  The apparent excess of $Z \rightarrow b \bar b$ events at LEP may be an
indication of new physics beyond the standard model. However, in either the
two-Higgs-doublet model or the minimal supersymmetric standard model, any
explanation would lead to an important new decay mode of the top quark and
suppresses the $t \rightarrow W b$ branching fraction, which goes against what
has been observed at the Tevatron. In the two-Higgs-doublet model, the
branching fraction of $Z \rightarrow b \bar b$ + a light boson which decays
predominantly into $b \bar b$ would be at least of order 10$^{-4}$.
