Third family hypercharge model for $R_{K^{(\ast )}}$ and aspects of the fermion mass problem

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′ particle with flavour-dependent couplings can modify the $\left[\overline{b_L}{\gamma }^{\rho }{s}_L\right]\left[\overline{{\mu }_L}{\gamma }_{\rho }{\mu }_L\right]$ effective vertex in the desired way. The Z′ contribution to $B_s-\overline{B_s}$ 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.