Triviality, perturbation theory and $Z\to b\overline{b}$

Abstract

We compute the large-$m_t$ contributions to the $Zb\overline{b}$ vertex in the Standard Model non-perturbatively using both the $1/\text{nc}$ and the $1/\text{nf}$ expansions. Triviality and its consequences for the perturbative result are systematically analyzed. In particular, we point out that the effect of triviality is already important at the two-loop level for a heavy Higgs ($600\text{gev}<M_H<1\text{tev}$) even when the top mass is below $200\text{gev}$.

Comments: 12pages (incl. figs.), TIT/HEP--258,CERN-TH.7287/94