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

TL;DR

This study investigates the properties of scalar mesons $f_0(980)$ and $f_0(1500)$ through $ar B_s^0$ decays using Perturbative QCD, providing predictions on branching ratios and CP asymmetries to distinguish meson structures.

Contribution

The paper offers the first detailed analysis of $f_0(980)$ and $f_0(1500)$ in $B_s$ decays within the Perturbative QCD framework, highlighting differences in decay patterns and CP asymmetries for different meson scenarios.

Findings

Branching ratio of $ar B_s^0 o f_0(980) ext{ extendash} ext{pi}^0$ is $(1.0 ext{ extendash}1.6) imes 10^{-7}$

Decay $ar B_s^0 o f_0(1500) ext{ extendash} ext{pi}^0$ can distinguish meson states

Significant differences in direct CP asymmetries for $f_0(1500)$ scenarios

Abstract

In this paper, we analyze the scalar mesons $f_0(980)$ and $f_0(1500)$ from the decays $\bar B^0_s \to f_0(980)\pi^0, f_0(1500)\pi^0$ within Perturbative QCD approach. From the leading order calculations, we find that (a) in the allowed mixing angle ranges, the branching ratio of $\bar B^0_s\to f_0(980)\pi^0$ is about $(1.0\sim1.6)\times 10^{-7}$, which is smaller than that of $\bar B^0_s\to f_0(980)K^0$ (the difference is a few times even one order); (b) the decay $\bar B^0_s \to f_0(1500)\pi^0$ 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 $\bar B^0_s \to f_0(1500)\pi^0$ for two scenarios also exists great difference. In scenario II, the variation range of the value ${\cal A} ^{dir}_{CP}(\bar B^0_s \to f_0(1500)\pi^0)$ 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 ${\cal A} ^{dir}_{CP}(\bar B^0_s \to f_0(1500)\pi^0)$ in scenario I is very large. Compared with the future data for the decay $\bar B^0_s \to f_0(1500)\pi^0$, it is ease to determine the nature of the scalar meson $f_0(1500)$.