The $α_s^3$ Corrections to the Effective Neutral Current and to the Z Decay Rate in the Heavy Top Quark Limit

Abstract

We find the effective neutral current in the heavy top quark limit up to and including the terms of order $α_s^3$. The result is then employed to compute the correction of the same order to the axial part of the Z decay rate into hadrons ($\G^h_Z$) induced by the top-bottom quark mass splitting. The calculations confirm the prediction made in a previous work of K.G.Ch. and J.H.Kühn (Phys. Lett. B 308 (1993) 127), namely, the effect of the singlet corrections of order $α^3_s$ to the axial part of the $\G^h_Z$ should not exceed 25\% - 30\% (depending on the values chosen for $α_s(M_Z)$ and $m_t$) of the magnitude of the leading (singlet) $α_s^2$ term.