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 kpc in the Milky Way, its (nu) over bar (e) spectrum can be precisely determined from the inverse beta-decay process (nu) over bar (e) + p -> e(+) + n, for which a 20 kiloton liquid-scintillator detector with the resolution similar to the Jiangmen Underground Neutrino Observatory may register more than 5000 events. We have to rely predominantly on the elastic neutrino-electron scattering nu + e(-) -> nu + e(-) and the elastic neutrino-proton scattering nu + p -> 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.