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

TL;DR

This paper proposes a $Z'$ model with extended electroweak symmetry to explain anomalies in $b o s \, \ell\bar\ell$ decays, fitting experimental data while predicting new flavor-changing processes.

Contribution

It introduces a $Z'$ model with specific gauge symmetry breaking that accounts for flavor anomalies and predicts observable rare decays beyond the Standard Model.

Findings

The model can fit $b\to s \mu\bar\mu$ anomalies within experimental constraints.

It predicts sizeable branching ratios for rare $B$ decays involving tau leptons.

The $Z'$ boson mediates flavor-changing neutral currents at tree level.

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 $Z'$ generate the $b\to s$ transition at tree level, leading to additional contributions to the $b \to s$ semileptonic operators ${\cal O}_{9,10}$. We find that although $B_s$-$\bar B_s$ mixing constrains the parameters severely, the model can produce values of ${\cal C}^{\rm NP}_{9,10}$ 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 $Z'$ boson in this model also generates tree-level FCNC's for the leptonic interactions that can accommodate the experimental central value of $R_K = {\cal B}(B\to K \mu \bar \mu)/{\cal B}(B\to K e\bar e)=0.75$. In this case, the model predicts sizeable branching ratios for $B\to K e \bar \tau$, $B\to K \tau \bar e$, and an enhancement of $B\to K \tau \bar \tau$ with respect to its SM value.