Solving the electron and muon g-2 anomalies in Z' models

We consider simultaneous explanations of the electron and muon g-2 anomalies through a single Z' of a U(1)' extension to the Standard Model (SM). We first perform a model-independent analysis of the viable flavour-dependent Z' couplings to leptons, which are subject to various strict experimental constraints. We show that only a narrow region of parameter space with an MeV-scale Z' can account for the two anomalies. Following the conclusions of this analysis, we then explore the ability of different classes of Z' models to realise these couplings, including the SM+U(1)', the N-Higgs Doublet Model+U(1)', and a Froggatt-Nielsen style scenario. In each case, the necessary combination of couplings cannot be obtained, owing to additional relations between the Z' couplings to charged leptons and neutrinos induced by the gauge structure, and to the stringency of neutrino scattering bounds. Hence, we conclude that no U(1)' extension can resolve both anomalies unless other new fields are also introduced. While most of our study assumes the Caesium (g-2)${}_e$ measurement, our findings in fact also hold in the case of the Rubidium measurement, despite the tension between the two.