Complete O(αs4) QCD corrections to hadronic Z decays

Corrections of order α(s)(4) for the axial singlet contributions for the decay rate of the Z boson into hadrons are evaluated in the limit of the heavy top quark mass. Combined with recently finished O(α(s)(4)) calculations of the nonsinglet corrections, the new results directly lead us to the first complete O(α(s)(4)) prediction for the total hadronic decay rate of the Z boson. The new O(α(s)(4)) term in Z-decay rate leads to a significant stabilization of the perturbative series, to a reduction of the theory uncertainty in the strong coupling constant α(s), as extracted from these measurements, and to a small shift of the central value.