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

We present a model to explain LHCbs 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.