Insight into $f_0(980)$ through the $B_{(s)}$ charmed decays

Abstract: Through analyzing the $B_{(s)}$ charmed decays $B^{0}\to \bar D_{0}f_0(980)$ and $B_{s}\to \bar D_{0}f_0(980)$ within the framework of the PQCD 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 $34^\circ\sim38^\circ$ and the other is falls into $142^\circ\sim154^\circ$. The former can overlap mostly with one of allowed angle regions extracted from the decay $B^{0}\to \bar D_{0}f_0(500)$. 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 $(1.2\sim1.8)\times10^{-7}$ when the mixing angle $\theta$ runs from $0^\circ$ to $180^\circ$. All of our results support the picture that the $f_0(980)$ is dominated by two quark component in the B decay dynamic mechanism. Furthermore, the $s\bar s$ component is more important than the $q\bar q=(u\bar u+d\bar d)/\sqrt{2}$ 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.