Crewther, R. J.Bass, S. D.Steffens, F. M.Thomas, A. W.2022-04-292022-04-292005-04-01Nuclear Physics B - Proceedings Supplements, v. 141, n. SPEC. ISS., p. 159-164, 2005.0920-5632http://hdl.handle.net/11449/230967The 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. © 2004 Elsevier B.V. All rights reserved.159-164engArtigo10.1016/j.nuclphysbps.2004.12.0242-s2.0-12144252467