Exact ${\alpha }_s$ Calculation of $b\to s+\gamma$, \ $b\to s+g$

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 $b\to s\gamma$. We find that higher dimensional effects are under control within $9\mathrm{\%}$ for $BR(b\rightarrow s \gamma)=(4.3\pm 0.37 )\times 10^{-4}$.