The large quark mass expansion of Λ(Z0 → hadrons) and Λ(τ− → vτ + hadrons)in the order αs3 Original Research Article

We present the analytical αs3 correction to the Z0 decay rate into hadrons. We calculate this correction up to (and including) terms of the order (mZ2/mtop2)3 in the large top quark mass expansion. We rely on the technique of the large mass expansion of individual Feynman diagrams and treat its application in detail. We convert the obtained results of six-flavour QCD to the results in the effective theory with five active flavours, checking the decoupling relation of the QCD coupling constant. We also derive the large charm quark mass expansion of the semihadronic τ lepton decay rate in the αs3 approximation.