On normalization of QCD effects in $O(m_t^2)$ electroweak corrections

摘要

We point out that, contrary to some recent claims, there is no intrinsiclong-distance uncertainty in perturbative calculation of the QCD effects in the$t \tb$ and $t \bb$ loops giving the electroweak corrections proportional to$m_t^2$. If these corrections are expressed in terms of the ``on-shell" mass$m_t$, 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 isexpressed in terms of $m_t$ defined at short distances. Applying theBrodsky-Lepage-Mackenzie criterion for determining the natural scale fornormalization of $\as$, we find that using the ``on-shell" mass makes thisscale numerically small in units of $m_t$. Specifically, we find that by thiscriterion the first QCD correction to the $O(m_t^2)$ terms is determined by$\as^\msb(0.15 m_t)$. Naturally, a full calculation of three-loop graphs isneeded to completely quantify the scale.