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

In view of both the latest LHCb measurement of $$ {R}_{K^{\left(\ast \right)}} $$ R K ∗ and the new 2 . 7 σ deviation reported by Belle II on $$ {B}^{+}\to {K}^{+}\nu \overline{\nu} $$ B + → K + ν ν ¯ 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) ′ extensions of the SM, without flavour violation, fail to simultaneously fit those observables and corroborate that they can modify $$ \textrm{BR}\left({B}^{+}\to {K}^{+}\nu \overline{\nu}\right) $$ BR B + → K + ν ν ¯ up to only a 10%. 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.