Scalar non-standard neutrino interactions in Galactic supernovae

We analyze the prospects for studying scalar non-standard interactions (SNSI) using the neutrino burst from a Galactic supernova. SNSI modify the resonant flavor conversion and, correspondingly, the neutronization burst signal, and may be identifiable in future multi-tonne-scale experiments such as DUNE. We show that, in the presence of SNSI, neutrinos propagating out of the dense supernova environment acquire a density-squared-dependent contribution to their mass-squared differences, which in turn modifies the energy levels of the neutrino mass eigenstates. This phenomenon is not present in less dense environments like the Earth or the Sun. For a given mass ordering, supernova neutrinos can improve the sensitivity to SNSI parameters by up to four orders of magnitude compared to that achievable with solar or terrestrial neutrino sources.