Lattice calculation of the branching ratio for some of the exclusive modes of b-->s gamma.

We calculate the leading-order matrix element for exclusive decays of b\ensuremath{\rightarrow}s\ensuremath{\gamma} in the quenched approximation of lattice QCD on a ${24}^{3}$\ifmmode\times\else\texttimes\fi{}48 lattice at \ensuremath{\beta}=6.2, using an O(a)-improved fermion action. The matrix element is used to extract the on-shell form factor ${\mathit{T}}_{1}$(${\mathit{q}}^{2}$=0) for B\ensuremath{\rightarrow}${\mathit{K}}^{\mathrm{*}}$\ensuremath{\gamma} and ${\mathit{B}}_{\mathit{s}}$\ensuremath{\rightarrow}\ensuremath{\varphi}\ensuremath{\gamma}, using two different assumptions about the ${\mathit{q}}^{2}$ dependence of the form factors for these decays. For B\ensuremath{\rightarrow}${\mathit{K}}^{\mathrm{*}}$\ensuremath{\gamma}, ${\mathit{T}}_{1}$(${\mathit{q}}^{2}$=0) is determined to be 0.${159}_{\mathrm{\ensuremath{-}}33}^{+34}$\ifmmode\pm\else\textpm\fi{}0.067 or 0.${124}_{\mathrm{\ensuremath{-}}18}^{+20}$\ifmmode\pm\else\textpm\fi{}0.022 in the two cases. We find the results to be consistent (in the standard model) with the CLEO experimental branching ratio of B(B\ensuremath{\rightarrow}${\mathit{K}}^{\mathrm{*}}$\ensuremath{\gamma})=(4.5\ifmmode\pm\else\textpm\fi{}1.5\ifmmode\pm\else\textpm\fi{}0.9)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$.