How Charged Can Neutrinos Be?

Abstract

We investigate how neutrinos may acquire small electric charges within the Standard Model framework while preserving electromagnetic gauge invariance. Instead of gauging the standard hypercharge generator $Y$, a linear combination of $Y$ and a new generator $X$ from a gaugable global $U(1)_X$ symmetry is embedded, under which neutrinos transform non-trivially. We demonstrate that minimal scenarios based on flavor-dependent $U(1)_X$ symmetries, such as $X = L_\alpha - L_\beta$, are incompatible with current neutrino oscillation data. In contrast, we have shown that only flavor-universal $U(1)_X$ symmetries-such as $U(1)_{B-L}$, which shifts both quark and lepton charges, and $U(1)_L$, which modifies only the lepton sector-can generate tiny neutrino charges consistent with observed masses and mixing. We also discuss the necessary connection between such charges and the Dirac nature of neutrinos. By analyzing the phenomenological implications in detail, our findings emphasize that constraints on neutrino charges should be evaluated within the specific framework of the $U(1)_X$ symmetry under consideration, rather than assuming a generic approach, as is often the case.