Nuclear de-excitations in low-energy charged-current $\nu_e$ scattering on $^{40}$Ar

Background: Large argon-based neutrino detectors, such as those planned for the Deep Underground Neutrino Experiment, have the potential to provide unique sensitivity to low-energy (few to tens of MeV) electron neutrinos produced by core-collapse supernovae. Despite their importance for neutrino energy reconstruction, nuclear de-excitations following charged-current $\nu_e$ absorption on $^{40}$Ar have never been studied in detail at supernova energies. Purpose: I develop a model of nuclear de-excitations that occur following the $^{40}\mathrm{Ar}(\nu_e,e^{-})^{40}\mathrm{K}^*$ reaction. This model is applied to the calculation of exclusive cross sections. Methods: A simple expression for the inclusive differential cross section is derived under the allowed approximation. Nuclear de-excitations are described using a combination of measured $\gamma$-ray decay schemes and the Hauser-Feshbach statistical model. All calculations are carried out using a novel Monte Carlo event generator called MARLEY (Model of Argon Reaction Low Energy Yields). Results: Various total and differential cross sections are presented. Two de-excitation modes, one involving only $\gamma$-rays and the other including single neutron emission, are found to be dominant at few tens-of-MeV energies. Conclusions: Nuclear de-excitations have a strong impact on the achievable energy resolution for supernova $\nu_e$ detection in liquid argon. Tagging events involving neutron emission, though difficult, could substantially improve energy reconstruction. Given a suitable calculation of the inclusive cross section, the MARLEY nuclear de-excitation model may readily be applied to other scattering processes.