Prospects for a flavour violating $Z^\prime$ explanation of $\Delta a_{\mu,e}$

TL;DR

This paper investigates a minimal leptophilic $Z'$ boson model with flavor-violating couplings to explain anomalies in muon and electron magnetic moments, analyzing experimental constraints and future collider signatures.

Contribution

It introduces a novel flavor-violating $Z'$ model that can explain muon magnetic moment anomalies while predicting SM-like electron moments, and assesses experimental and collider signatures.

Findings

The model can account for $ riangle a_$ tensions.

Constraints from lepton flavor universality and rare decays are significant.

Future muon collider signatures include the $ au^+ au^-$ forward-backward asymmetry.

Abstract

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^- \to\tau^+\tau^- $ forward-backward asymmetry as a key probe of the model.