\begin{document}$ CP $\end{document} violations of the \begin{document}$ B^-\rightarrow K^- \pi^+\pi^- $\end{document} decay with and without the \begin{document}$ a_0^0(980)-f_0(980) $\end{document} mixing mechanism and observe that the localized \begin{document}$ CP $\end{document} violation can be enhanced by this mixing effect when the mass of the \begin{document}$ \pi^+\pi^- $\end{document} pair is in the vicinity of the \begin{document}$ f_0(980) $\end{document} resonance. The corresponding theoretical prediction results are \begin{document}${\cal{A}}_{CP}(B^-\rightarrow K f_0 \rightarrow K^-\pi^+\pi^-)= [0.126,\ 0.338]$\end{document} (\begin{document}$ 0.232\pm0.106 $\end{document} with the central value form) and \begin{document}$ {\cal{A}}_{CP}(B^-\rightarrow K^- f_0(a_0) \rightarrow K^-\pi^+\pi^-)=[0.230, 0.615] $\end{document} (\begin{document}$ 0.423\pm0.193 $\end{document} with the central value form), respectively. Meanwhile, we also calculate the branching fraction of the \begin{document}$B^-\rightarrow K^-f_0(980)\rightarrow K^-\pi^+\pi^-$\end{document} decay, which is consistent with the experimental results. We suggest that the \begin{document}$ a_0^0(980)-f_0(980) $\end{document} mixing mechanism should be considered when theoretically and experimentally studying the \begin{document}$ CP $\end{document} violation of the B or D meson decays."> Impact of <inline-formula><tex-math id="M1">\begin{document}${ {\boldsymbol a}_{\bf 0}^{\bf {0}}(980)-{\boldsymbol f}_{\bf {0}}(980) }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/0fed4879-aaff-4641-81d5-aaf8b8be0303/CPC-2022-0096_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/0fed4879-aaff-4641-81d5-aaf8b8be0303/CPC-2022-0096_M1.png"/></alternatives></inline-formula> mixing on the localized <i>CP</i> violations of the <inline-formula><tex-math id="M3">\begin{document}${{\boldsymbol B}^-{\bf\rightarrow} {\boldsymbol K}^- \boldsymbol\pi^+\boldsymbol\pi^- }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/0fed4879-aaff-4641-81d5-aaf8b8be0303/CPC-2022-0096_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/0fed4879-aaff-4641-81d5-aaf8b8be0303/CPC-2022-0096_M3.png"/></alternatives></inline-formula> decay -
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