Constraints on New Neutrino Interactions via Light Abelian Vector Bosons

We calculate new constraints on extra neutrino interactions via light Abelian vector bosons, where the boson mass arises from Stuckelberg mechanism. We use the requirement that $Z$, $W$, and kaon decays, as well as electron-neutrino scattering, are not altered by the new interactions beyond what is allowed by experimental uncertainties. These constraints are strong and apply to neutrinophilic dark matter, where interactions of neutrinos and dark matter via a new gauge boson are important. In particular, we show that models where neutrino interactions are needed to solve the small-scale structure problems in the $\Lambda$CDM cosmology are constrained.