$B \to K^* + γ$ and $B_s \to ϕ+ γ$ on the Lattice

Abstract

A lattice calculation of the form factors that determine the ``hadronization ratios'', such as $R_{K^*}$ and $R_ϕ$, where $R_{K^*} \equiv [Γ($B \to K^* γ$)/Γ(b \to s γ)]$, 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 $R_{K^*} =(6.0\pm1.2\pm3.4)\%$; we also find $R_ϕ=(6.6\pm1.3\pm3.7)\%$.