  The possibility of explaining the current value of the muon anomalous
magnetic moment in models with an additional U(1) gauge symmetry that has
kinetic mixing with hypercharge are increasingly constrained by dark photon
searches at electron accelerators. Here we present a scenario in which the
couplings of new, light gauge bosons to standard model leptons are naturally
weak and flavor non-universal. A vector-like state that mixes with standard
model leptons serves as a portal between the dark and standard model sectors.
The flavor symmetry of the model assures that the induced couplings of the new
gauge sector to leptons of the first generation are very small and
lepton-flavor-violating processes are adequately suppressed. The model provides
a framework for constructing ultraviolet complete theories in which new, light
gauge fields couple weakly and dominantly to leptons of the second or third
generations.
