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 nonuniversal $\log m_t$ contribution to the $Zb\bar b$ vertex.
 Publication:

arXiv eprints
 Pub Date:
 April 1995
 arXiv:
 arXiv:hepph/9504347
 Bibcode:
 1995hep.ph....4347P
 Keywords:

 High Energy Physics  Phenomenology
 EPrint:
 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 58, 1995. To appear in the proceedings