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 $\mathcal{O}(10)$ 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 $ν_e$ 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 $σ(E_ν)$ for charged-current $ν_e$ absorption on argon. In the context of a simulated extraction of supernova $ν_e$ spectral parameters from a toy analysis, we investigate the impact of $σ(E_ν)$ modeling uncertainties on DUNE's supernova neutrino physics sensitivity for the first time. We find that the currently large theoretical uncertainties on $σ(E_ν)$ must be substantially reduced before the $ν_e$ 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 $σ(E_ν)$ 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 $σ(E_ν)$. A direct measurement of low-energy $ν_e$-argon scattering would be invaluable for improving the theoretical precision to the needed level.