Third family hypercharge model for R K ∗ \[ {R}_{K^{\left(\ast \right)}} \] and aspects of the fermion mass problem

We present a model to explain LHCb’s recent measurements of RK and RK∗\[ {R}_{K^{\left(\ast \right)}} \] 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′ particle with flavour-dependent couplings can modify the bL¯γρsLμL¯γρμL\[ \left[\overline{b_L}{\gamma}^{\rho }{s}_L\right]\left[\overline{\mu_L}{\gamma}_{\rho }{\mu}_L\right] \] effective vertex in the desired way. The Z′ contribution to Bs−Bs¯\[ {B}_s-\overline{B_s} \] mixing is suppressed by a small mixing angle connected to Vts, making the constraint coming from its measurement easier to satisfy. The model can explain RK and RK*\[ {R}_{K^{*}} \] whilst simultaneously passing other constraints, including measurements of the lepton flavour universality of Z couplings.