QCD corrections to the Z decay rate

Corrections to the Z decay rate are calculated in perturbative QCD. The axial vector current induced rate differs in order αs2 from the rates induced by the vector current and the electromagnetic current respectively. The analytical result for the additional term is presented. Furthermore the interplay between QCD corrections and the non-vanishing mass of the b quark has an important effect on the decay rate of the Z boson. Large logarithms of MZ2/mb2 are absorbed through the use of the running b-quark mass. The next to leading corrections are evaluated in first order for the axial part of the Z decay rate, the next to leading corrections for the vector part are calculated up to and including the third order in αs. The result is applied to the Z rate and to the e+e- cross section into bantib at lower energies