Estimate of B ( B ¯ → X s γ ) at O ( α s 2 )

Combining our results for various $O({\ensuremath{\alpha}}_{s}^{2})$ corrections to the weak radiative $B$-meson decay, we are able to present the first estimate of the branching ratio at the next-to-next-to-leading order in QCD. We find $\mathcal{B}(\overline{B}\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma})=(3.15\ifmmode\pm\else\textpm\fi{}0.23)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ for ${E}_{\ensuremath{\gamma}}>1.6\text{ }\text{ }\mathrm{GeV}$ in the $\overline{B}$-meson rest frame. The four types of uncertainties: nonperturbative (5%), parametric (3%), higher-order (3%), and ${m}_{c}$-interpolation ambiguity (3%) have been added in quadrature to obtain the total error.