$B\to K^{\ast }+\gamma$ and $B_s\to \varphi +\gamma$ on the Lattice

A lattice calculation of the form factors that determine the ``hadronization ratios’', such as $R_{K^{\ast }}$ and $R_{\varphi }$, where $R_{K^{\ast }}\equiv [\mathrm{\Gamma }($B \to K^* \gamma$)\mathrm{/}\mathrm{\Gamma }(b\to s\gamma )]$, is presented in the quenched approximation. Lattice data shows strong evidence for the scaling law suggested by heavy quark symmetry for one of the form factors ({\it i.e.}\ $T_2$). The data also gives strong support for the simple pole ansatz for the $q^2$ dependence of $T_2$ in the range of available $q^2$. We thus find $T_2(0) = .10 \pm.01\pm.03$yielding$R_{K^*} =(6.0\pm1.2\pm3.4)%$;wealsofind$R_{\phi}=(6.6\pm1.3\pm3.7)%$.