Current Algebra Approach to Heavy Top Effects in $Z \rightarrow b+ \bar{b}$

The $O(\alpha m_t^2/m_w^2)$ and $O(\alpha \alpha_s m_t^2/m_w^2)$ corrections to the partial decay width $\Gamma(Z \rightarrow b + \bar{b})$ are computed using the current algebra formulation of radiative corrections. This framework allows one to easily enforce the relevant Ward identity that greatly simplifies the calculations. As a result, the one-loop $O(\alpha m_t^2/m_w^2)$ contribution is computed through the investigation of only two convergent diagrams. The computation of the QCD corrections to the one-loop $O(\alpha m_t^2/m_w^2)$ term involves fewer diagrams than in the standard approach. In particular, the number of infrared divergent contribution is reduced. The calculation is performed in the dimensional regularization scheme and no term more divergent than $\frac{1}{n-4}$ is found. Our result confirms the screening of the one-loop top mass effect recently found by Fleischer {\em et al.}.