Is it possible to explain the muon and electron $g-2$ in a $Z^{\prime }$ model?

Abstract

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

22 pages, 8 figures

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