Fermiophobic $Z^{\prime }$ model for simultaneously explaining the muon anomalies $R_{K^{(\ast )}}$ and $(g-2{)}_{\mu }$

Abstract

We discuss a simple renormalisable, gauge invariant model with a fermiophobic $Z^{\prime }$ boson: it has no couplings to the three Standard Model (SM) chiral families, but does couple to a fourth vector-like (VL) family. The SM Higgs couples to the fourth VL lepton, leading to an enhanced contribution to the muon anomalous magnetic moment ${\left(g-2\right)}_{\mu }$. The latter contribution requires a non-vanishing coupling of $Z^{\prime }$ to right-handed muons, which arises within this model due to mixing effects between the SM and VL fermions, along with $Z^{\prime }$ couplings to the second generation SM lepton doublet and third generation SM quark doublet. This model can simultaneously account for the measured $B$-decay ratios $R_{K^{(\ast )}}$ and ${\left(g-2\right)}_{\mu }$. We identify the parameter space where this explanation is consistent with existing experimental constraints coming from $B_s-{\bar{B}}_s$ mixing, neutrino trident production and collider searches. We also check that the SM Higgs coupling to the fourth VL lepton does not produce a dangerous contribution to the Higgs diphoton decay.

26 pages, 12 Figures, 3 Tables

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