Eur. Phys. J. C (2022) 82: 844
https://doi.org/10.1140/epjc/s10052-022-10776-1

Regular Article - Theoretical Physics

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

Laboratoire de Physique de Clermont (UMR 6533), CNRS/IN2P3, Univ. Clermont Auvergne, 4 Av. Blaise Pascal, Aubière, 63178, Cedex, France

^a jonathan.kriewald@clermont.in2p3.fr

Received: 4 July 2022
Accepted: 31 August 2022
Published online: 28 September 2022

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 ($\mathrm{\Delta }{a}_{\mu ,e}$) 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 $\mathrm{\Delta }{a}_{\mu }$, 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 $\mathrm{\Delta }{a}_{\mu }$, but $\mathrm{\Delta }{a}_e$ 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.