Is it possible to explain the muon and electron g-2 in a Z' model?

In order to address this question, we consider a simple renormalizable and gauge invariant model in which the Z' only has couplings to the electron and muon and their associated neutrinos, arising from mixing with a heavy vectorlike fourth family of leptons. Within this model we discuss the contributions to the electron and muon anomalous magnetic moments from Z' exchange, subject to the constraints from mu -> e gamma and neutrino trident production. Using analytic and numerical arguments, we find that such a Z' model can account for either the electron or the muon g-2 anomalies, but not both, while remaining consistent with the experimental constraints from mu -> e gamma and neutrino trident production.