Third Family Hypercharge Model for $R_{K^{(\ast)}}$ and Aspects of the Fermion Mass Problem

TL;DR

This paper proposes a new gauge symmetry-based model that explains recent LHCb anomalies in B-meson decays by introducing a heavy Z' boson, addressing fermion mass hierarchy and flavor constraints.

Contribution

It introduces an anomaly-free U(1)_F gauge symmetry model that accounts for R_K and R_{K*} anomalies without extending the fermion content beyond the Standard Model.

Findings

The model can explain R_K and R_{K*} measurements.

It satisfies constraints from B_s mixing and Z couplings.

The Z' boson mediates flavor-changing processes effectively.

Abstract

We present a model to explain LHCb's recent measurements of $R_K$ and $R_{K^{\ast}}$ based on an anomaly-free, spontaneously-broken $U(1)_F$ gauge symmetry, without any fermionic fields beyond those of the Standard Model (SM). The model explains the hierarchical heaviness of the third family and the smallness of quark mixing. The $U(1)_F$ charges of the third family of SM fields and the Higgs doublet are set equal to their respective hypercharges. A heavy $Z^\prime$ particle with flavour-dependent couplings can modify the $[\overline{b_L} \gamma^\rho s_L][\overline{\mu_L} \gamma_\rho \mu_L]$ effective vertex in the desired way. The $Z^\prime$ contribution to $B_s-\overline{B_s}$ mixing is suppressed by a small mixing angle connected to $V_{ts}$, making the constraint coming from its measurement easier to satisfy. The model can explain $R_K$ and $R_{K^{(\ast)}}$ whilst simultaneously passing other constraints, including measurements of the lepton flavour universality of $Z$ couplings.