QCD corrections to large-$m_t$ electroweak effects in $\Delta r$. An effective field theory point of view

Abstract

By using effective field theory techniques for the standard model, we discuss the issue of what $\mu$ scale is the appropriate one in the QCD corrections to the large-$\text{mt}$ electroweak contributions to $\Delta r$. This needs the construction of an effective field theory below the top quark. We argue that, while matching corrections do verify the simple prescription of taking $\mu \simeq \text{mt}$ in $\text{a}(\text{m})$, logarithmic (i.e. $\sim \log \text{mt}$) corrections do not, and require the use of the running $\text{a}(\mu )$ in the corresponding renormalization group equation.

Comments: 13 pages and one figure available by fax from peris@cernvm.cern.ch TeX file. Uses phyzzx. CERN-TH-7446/94. Section on $Z\to b\bar{b}$ is removed