$B\to f_0(980)K$ Decays and Subleading Corrections

Abstract

The decay $B\to f_0(980)K is studied within the framework of QCD factorization and the two-quark scenario for $f_0(980)$. There are two distinct penguin contributions and their interference depends on the unknown mixing angle $\theta$ of strange and nonstrange quark contents of $f_0(980)$: destructive for $0<\theta<\pi/2$ and constructive for $\pi/2<\theta<\pi$. The QCD sum rule method is applied to evaluate the leading-twist light-cone distribution amplitudes and the scalar decay constant of $f_0$. We conclude that the short-distance approach is not adequate to explain the observed large rates of $f_0K^-$ and $f_0\ov K^0$. Among many possible subleading corrections, we study and estimate the contributions from the three-parton Fock states of the $f_0$ and from the intrinsic gluon inside the $B$ meson. It is found that the spectator gluon of the $B$ meson may play an eminent role for the enhancement of $f_0(980)K$. We point out that if $f_0(980)$ is a four-quark state as widely perceived, there will exist extra diagrams contributing to $B\to f_0(980)K$. However, in practice it is difficult to make quantitative predictions based on the four-quark picture for $f_0(980)$ as it involves additional nonfactorizable contributions that are difficult to estimate and the calculations of the decay constant and form factors of $f_0(980)$ are beyond the conventional quark model.