A Model of Vector-like Leptons for the Muon $g-2$ and the $W$ Boson Mass

Abstract

We consider a simple extension of the Standard Model (SM) with a vector-like lepton and a local $U(1{)}^{\prime }$ symmetry, motivated by the recent experimental anomalies in the muon $g-2$ and the $W$ boson mass. The $U(1{)}^{\prime }$ symmetry is spontaneously broken by the VEVs of the dark Higgs scalar and the second Higgs doublet, giving rise to the mixing between the muon and the vector-like lepton. As a result, we obtain the desirable corrections to the muon $g-2$ and the $W$ boson mass simultaneously, dominantly due to the $Z^{\prime }$ gauge interactions for the vector-like lepton and the second Higgs doublet, respectively. We also discuss the consistency of the model with the $Z$ boson decay width, the Higgs couplings and the dilepton bounds.

18 pages, 4 figures, v2: references and discussion on dilepton bounds added, v3: version to be published in Eur. Phys. J. C

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