Abstract
We compute the sub-leading heavy quark mass corrections to the vector quark current of the effective QCD obtained after integrating out heavy quarks. The result is then used to analytically evaluate non-leading charm (top) quark mass corrections to the inclusive τ semihadronic decay rate and the Z-boson decay width into hadrons, respectively. Numerically, the corrections turn out to be small. This provides additional support to recent claims that the measurement of the decay rate suits very well the unambiguous determination of the value of the quark-gluon coupling constant α s at the scale of the τ mass.
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