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

Abstract

The $\bar B_s^0\to (D^0,\bar D^0) π^+π^-$ 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 $γ$. In this work, we study S-wave $π^+π^-$ 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 $\bar B_s^0\to (D^0,\bar D^0) (π^+π^-)_S$ can reach the order of $10^{-6}$, and significant interferences exist in $\bar B_s^0\to D_{CP} (π^+π^-)_S$. The future measurement can not only provide useful constraints on the CKM angle $γ$ but is also helpful to explore the multi-body decay mechanism of heavy mesons.