\begin{document}$\bar B_s^0\to (D^0,\bar D^0) \pi^+\pi^-$\end{document} is induced by the \begin{document}$b\to c \bar us$\end{document}/\begin{document}$b \to u\bar cs$\end{document} transitions, which can interfere if a CP-eigenstate \begin{document}$D_{\rm CP}$\end{document} is formed. The interference contribution is sensitive to the CKM angle \begin{document}$\gamma$\end{document}. In this work, we study the S-wave \begin{document}$\pi^+\pi^-$\end{document} contributions to the process in the perturbative QCD factorization. In the factorization framework, we adopt two-meson light-cone distribution amplitudes, whose normalization is parametrized by the S-wave time-like two-pion form factor with resonance contributions from \begin{document}$f_0(500)$\end{document}, \begin{document}$f_0(980),f_0(1500),f_0(1790)$\end{document}. We find that the branching ratio of \begin{document}$\bar B_s^0\to (D^0,\bar D^0) (\pi^+\pi^-)_S$\end{document} is of the order of \begin{document}$10^{-6}$\end{document}, and that significant interference exists in \begin{document}$\bar B_s^0\to D_{\rm CP} (\pi^+\pi^-)_S$\end{document}. Future measurement could not only provide useful constraints on the CKM angle \begin{document}$\gamma$\end{document}, but would also be helpful for exploring the multi-body decay mechanism of heavy mesons."> <i>S</i>-wave contributions to <inline-formula><tex-math id="M260">\begin{document}${{{\bar B}_s^0\to (D^0,{\bar D}^0)\pi^+\pi^-}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/44df9c14-e75a-4a24-abec-2fd28ccc9152/CPC-2019-0088_M260.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/44df9c14-e75a-4a24-abec-2fd28ccc9152/CPC-2019-0088_M260.png"/></alternatives></inline-formula> in the perturbative QCD framework -
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