Two-loop matching of the dipole operators for $b\to s\gamma$ and $b\to sgluon$

Abstract

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 one group [1], we present a detailed re-calculation using a different method. Our results are in complete agreement with those in ref. [1].

Comments: 24 pages, latex, 6 figures included