Explaining B \to K pi anomaly with non-universal Z' boson

Abstract

We study the effect of non-universal $Z'$ boson in the decay modes $B \to K π$. In the standard model these modes receive dominant contributions from $b \to s$ QCD penguins. Therefore, in this limit one expects $S_{π^0 K^0} \approx \sin 2 β$, $A_{π^0 K^0} \approx 0$ and $A_{π^0 K^-} \approx A_{π^+ K^-}$. The corrections due to the presence of small non-penguin contributions is found to yield $S_{π^0 K^0} > \sin 2 β$ and $ΔA_{CP}(K π) \simeq 2.5 %$. However, the measured value of $S_{π^0 K^0}$ is less than $ \sin 2 β$ and $ΔA_{CP}(K π) \simeq 15 %$. We show the model with a non-universal $Z'$ boson can successfully explain these anomalies.