Study of f_0(980) and f_0(1500) from B_s \to f_0(980)\pi, f_0(1500)\pi Decays

Abstract

In this paper, we analyze the scalar mesons $f_0(980)$ and $f_0(1500)$ from the decays ${\bar{B}}_s^0\to f_0(980){\pi }^0,f_0(1500){\pi }^0$ within Perturbative QCD approach. From the leading order calculations, we find that (a) in the allowed mixing angle ranges, the branching ratio of ${\bar{B}}_s^0\to f_0(980){\pi }^0$ is about $(1.0\sim 1.6)\times 10^{-7}$, which is smaller than that of ${\bar{B}}_s^0\to f_0(980)K^0$ (the difference is a few times even one order); (b) the decay ${\bar{B}}_s^0\to f_0(1500){\pi }^0$ is better to distinguish between the lowest lying state or the first excited state for $f_0(1500)$, because the branching ratios for two scenarios have about one-order difference in most of the mixing angle ranges; and (c) the direct CP asymmetries of ${\bar{B}}_s^0\to f_0(1500){\pi }^0$ for two scenarios also exists great difference. In scenario II, the variation range of the value ${\mathcal{A}}_{CP}^{dir}({\bar{B}}_s^0\to f_0(1500){\pi }^0)$ according to the mixing angle is very small, except for the values corresponding to the mixing angles being near $90^{\circ }$ or $270^{\circ }$, while the variation range of ${\mathcal{A}}_{CP}^{dir}({\bar{B}}_s^0\to f_0(1500){\pi }^0)$ in scenario I is very large. Compared with the future data for the decay ${\bar{B}}_s^0\to f_0(1500){\pi }^0$, it is ease to determine the nature of the scalar meson $f_0(1500)$.

Comments: 16 pages, 3 figures, Revtex