  We go through several previous corrections and contributions to the muon
$g-2$, starting from the dark photon hypothesis to the dark Z. We explore the
inputs from a dark Z boson virtual mediator in a first order loop. We consider
not only the QED like contributions in the theory but also weak interactions.
We obtain a new factor that adds corrections to the form factor associated with
the anomalous magnetic moment. We show our result is favorable in new
unexplored windows in the mass-coupling parameter space.
