QCD corrections to large-mt electroweak effects in Δr. An effective field theory point of view

By using effective field theory techniques for the standard model, we discuss the issue of what μ scale is the appropriate one in the QCD corrections to the large-mt electroweak contributions to Δr. 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 μ ∼- mt in αs(μ), logarithmic (i.e. ∼ log mt corrections do not, and require the use of the running αs(μ) in the corresponding renormalization group equation.