TTP93-07 Neutral Current in the Heavy Top Quark Limit and the Renormalization

We use a simple renormalization group argument to demonstrate that the large top mass limit of the axial neutral current in QCD is unambiguously determined by the renormalization of the singlet axial current and suggests a natural scheme independent normalization condition for the latter. By calculating the anomalous dimension of the singlet axial current at three-loop level in the $\msbar$ scheme we derive the result for the top quark decoupling from the axial neutral current valid up to (and including) the terms of order $\as^2$.