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="CPC-2025-0328_M1.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="CPC-2025-0328_M1.png"/></alternatives></inline-formula>

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