LOOKING AT THE QCD CORRECTIONS FOR LARGE $M_t$: AN EFFECTIVE LAGRANGIAN POINT OF VIEW

Abstract

We discuss the QCD corrections to the large-$m_t$ electroweak contributions to $\Delta r$ and to the process $Z\to b\bar{b}$ as two of the most representative examples. This needs the construction of an effetive field theory below the top quark. We discuss the issue of what $\mu$ scale is the appropriate one at every stage and argue that, while matching corrections do verify the simple prescription of taking $\mu \simeq m_t$ in ${\alpha }_s(\mu )$, logarithmic (i.e. $\sim \log m_t$) corrections do not, and require the use of the running ${\alpha }_s(\mu )$ in the corresponding renormalization group equations. In particular we obtain the ${\alpha }_s$ correction to the non-universal $\log m_t$ contribution to the $Zb\bar{b}$ vertex.

Comments: Latex with macro appended at the beginning of file. Talk given at the Ringberg Workshop ``Perspectives for electroweak interactions in $e^{+}{e}^{-}$ collisions", Ringberg Castle, Germany, February 5--8, 1995. To appear in the proceedings