Lattice calculation of the decaysB→K*+γ andBs→φ+γ

A lattice calculation of the form factors that determine the ‘‘hadronization ratios,’’ such as ${\mathit{R}}_{\mathit{K}}^{\mathrm{*}}$ and ${\mathit{R}}_{\mathrm{\phi }}$, where ${\mathit{R}}_{\mathit{K}}^{\mathrm{*}}$≡[Γ(B→${\mathit{K}}^{\mathrm{*}}$γ)/Γ(b→sγ)], 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 (i.e., ${\mathit{T}}_2$). The data also gives strong support for the simple pole ansatz for the ${\mathit{q}}^2$ dependence of ${\mathit{T}}_2$ in the range of available ${\mathit{q}}^2$. We thus find ${\mathit{T}}_2$(0)=0.10±0.01±0.03, yielding ${\mathit{R}}_{\mathit{K}}^{\mathrm{*}}$=(6.0±1.2±3.4)%; we also find ${\mathit{R}}_{\mathrm{\phi }}$=(6.6±1.3±3.7)%.