COMPLETE QCD CORRECTIONS OF ORDER ALPHA(S)(2) TO THE Z DECAY-RATE

The axial part of the Z decay rate into hadrons (GAMMA(Z)A) gets extra singlet contributions due to the huge splitting between top and botto m quark masses. By treating the axial neutral current in the large top -mass limit we partially re-derive in a systematic manner the known re sults on the contribution of the alpha(s)2 order anomalous ''double tr iangle'' diagrams to GAMMA(Z)A and resolve an ambiguity concerning the scale at which the strong coupling constant alpha(s) is to be taken i n these diagrams. We evaluate and sum all leading log and next-to-lead ing log QCD corrections of orders alpha(s)1+n [ln(M(Z)/4m(t)2)]n and a lpha(s)2+n [ln (M(Z)/4m(t)2]n respectively. We examine the sensitivity of our results to a change of the renormalization scales to estimate the size of yet unknown corrections of order alpha(s)3 to GAMMA(Z)A. T he analysis implies that the corrections might change the magnitude of the singlet term by up to 30% while they hardly might be of noticeabl e numerical significance in comparison with the total contribution fro m non-singlet terms.