  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.
