The $Z \to b \bar b$ Excess and Top Decay

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$^{-4}$.