The ${\alpha }_s^3$ 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 ${\alpha }_s^3$. The result is then employed to compute the correction of the same order to the axial part of the Z decay rate into hadrons (${\text{G}}_Z^h$) 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 ${\alpha }_s^3$ to the axial part of the ${\text{G}}_Z^h$ should not exceed 25\% - 30\% (depending on the values chosen for ${\alpha }_s(M_Z)$ and $m_t$) of the magnitude of the leading (singlet) ${\alpha }_s^2$ term.

Comments: 11 pages, LATEX, no figures, Preprint TTP93-38,INR-842/93 , December 1993