Supernova Bursts as a Probe of Neutrino Nature via $CEνNS$ Coherent Scattering

Abstract: The Resonant Spin-Flavor Precession (RSFP) of core-collapse supernova neutrinos within the framework of the quantum density matrix formalism is studied. The cooling duration of SN1987A severely constraints standard RSFP models for Dirac Neutrinos. Using the properties of the outer stellar envelope where resonant conversion could occur after thermal decoupling, we show that for neutrino magnetic moments in the range $μ_ν\sim 10^{-14} - 10^{-12} μ_B$, adiabatic conversion in the envelope ($R > 1000$ km) leads to macroscopic helicity inversion without violating cooling bounds.This RSFP neutrino helicity change induces different signatures for Dirac or Majorana neutrinos in Coherent Elastic Neutrino-Nucleus Scattering (CE$ν$NS) detectors. For Dirac neutrino, a massive flux deficit for Dirac neutrinos due to sterile conversion should be seen. For Majorana neutrinos, the flux will not change but a modification to its spectral decomposition of the cross section should be seen due to the transition from left-handed electron neutrinos to right-handed $μ$ or $τ$ anti-neutrinos. An experimental strategy is proposed to minimize the astrophysical uncertainties using the high-energy neutrino tail ($E \approx 1$ GeV) which evades RSFP to normalize the signal. This ratio-based approach effectively cancels astrophysical uncertainties, allowing future detectors to distinguish the fundamental nature of the neutrino and probe magnetic moments down to $10^{-14} μ_B$, two orders of magnitude beyond current solar limits.