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The $\bar B_s^0\to (D^0,\bar D^0) \pi^+\pi^-$ is induced by the $b\to c \barus$/$b \to u\bar cs$ transition, and can interfere if a CP-eigenstate $D_{\rmCP}$ is formed. The interference contribution is sensitive to the CKM angle$\gamma$. In this work, we study S-wave $\pi^+\pi^-$ contributions to theprocess in the perturbative QCD factorization. Under the factorizationframework, we adopt two-meson light-cone distribution amplitudes, whosenormalization is parametrized by the S-wave time-like two-pion form factor withthe resonance contributions from $f_0(500)$, $f_0(980),f_0(1500),f_0(1790)$. Wefind the branching ratios of $\bar B_s^0\to (D^0,\bar D^0) (\pi^+\pi^-)_S$ canreach the order of $10^{-6}$, and significant interferences exist in $\barB_s^0\to D_{CP} (\pi^+\pi^-)_S$. The future measurement can not only provideuseful constraints on the CKM angle $\gamma$ but is also helpful to explore themulti-body decay mechanism of heavy mesons.

S-wave contributions in $\bar B_s^0\to (D^0,\bar D^0)\pi^+\pi^- $ within perturbative QCD approach