<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>model for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>b</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>s</mml:mi><mml:mo>ℓ</mml:mo><mml:mover accent="true"><mml:mrow><mml:mo>ℓ</mml:mo></mml:mrow><mml:mrow><mml:mo accent="true" stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:math>flavor anomalies

We study the implications of flavor-changing neutral currents (FCNC's) in a model with the $SU(2{)}_{l}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{h}\ifmmode\times\else\texttimes\fi{}U(1{)}_{Y}$ electroweak gauge symmetry for several anomalies appearing in $b\ensuremath{\rightarrow}s\ensuremath{\ell}\overline{\ensuremath{\ell}}$ induced $B$ decays in LHCb data. In this model, $SU(2{)}_{l}$ and $SU(2{)}_{h}$ govern the left-handed fermions in the first two generations and the third generation, respectively. The physical $Z$ and ${Z}^{\ensuremath{'}}$ generate the $b\ensuremath{\rightarrow}s$ transition at tree level, leading to additional contributions to the $b\ensuremath{\rightarrow}s$ semileptonic operators ${\mathcal{O}}_{9,10}$. We find that although ${B}_{s}\text{\ensuremath{-}}{\overline{B}}_{s}$ mixing constrains the parameters severely, the model can produce values of ${\mathcal{C}}_{9,10}^{\mathrm{NP}}$ in the range determined by Descotes-Genon et al. (Global analysis of $b\ensuremath{\rightarrow}s\ensuremath{\ell}\ensuremath{\ell}$ anomalies, arXiv:1510.04239) for this scenario to improve the global fit of observables in decays induced by the $b\ensuremath{\rightarrow}s\ensuremath{\mu}\overline{\ensuremath{\mu}}$ transition. The ${Z}^{\ensuremath{'}}$ boson in this model also generates tree-level FCNC's for the leptonic interactions that can accommodate the experimental central value of ${R}_{K}=\mathcal{B}(B\ensuremath{\rightarrow}K\ensuremath{\mu}\overline{\ensuremath{\mu}})/\mathcal{B}(B\ensuremath{\rightarrow}Ke\overline{e})=0.75$. In this case, the model predicts sizable branching ratios for $B\ensuremath{\rightarrow}Ke\overline{\ensuremath{\tau}}$, $B\ensuremath{\rightarrow}K\ensuremath{\tau}\overline{e}$, and an enhancement of $B\ensuremath{\rightarrow}K\ensuremath{\tau}\overline{\ensuremath{\tau}}$ with respect to its standard model value.