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 bottom quark masses. By treating the axial neutral current in the large top-mass limit we partially re-derive in a systematic manner the known results on the contribution of the alpha(s)2 order anomalous ''double triangle'' diagrams to GAMMA(Z)A and resolve an ambiguity concerning the scale at which the strong coupling constant alpha(s) is to be taken in these diagrams. We evaluate and sum all leading log and next-to-leading log QCD corrections of orders alpha(s)1+n [ln(M(Z)/4m(t)2)]n and alpha(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. The analysis implies that the corrections might change the magnitude of the singlet term by up to 30% while they hardly might be of noticeable numerical significance in comparison with the total contribution from non-singlet terms.