B→φKandB→φXsin the heavy quark limit

We study $\overrightarrow{B}\phi K$ and $\overrightarrow{B}\phi X_s$ 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 $Br\left(\overrightarrow{B}\phi K\right)$ is predicted to be in the range $\left[F_1^{\overrightarrow{B}K}{(m}_{\phi }^2\right)/0.33\mathrm{}{]}^2(3.2\mathrm{}-4.5)\times {10}^{-6}$ that is within the one σ allowed region from the central value of $6.2\times {10}^{-6}$ measured by CLEO Collaboration, but outside the one σ allowed region from the central value of $17.2\times {10}^{-6}$ measured by BELLE Collaboration for reasonable $F_1^{\overrightarrow{B}K}.$ For the semi-inclusive decay $\overrightarrow{B}\phi X_s$ we also include initial bound state effects in the heavy quark limit that decreases the branching ratio by about 10%. $Br\left(\overrightarrow{B}\phi X_s\right)$ is predicted to be in the range $(4.8\mathrm{}-6.6)\times {10}^{-5}.$