Corrections of order ${\cal O}(G_F M_t^2 \as^2)$ to the $\rho$ parameter

Abstract

The three-loop QCD corrections to the $\rho$ parameter from top and bottom quark loops are calculated. The result differs from the one recently calculated by Avdeev et al. As function of the pole mass the numerical value is given by $\drho=\frac{3G_F M_t^2}{8\sqrt{2}\pi^2}(1- 2.8599 \api - 14.594 (\api)^2 )$.