Two-loop matching of the dipole operators forb→sγandb→sg

The order ${\alpha }_s$ corrections to the Wilson coefficients of the dipole operators ${(O}_7{,O}_8)$ at the matching scale $\mu {=m}_W$ are a crucial ingredient for a complete next-to-leading logarithmic calculation of the branching ratio for $b\to s\gamma$. Given the phenomenological relevance and the fact that this two-loop calculation has been done so far only by Adel and Yao, we present a detailed recalculation using a different method. Our results are in complete agreement with those of Adel and Yao.