Prospects for a flavour violating Z^prime explanation of Delta a_{mu ,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 (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.