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 $34^{\circ }\sim 38^{\circ }$ and the other is falls into $142^{\circ }\sim 154^{\circ }$. 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 $(1.2\sim 1.8)\times 10^{-7}$ 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.

Comments: 15 pages, 4 figures