Corrections of $Z'$ to the Magnetic Moment of the Muon

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.