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

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 $10\mathrm{k}\mathrm{p}\mathrm{c}$ in the Milky Way, its ${\bar{\nu }}_e^{}$ spectrum can be precisely determined from the inverse beta-decay process ${\bar{\nu }}_e^{}+p\to e^{+}+n$, for which a $20\mathrm{k}\mathrm{i}\mathrm{l}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{n}$ 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 $\nu + e^- \to \nu + e^-$andtheelasticneutrino-protonscattering$\nu + p \to \nu

• p$forthespectraof$\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.