Time-of-Flight Constraints on Neutrino Millicharge from Supernova Neutrinos in Galactic Magnetic Fields

Abstract

A millicharged neutrino propagating through magnetic fields experiences a small Lorentz-force deflection, which induces a geometric time delay. In the ultra-relativistic regime relevant for supernova neutrinos, this delay scales as $q_\nu^2 E_\nu^{-2}$, where $q_\nu$ and $E_\nu$ denote the neutrino millicharge and energy, respectively, and thus shares the same leading energy dependence as the standard time-of-flight delay induced by neutrino mass. Motivated by this similarity, we propose a framework to reinterpret supernova time-of-flight limits on neutrino mass as constraints on neutrino millicharge. We express both effects in terms of a common $E_\nu^{-2}$ dispersion coefficient and compute the millicharge-induced contribution using a line-of-sight-dependent magnetic delay kernel, extending the original SN1987A uniform-field estimate. Applying this translation to existing SN1987A limits and to projected sensitivities for future Galactic core-collapse supernova observations, we obtain bounds ranging from the $\sim 10^{-17}\, e$ level for SN1987A to the low-$10^{-19}\, e$ regime for next-generation Galactic bursts, with optimistic combinations of detector sensitivity and Galactic sightline approaching $\sim 10^{-20}\, e$. We compare these results with other bounds in the literature and discuss how nonzero neutrino mass affects the interpretation.