Towards a complete reconstruction of supernova neutrino spectra in future large liquid-scintillator detectors

Abstract

In this paper, we show how to carry out a relatively more realistic and complete reconstruction of supernova neutrino spectra in the future large liquid-scintillator detectors, by implementing the method of singular value decomposition with a proper regularization. For a core-collapse supernova at a distance of $10\mathrm{kpc}$ in the Milky Way, its ${\overline{\nu }}_e^{}$ spectrum can be precisely determined from the inverse beta-decay process ${\overline{\nu }}_e^{}+p\to e^{+}+n$, for which a $20\mathrm{kiloton}$ liquid-scintillator detector with the resolution similar to the Jiangmen Underground Neutrino Observatory (JUNO) may register more than 5000 events. We have to rely predominantly on the elastic neutrino-electron scattering $\nu +e^{-}\to \nu +e^{-}$ and the elastic neutrino-proton scattering $\nu +p\to \nu +p$ for the spectra of ${\nu }_e^{}$ and ${\nu }_x^{}$, where $\nu$ denotes collectively neutrinos and antineutrinos of all three flavors and ${\nu }_x^{}$ for ${\nu }_{\mu }^{}$ and ${\nu }_{\tau }^{}$ as well as their antiparticles. To demonstrate the validity of our approach, we also attempt to reconstruct the neutrino spectra by using the time-integrated neutrino data from the latest numerical simulations of delayed neutrino-driven supernova explosions.

Comments: 26 pages, 6 figures, more discussions, final version in PRD