Abstract
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.
Highlights
Which constitutes a 2.4σ tension with the Standard Model (SM) [9]
The cross-section including new physics should not deviate from the SM cross-section by more than about 10% [79,81], and this restriction sets a strong limit on the parameter space
While the status of (g − 2)μ has been solidified by the recent Fermilab measurement, there is considerably more uncertainty surrounding (g − 2)e
Summary
In the most general framework, a new Z with familydependent charged lepton couplings leads to flavour violation. Rewriting the charged lepton interactions in terms of vector and axial couplings, CV (A) f = (CR f ± CL f )/2, gives. Z − Z mass mixing, which is generated if the SM Higgs sector is charged under the U (1) (flavour universal). The combination of these three contributions can generate variety of vector and axial couplings. We will firstly survey the parameter space in a model-independent way in terms of the effective leptonZ couplings defined in Eg.
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