A $Z^{\prime }$ Model for $b\to s\ell \bar{\ell }$ Flavour Anomalies

Abstract

We study the implications of flavour-changing neutral currents (FCNC's) in a model with the $SU(2{)}_l\times SU(2{)}_h\times U(1{)}_Y$ electroweak gauge symmetry for several anomalies appearing in $b\to s\ell \bar{\ell }$ 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 $Z^{\prime }$ generate the $b\to s$ transition at tree level, leading to additional contributions to the $b\to s$ semileptonic operators ${\mathcal{O}}_{9,10}$. We find that although $B_s$-${\bar{B}}_s$ mixing constrains the parameters severely, the model can produce values of ${\mathcal{C}}_{9,10}^{\mathrm{NP}}$ in the range determined by Descotes-Genon {\it et. al.} in Ref.~\cite{Descotes-Genon:2015uva} for this scenario to improve the global fit of observables in decays induced by the $b\to s\mu \bar{\mu }$ transition. The $Z^{\prime }$ boson in this model also generates tree-level FCNC's for the leptonic interactions that can accommodate the experimental central value of $R_K=\mathcal{B}(B\to K\mu \bar{\mu })/\mathcal{B}(B\to Ke\bar{e})=0.75$. In this case, the model predicts sizeable branching ratios for $B\to Ke\bar{\tau }$, $B\to K\tau \bar{e}$, and an enhancement of $B\to K\tau \bar{\tau }$ with respect to its SM value.

Comments: ReTex, 13 pages with two figures. A few typos corrected and several references added