\begin{document}$ \pi^0 - \eta - \eta' $\end{document} mixing effect on the \begin{document}$ CP $\end{document}-asymmetries of \begin{document}$ B\to K\pi $\end{document} processes is examined for the first time. It is found that this mixing effect presents significant uncertainty for both the \begin{document}$ CP $\end{document}-asymmetry sum rule of \begin{document}$ B\to K\pi $\end{document} processes and the \begin{document}$ CP $\end{document}-asymmetry difference of \begin{document}$ B^+\to K^+\pi^0 $\end{document} and \begin{document}$ B^0\to K^+\pi^- $\end{document}, potentially obscuring the significance of the \begin{document}$ K\pi $\end{document}-puzzle. As the correction caused by the \begin{document}$ \pi^0 - \eta - \eta' $\end{document} mixing effect is highly dependent on four strong non-perturbative phases, a definitive conclusion is currently unavailable."> Potential pollution of the <i>K</i><i>π</i>-puzzle by the isospin-breaking <i>π</i><sup>0</sup>-<i>η</i>-<i>η</i>' mixing effect -
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