$B\to \phi K$ and $B\to \phi X_s$ in the Heavy Quark Limit

Abstract

We study $B\to \phi K$ and $B\to \phi X_s$ decays in the heavy quark limit using perturbative QCD. The next leading order corrections introduce substantial modifications to the naive factorization results (more than 50%). The branching ratio $Br(B\to \phi K)$ is predicted to be in the range $(F^{B\to K}_1(m^2_\phi)/0.33)^2(3.5\sim 4.2) \times 10^{-6}$ which is within the one $\sigma$ allowed region from the central value of $6.2\times 10^{-6}$ measured by CLEO, but outside the one $\sigma$ allowed region from the central value of $17.2\times 10^{-6}$ measured by BELLE for reasonable $F_1^{B\to K}$. For the semi-inclusive decay $B\to \phi X_s$ we also include initial bound state effect in the heavy quark limit which decreases the branching ratio by about 10%. $Br(B\to \phi X_s)$ is predicted to be in the range $(5.1\sim 6.3)\times 10^{-5}$.