Addressing the LHC flavour anomalies with horizontal gauge symmetries

We study the impact of an additional $U(1{)}^{\mathrm{\prime }}$ gauge symmetry with flavour-dependent charges for quarks and leptons on the LHC flavour anomalies observed in $B\to K^{\ast }{\mu }^{+}{\mu }^{-}$, $R(K)=B\to K{\mu }^{+}{\mu }^{-}\mathrm{/}B\to K{e}^{+}{e}^{-}$, and $h\to \mu \tau$. In its minimal version with two scalar doublets, the resulting model naturally explains the deviations from the Standard Model observed in $B\to K^{\ast }{\mu }^{+}{\mu }^{-}$ and $R(K)$. The CMS access in $h \to \mu\tau$ can be explained by introducing a third scalar doublet, which gives rise to a prediction for $\tau \to 3\mu$. We investigate constraints from flavour observables and direct LHC searches for $pp\to Z^{\mathrm{\prime }}\to {\mu }^{+}{\mu }^{-}$. Our model successfully generates the measured fermion-mixing matrices and does not require vector-like fermions, unlike previous attempts to explain these anomalies.