$B$ meson anomalies and large $B^{+}\to K^{+}\nu \bar{\nu }$ in non-universal $U(1{)}^{\mathrm{\prime }}$ models

In view of both the latest LHCb measurement of $R_{K^{(\ast )}}$ and the new $2.8\sigma$ deviation reported by Belle II on $B^{+}\to K^{+}\nu \bar{\nu }$ decays, we present a fit to the $B$ meson anomalies for various one and two dimensional hypothesis including complex Wilson coefficients. We show in a model-independent way that the generic non-universal $U(1{)}^{\mathrm{\prime }}$ extensions of the SM, without flavour violation, fail to simultaneously fit those observables and corroborate that they can modify $\mathrm{B}\mathrm{R}(B^{+}\to K^{+}\nu \bar{\nu })$ up to only a $10\mathrm{\%}$. In view of this deficit, we propose a new way in which those models can accommodate the data at tree level by introducing lepton flavour violating couplings and non-diagonal elements of the charged lepton mixing matrix, with implications in future charged lepton flavour violation searches.