Normalization of QCD effects on O(mt2) electroweak corrections

We point out that, contrary to some recent claims, there is no intrinsic long-distance uncertainty in the perturbative calculation of the QCD effects in the tt̄ and tb̄ loops giving the electroweak corrections proportional to mt2. If these corrections are expressed in terms of the "on-shell" mass mt, the only ambiguity arising is that associated with the definition of the "on-shell" mass of a quark. The latter is entirely eliminated if the result is expressed in terms of mt defined at short distances. Applying the Brodsky-Lepage-Mackenzie criterion for determining the natural scale for normalization of αs, we find that using the "on-shell" mass makes this scale numerically small in units of mt. Specifically, we find that by this criterion the first QCD correction to the O(mt2) terms is determined by αsMS̄(0.15mt). Naturally, a full calculation of three-loop graphs is needed to completely quantify the scale.