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

TL;DR

This paper explores whether a simple $Z'$ gauge boson model can explain the anomalous magnetic moments of the electron and muon, finding it can only account for one at a time due to experimental constraints.

Contribution

The study introduces a minimal $Z'$ model with specific lepton couplings and analyzes its ability to explain $g-2$ anomalies within experimental bounds.

Findings

The $Z'$ can explain either the electron or muon $g-2$ anomaly, but not both simultaneously.

The model remains consistent with constraints from $ ext{mu} ightarrow e ext{gamma}$ and neutrino trident production.

Analytic and numerical methods are used to evaluate the model's viability.

Abstract

In order to address this question, we consider a simple renormalisable 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 vector-like 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 $\mu \rightarrow e \gamma$ 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 $\mu \rightarrow e \gamma$ and neutrino trident production.