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 $Δr$ 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 $μ$ scale is the appropriate one at every stage and argue that, while matching corrections do verify the simple prescription of taking $μ\simeq m_t$ in $α_s(μ)$, logarithmic (i.e. $\sim \log m_t$) corrections do not, and require the use of the running $α_s(μ)$ in the corresponding renormalization group equations. In particular we obtain the $α_s$ correction to the non-universal $\log m_t$ contribution to the $Zb\bar b$ vertex.