Revisiting Reactor Anti-Neutrino 5 MeV Bump with $^{13}$C Neutral-Current Interaction

For the first time, we comprehensively examine the potential of a neutral-current interaction of reactor neutrino with $^{13}$C emitting a 3.685 MeV photon to identify the origin of the 5 MeV bump in reactor antineutrino spectra observed through the inverse beta decay (IBD) process. This anomaly may be due to new physics, reactor antineutrino flux inaccuracies, or IBD systematics. The 3.685 MeV photon released during the de-excitation of $^{13}$C$^\ast$ to its ground state is observable in liquid scintillator detectors. Remarkably, we confirm the powerfulness of our proposal by completely ruling out a new physics scenario explaining the bump from the existing NEOS data. We also explore the potential of current and forthcoming experiments, including solar neutrino studies at JUNO, pion and muon decay-at-rest experiments at OscSNS, and isotope decay-at-rest studies at Yemilab, to measure the cross-section precisely enough to distinguish the expected bump and the theoretical flux models via our channel. Additionally, we propose a novel method to track the time evolution of reactor isotopes by analyzing the $^{13}$C signal, which yields critical insights into the contributions of $^{235}$U and $^{239}$Pu to the bump, acting as a robust tool.