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

Abstract

Abstract We consider simultaneous explanations of the electron and muon $$g-2$$ g - 2 anomalies through a single $$Z'$$ Z ′ of a $$U(1)'$$ U ( 1 ) ′ extension to the Standard Model (SM). We first perform a model-independent analysis of the viable flavour-dependent $$Z'$$ 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 $$Z'$$ Z ′ can account for the two anomalies. Following the conclusions of this analysis, we then explore the ability of different classes of $$Z'$$ Z ′ models to realise these couplings, including the SM $$+U(1)'$$ + U ( 1 ) ′ , the N-Higgs Doublet Model $$+U(1)'$$ + 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 $$Z'$$ 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 $$U(1)'$$ U ( 1 ) ′ extension can resolve both anomalies unless other new fields are also introduced. While most of our study assumes the Caesium $$(g-2)_e$$ ( g - 2 ) e measurement, our findings in fact also hold in the case of the Rubidium measurement, despite the tension between the two.