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We quantify the effect of gauge bosons from a weakly coupled lepton flavordependent $U(1)'$ interaction on the matter background in the evolution ofsolar, atmospheric, reactor and long-baseline accelerator neutrinos in theglobal analysis of oscillation data. The analysis is performed for interactionlengths ranging from the Sun-Earth distance to effective contact neutrinointeractions. We survey $\sim 10000$ set of models characterized by the sixrelevant fermion $U(1)'$ charges and find that in all cases, constraints on thecoupling 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 possiblein the contact interaction limit. We explicitly quantify the constraints for avariety 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 theconstraints imposed by our oscillation analysis with the strongest bounds fromfifth force searches, violation of equivalence principle as well as bounds fromscattering experiments and white dwarf cooling. Our results show thatgenerically, the oscillation analysis improves over the existing bounds fromgravity tests for $Z'$ lighter than $\sim 10^{-8} \to 10^{-11}$ eV depending onthe specific couplings. In the contact interaction limit, we find that for mostmodels listed above there are values of $g'$ and $M_{Z'}$ for which theoscillation analysis provides constraints beyond those imposed by laboratoryexperiments. Finally we illustrate the range of $Z'$ and couplings leading to aviable LMA-D solution for two sets of models.

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