Electron-induced single-pion production to constrain the neutron structure in $^{40}$Ar. A proof of concept

We study electron-induced single-pion production as a way to constrain the neutron structure of $^{40}$Ar, information that is necessary for neutrino experiments using argon detectors. The proposed experimental signal consists in detecting in coincidence the scattered electron, a proton and a $\pi^-$. We performed simulations compatible with the experimental conditions of the MAMI (University of Mainz) and CLAS (Jefferson Lab) facilities. We have computed cross sections and evaluated the main backgrounds. MAMI is a three-spectrometer system with extremely good energy resolution and small acceptances. We found that, by choosing specific values of the final particle's momenta, the shell structure can be well resolved, with negligible background contributions. CLAS is a large solid angle detector with poorer energy resolution. In both cases, the background can be kept under control by performing cuts in missing energy and missing momentum; however, in CLAS, the shell structure cannot be resolved due to the energy resolution. We conclude that MAMI is particularly appropriate for the proposed experiment, whereas CLAS is better suited for other studies.