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

TL;DR

This paper proposes a gauge-invariant, fermiophobic $Z'$ model with a fourth vector-like family that can simultaneously explain the muon anomalous magnetic moment and B-decay anomalies, consistent with current experimental constraints.

Contribution

It introduces a novel $Z'$ model coupling to a fourth vector-like family, providing a unified explanation for muon and B-decay anomalies.

Findings

Model explains $R_{K^{(*)}}$ and $(g-2)_{}$ anomalies simultaneously.

Parameter space consistent with experimental constraints identified.

Higgs coupling effects on diphoton decay are negligible.

Abstract

We discuss a simple renormalisable, gauge invariant model with a fermiophobic $Z'$ 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 $Z'$ to right-handed muons, which arises within this model due to mixing effects between the SM and VL fermions, along with $Z'$ 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 $R_{K^{(*)}}$ 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.