Considerations Concerning the QCD Corrections to $Δρ$

Using recent results of Avdeev et al. and an expansion for $\mu_t/\mms$ ($M_t$ is the pole mass and $\mu_t\equiv \hat{m_t}(\mu_t)$ ), it is shown that when deltarho is expressed in terms of $\hat{m_t}^2(M_t)$, the QCD correction is only $(2-3)\times 10^{-3}$ in the NLO approximation. As a consequence, in terms of $M_t^2$ the correction to $\dr$ is almost entirely contained in $\mmss/M_t^2$, a pure QCD effect. The latter is studied using various optimization procedures, and the results compared with the expansion proposed by Avdeev et al.. Implications for \ew physics are discussed. Threshold effects are analyzed on the basis of a simple sum rule.