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

Abstract

The ${\bar{B}}_s^0\to (D^0,{\bar{D}}^0){\pi }^{+}{\pi }^{-}$ is induced by the $b\to c\bar{u}s$/$b\to u\bar{c}s$ transition, and can interfere if a CP-eigenstate $D_{\mathrm{CP}}$ 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.

12 pages,3 figures