Decoupling heavy particles simultaneously

Abstract

The renormalization group is extended to cases where several heavy particles are decoupled at the same time. This involves large logarithms which are scale-invariant and so cannot be eliminated by a change of renormalization scheme. A set of scale-invariant running couplings, one for each heavy particle, is constructed without reference to intermediate thresholds. The entire heavy-quark correction to the axial charge of the weak neutral current is derived to next-to-leading order, and checked in leading order by evaluating diagrams explicitly. The mechanism for cancelling contributions from the top and bottom quarks in the equal-mass limit is surprisingly non-trivial.

6 pages, 4 figures. Talk presented at the "QCD Down Under" Workshop, Barossa Valley and Adelaide, Australia, 10-19 March 2004, with ref 8 now linked to hep-ph/0507278