\begin{document}$ V\left\{\rho^{0}(770),\,\omega(782),\,\phi(1020)\right\} $\end{document} to \begin{document}$ \pi^+ \pi^- $\end{document} meson pairs. \begin{document}$ \rho^{0}(770) $\end{document} can decay directly into \begin{document}$ \pi^+ \pi^- $\end{document} meson pairs; both \begin{document}$ \omega(782) $\end{document} and \begin{document}$ \phi(1020) $\end{document} can also decay into \begin{document}$ \pi^+ \pi^- $\end{document} meson pairs, with a small contribution from isospin symmetry breaking. The main contribution for the middle state vector meson \begin{document}$ \rho^{0}(770)-\omega(782)-\phi(1020) $\end{document} interference is the mix of \begin{document}$ \rho^{0}(770) $\end{document}, \begin{document}$ \omega(782)-\rho^{0}(770) $\end{document}, and \begin{document}$ \phi(1020)-\rho^{0}(770) $\end{document}. We calculated the CP asymmetry and decay branching ratio for \begin{document}$ \bar{B}^0_{s} \rightarrow \pi^+ \pi^- \pi^0 (\bar K ^{0}) $\end{document}within the framework of QCD factorization and compared them with previous studies. We also analyzed the \begin{document}$ \bar{B}^0_{s} \rightarrow \pi^+ \pi^- \eta(\eta^{(')}) $\end{document} decay process. The results show that the CP asymmetry of these four decay processes is significantly enhanced, especially for the \begin{document}$ \bar{B}^0_{s} \rightarrow \pi^+ \pi^- \bar K ^{0} $\end{document} decay process. Moreover, the decay branching ratio also changes under the resonance effect. These results might provide support for the experimental analysis of the \begin{document}$ \bar B^{0}_s $\end{document} meson."> Role and contribution of the resonance effect for the decay process of <inline-formula><tex-math id="M1">\begin{document}${ \bar {\boldsymbol B}^{\bf 0}_{\boldsymbol s} \boldsymbol\rightarrow \boldsymbol\pi^{+}\boldsymbol\pi^{-}{\boldsymbol P}}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/3e060cc7-35fc-4043-93f8-4c0ead95c467/CPC-2025-0328_M1.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/3e060cc7-35fc-4043-93f8-4c0ead95c467/CPC-2025-0328_M1.png"/></alternatives></inline-formula> -
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