Prospects for a flavour violating $Z^\prime$ explanation of $Δa_{μ,e}$

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 (∆a µ,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 ∆a µ , albeit subject to stringent experimental constraints. Here we explore a minimal extension of the Standard Model via a leptophilic vector boson Z , 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 τ decays) and from rare charged lepton flavour violating transitions. Once these are accommodated, one can saturate the tensions in ∆a µ , but ∆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 at a future muon collider, emphasising the role of the µ + µ − → τ + τ − forward-backward asymmetry as a key probe of the model.