Two-body charmed B(Bs) decays involving a light scalar meson

Based on the assumption of two-quark structure for the light scalar mesons, within the framework of perturbative QCD approach, we investigate the $B_{q}\to D_{(s)}^{(*)} S(q=u,d,s)$ decays induced by $b\to u $ transition, where $S$ denotes a light scalar meson. Under two different scenarios, we calculate the branching ratios of 96 decay modes totally, which are in the range of $10^{-5}$ to $10^{-8}$. The comparison between our predictions and the experimental data will allow us to probe the inner structure of the scalar mesons. In the standard model, since all decays can only occur through tree operators, there are no $CP$ asymmetries. From our calculations, it has been shown that the annihilation type diagrams, especially the nonfactorizable annihilation diagrams, play important roles in the decay amplitudes, especially for these color-suppressed and pure annihilation type decay modes. We also find that the branching ratios of color-allowed type decays are sensitive to the different scenarios, so the measurements of them will be ideal places to differentiate the different scenarios. It can be found that the ratios between $Br(B^0\to D^{(*)0}\sigma)$ and $Br(B^0\to D^{(*)0}f_0)$, and between $Br(B^+\to D^{(*)+}\sigma)$ and $Br(B^{+}\to D^{(*)+}f_0)$ can be used to determine the mixing angle of $\sigma$ and $f_0$.