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

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.