Getting the Most from Detection of Galactic Supernova Neutrinos in Future Large Liquid-Scintillator Detectors

Future large liquid-scintillator detectors can be implemented to observe neutrinos from a core-collapse supernova (SN) in our galaxy in various reaction channels: (1) The inverse beta decay $\overline{\nu}^{}_e + p \to n + e^+$; (2) The elastic neutrino-proton scattering $\nu + p \to \nu + p$; (3) The elastic neutrino-electron scattering $\nu + e^- \to \nu + e^-$; (4) The charged-current $\nu^{}_e$ interaction $\nu^{}_e + {^{12}}{\rm C} \to e^- + {^{12}}{\rm N}$; (5) The charged-current $\overline{\nu}^{}_e$ interaction $\overline{\nu}^{}_e + {^{12}}{\rm C} \to e^+ + {^{12}}{\rm B}$; (6) The neutral-current interaction $\nu + {^{12}}{\rm C} \to \nu + {^{12}}{\rm C}^*$. The less abundant $^{13}{\rm C}$ atoms in the liquid scintillator are also considered as a target, and both the charged-current interaction $\nu^{}_e + {^{13}}{\rm C} \to e^- + {^{13}}{\rm N}$ and the neutral-current interaction $\nu + {^{13}}{\rm C} \to \nu + {^{13}}{\rm C}^*$ are taken into account. In this work, we show for the first time that a global analysis of all these channels at a single {liquid-}scintillator detector, such as Jiangmen Underground Neutrino Observatory (JUNO), is very important to test the average-energy hierarchy of SN neutrinos and how the total energy is partitioned among neutrino flavors. In addition, the dominant channels for reconstructing neutrino spectra and the impact of other channels are discussed in great detail.