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

## TL;DR

This paper investigates S-wave contributions in the decay of _s^0 to D^0 or  D^0 and two pions using perturbative QCD, highlighting potential for CKM angle  measurement and decay mechanism insights.

## Contribution

It introduces a perturbative QCD approach with two-meson distribution amplitudes to analyze S-wave effects in _s^0 decays, including resonance contributions.

## Key findings

- Branching ratios can reach  imes 10^{-6}
- Significant interference effects in CP eigenstate decays
- Future measurements can constrain CKM angle 

## Abstract

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.