  One of the major motivations to search for a dark gauge boson of MeV-GeV
scale is the long-standing muon g-2 anomaly. Because of active searches such as
fixed target experiments and rare meson decays, the muon g-2 favored parameter
region has been rapidly reduced. With the most recent data, it is practically
excluded now in the popular dark photon model. We overview the issue and
investigate a potentially alternative model based on the gauged lepton number
or U(1)_L. The muon g-2 favored parameter region of the U(1)_L survives all the
constraints that were critical in the dark photon case, yet it is disfavored by
the new constraints from the large flux neutrino experiments.
