Agradecimentos: We are grateful to Andre de Gouvea for an illuminating discussion and email correspondence. We also thank Pedro A. N. Machado and Manibrata Sen for useful discussions. We wish to acknowledge the Center for Theoretical Underground Physics and Related Areas (CETUP*) and the Institute for Underground Science at SURF for hospitality and for providing a stimulating environment. The work of YP was supported by the Sao Paulo Research Foundation (FAPESP) Grant No. 2023/10734-3 and 2023/01467-1 and by the National Council for Scientific and Technological Development (CNPq) Grant No. 151168/2023-7.S.J. thanks Centro de Ciencias Naturais e Humanas at Universidade Federal do ABC and ICTP South American Institute for Fundamental Research for their warm hospitality during the completion of this work.r S.J. thanks Centro de Ciencias Naturais e Humanas at Universidade Federal do ABC and ICTP South American Institute for Fundamental Research for their warm hospitality during the completion of this work Ver menos

Abstract: We show that non-standard neutrino interactions (NSI) can notably modify the pattern of resonant flavor conversion of neutrinos within supernovae and significantly impact the neutronization burst signal in forthcoming experiments such as the Deep Underground Neutrino Experiment (DUNE). The presence of NSI can invert the energy levels of neutrino matter eigenstates and even induce a new resonance in the inner parts close to the protoneutron star. We demonstrate how DUNE can use these new configurations of energy levels to have sensitivity to NSIs down to O(0.1). We also elucidate how the effect may result in a puzzling confusion of normal and inverted mass orderings by highlighting the emergence or vanishing of the neutronization peak, which distinguishes between the two mass orderings. Potential implications are analyzed thoroughly Ver menos