Effective Lagrangian for $b \rightarrow s$ Processes with QCD-Corrections

We present a complete calculation of the effective lagrangian for $b \rightarrow s$ processes with $QCD$ corrections, in the leading logarithm approximation, for the cases $m_t=m_w$ and $m_t \gg m_w$. The effective lagrangian is then applied to estimate the $b \rightarrow s \gamma$ decay rate. We find that it is enhanced by a factor of 6 for the case $m_t=m_w$, and a factor of about 2 for $m_t \gg m_w$. Our results differ from those found in the literature, but are not very different numerically for $m_t=m_w$.