Neutrino Oscillation Constraints on U(1) Models: from Non-Standard Interactions to Long-Range Forces

We quantify the effect of gauge bosons from a weakly coupled lepton flavor dependent $U(1)$ interaction on the matter background in the evolution of solar, atmospheric, reactor and long-baseline accelerator neutrinos in the global analysis of oscillation data. The analysis is performed for interaction lengths ranging from the Sun-Earth distance to effective contact neutrino interactions. We survey $sim 10000$ set of models characterized by the six relevant fermion $U(1)$ charges and find that in all cases, constraints on the coupling and mass of the $Z$ can be derived. We also find that about 5% of the $U(1)$ model charges lead to a viable LMA-D solution but this is only possible in the contact interaction limit. We explicitly quantify the constraints for a variety of models including $U(1)_{B-3L_e}$, $U(1)_{B-3L_mu}$, $U(1)_{B-3L_tau}$, $U(1)_{B-frac{3}{2}(L_mu+L_tau)}$, $U(1)_{L_e-L_mu}$, $U(1)_{L_e-L_tau}$, $U(1)_{L_e-frac{1}{2}(L_mu+L_tau)}$. We compare the constraints imposed by our oscillation analysis with the strongest bounds from fifth force searches, violation of equivalence principle as well as bounds from scattering experiments and white dwarf cooling. Our results show that generically, the oscillation analysis improves over the existing bounds from gravity tests for $Z$ lighter than $sim 10^{-8} to 10^{-11}$ eV depending on the specific couplings. In the contact interaction limit, we find that for most models listed above there are values of $g$ and $M_{Z}$ for which the oscillation analysis provides constraints beyond those imposed by laboratory experiments. Finally we illustrate the range of $Z$ and couplings leading to a viable LMA-D solution for two sets of models.