  The $\bar B_s^0\to (D^0,\bar D^0) \pi^+\pi^-$ is induced by the $b\to c \bar
us$/$b \to u\bar cs$ transition, and can interfere if a CP-eigenstate $D_{\rm
CP}$ is formed. The interference contribution is sensitive to the CKM angle
$\gamma$. In this work, we study S-wave $\pi^+\pi^-$ contributions to the
process in the perturbative QCD factorization. Under 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
the resonance contributions from $f_0(500)$, $f_0(980),f_0(1500),f_0(1790)$. We
find the branching ratios of $\bar B_s^0\to (D^0,\bar D^0) (\pi^+\pi^-)_S$ can
reach the order of $10^{-6}$, and significant interferences exist in $\bar
B_s^0\to D_{CP} (\pi^+\pi^-)_S$. The future measurement can not only provide
useful constraints on the CKM angle $\gamma$ but is also helpful to explore the
multi-body decay mechanism of heavy mesons.

High Energy Physics - Phenomenology