Qcd Corrections to ∆ρ*

We discuss a simple method to evaluate the QCD corrections to ∆ρ. It assumes that the perturbative expansion in terms of MS parameters is meaningful and, unlike other studies, exploits significant available information concerning O(ˆ α 2 s) corrections. This approach leads to an enhancement of ∼ 26% relative to the conventional evaluation. QCD corrections to the Z 0 → b ¯ b amplitude are also considered. Implications for electroweak physics are briefly discussed. The O(αα s) corrections to the electroweak amplitudes ∆ρ and ∆r have been the object of detailed studies in the past [1]. These analyses have been recently extended to the contributions proportional to m 2 t in the Z 0 → b ¯ b amplitude [2]. In a recent paper, Smith and Voloshin (S-V) have reexamined the O(αα s) corrections to ∆ρ by a detailed investigation of the relevant Feynman diagrams involving the t-b isodoublet [3]. Because of the large mass of the top quark and the fact that ∆ρ is evaluated at a much smaller scale, namely q 2 = 0, the conventional wisdom is that the Feynman integrals are dominated by euclidean gluon momenta k ∼ m t [4]. In fact, in most of the published calculations, ˆ α s is evaluated at m t , with the casesˆα s (2m t) andˆα s (m t /2) sometimes considered to estimate the theoretical error. However, in the case of ∆ρ, S-V find a significant sensitivity to scales ∼ 0.15m t. Specifically, employing the V-scheme running coupling [5], carrying out