Impact of cross-section uncertainties on supernova neutrino spectral parameter fitting in the Deep Underground Neutrino Experiment

A primary goal of the upcoming Deep Underground Neutrino Experiment (DUNE) is to measure the $O\left(10\right)\text{}\text{}\mathrm{MeV}$ neutrinos produced by a Galactic core-collapse supernova if one should occur during the lifetime of the experiment. The liquid-argon-based detectors planned for DUNE are expected to be uniquely sensitive to the ${\nu }_{e}$ component of the supernova flux, enabling a wide variety of physics and astrophysics measurements. A key requirement for a correct interpretation of these measurements is a good understanding of the energy-dependent total cross section $\sigma \left({E}_{\nu }\right)$ for charged-current ${\nu }_{e}$ absorption on argon. In the context of a simulated extraction of supernova ${\nu }_{e}$ spectral parameters from a toy analysis, we investigate the impact of $\sigma \left({E}_{\nu }\right)$ modeling uncertainties on DUNE's supernova neutrino physics sensitivity for the first time. We find that the currently large theoretical uncertainties on $\sigma \left({E}_{\nu }\right)$ must be substantially reduced before the ${\nu }_{e}$ flux parameters can be extracted reliably; in the absence of external constraints, a measurement of the integrated neutrino luminosity with less than 10% bias with DUNE requires $\sigma \left({E}_{\nu }\right)$ to be known to about 5%. The neutrino spectral shape parameters can be known to better than 10% for a 20% uncertainty on the cross-section scale, although they will be sensitive to uncertainties on the shape of $\sigma \left({E}_{\nu }\right)$. A direct measurement of low-energy ${\nu }_{e}$-argon scattering would be invaluable for improving the theoretical precision to the needed level.