Prospects for a flavour violating $Z^\prime $ explanation of $\Delta a_{\mu ,e}$
Résumé
The apparent tensions emerging from the comparison of experimental data of the anomalous magnetic moments of the muon and electron to the Standard Model predictions ($\Delta a_{\mu ,e}$) could be interpreted as a potential signal of New Physics. Models encompassing a light vector boson have been known to offer a satisfactory explanation to $\Delta a_{\mu }$, albeit subject to stringent experimental constraints. Here we explore a minimal extension of the Standard Model via a leptophilic vector boson $Z^\prime $, under the hypothesis of strictly flavour-violating couplings of the latter to leptons. The most constraining observables to this ad-hoc construction emerge from lepton flavour universality violation (in Z and $\tau $ decays) and from rare charged lepton flavour violating transitions. Once these are accommodated, one can saturate the tensions in $\Delta a_{\mu }$, but $\Delta a_{e}$ is predicted to be Standard Model-like. We infer prospects for several observables, including leptonic Z decays and several charged lepton flavour violating processes. We also discuss potential signatures of the considered $Z^\prime $ at a future muon collider, emphasising the role of the $\mu ^+\mu ^- \rightarrow \tau ^+\tau ^- $ forward-backward asymmetry as a key probe of the model.