Through analyzing the $B_{(s)}$ charmed decays $B^0\to {\overline{D}}_0{f}_0(980)$ and $B_s\to {\overline{D}}_0{f}_0(980)$ within the framework of the perturbative QCD factorization approach and comparing with the current data, we find that there are two possible regions for the $f_0(980)-f_0(500)$ mixing angle $\theta$: one is centered at 34°–38° and the other falls into 142°–154°. The former can overlap mostly with one of the allowed angle regions extracted from the decay $B^0\to {\overline{D}}_0{f}_0(500)$. The branching fractions of $B_s$ decay modes are less sensitive to the mixing angle compared with those of $B$ decay modes. Especially, for the decay $B_s\to D^0{f}_0(980)$, its branching fraction changes only slightly between $(1.2–1.8)\times {10}^{-7}$ when the mixing angle $\theta$ runs from 0° to 180°. All of our results support the picture that the $f_0(980)$ is dominated by the two-quark component in the $B$ decay dynamic mechanism. Furthermore, the $s\overline{s}$ component is more important than the $q\overline{q}=(u\overline{u}+d\overline{d})/\sqrt{2}$ component. This point is different from $f_0(500)/\sigma$. Last but not least, our picture is not in conflict with the popular four-quark explanation.

• Received 19 January 2016

DOI:https://doi.org/10.1103/PhysRevD.93.054034