Exact $α_s$ Calculation of $b\rightarrow s + γ$, \ $b\rightarrow s + g$

We present an exact $\alpha_s$ calculation of the Wilson coefficients associated with the dipole moment operators. We also give an estimate of the branching ratio for $b\rightarrow s \gamma$. We find that higher dimensional effects are under control within $9\%$ for $BR(b\rightarrow s \gamma)=(4.3\pm 0.37 )\times 10^{-4}$.