$O\left({\alpha }_s\right)$ calculation of the decays $b\to s+\gamma$ and $b\to s+g$

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% for $B(b\to s\gamma )=(4.3\mathrm{}\pm 0.37)\times {10}^{-4\mathrm{}}$.