TTP93-15 Mass Effects in Higher Order QCD Corrections to the

The partial decay rate \mbox{$\Gamma(Z\rightarrow b\bar{b})$} of

the $Z$-boson is significantly affected by 

higher order QCD corrections. Of particular interest is the influence of the non-\ vanishing bottom quark mass. Radiative corrections to the quadratic mass term of the partial $Z$-width are computed in perturbative QCD.

The calculation of the third order  

${\cal O}(\alpha_s^3 m_b^2/M_Z^2)$ contribution for the vector induced rate and of the second order ${\cal O}(\alpha_s^2 m_b^2/M_Z^2)$ correction for the axial induced rate is described. The numerical influence of the results and the theoretical uncertainties are discussed.