. This article will introduce the form-factors of the $\Delta$, discuss what might be learned about the elastic form-factors from these new data, describe ongoing efforts in calculation and measurement, and outline the possibility of future measurements.