New Power to Measure Supernova $\nu_e$ with Large Liquid Scintillator Detectors

We examine the prospects for detecting supernova $\nu_e$ in JUNO, RENO-50, LENA, or other approved or proposed large liquid scintillator detectors. The main detection channels for supernova $\nu_e$ in a liquid scintillator are its elastic scattering with electrons and its charged-current interaction with the $^{12}$C nucleus. In existing scintillator detectors, the numbers of events from these interactions are too small to be very useful. However, at the 20-kton scale planned for the new detectors, these channels become powerful tools for probing the $\nu_e$ emission. We find that the $\nu_e$ spectrum can be well measured, to better than $\sim 40\%$ precision for the total energy and better than $\sim 25\%$ precision for the average energy. This is adequate to distinguish even close average energies, e.g., 11 MeV and 14 MeV, which will test the predictions of supernova models. In addition, it will help set constraints on neutrino mixing effects in supernovae by testing non-thermal spectra. Without such large liquid scintillator detectors (or Super-Kamiokande with added gadolinium, which has similar capabilities), supernova $\nu_e$ will be measured poorly, holding back progress on understanding supernovae, neutrinos, and possible new physics.