Abstract
Four-body decay of the ${Z}^{0}$ into one heavy fermion (${M}_{h}\ensuremath{\ge}50$ GeV) and three light fermions has been calculated at $O({{\ensuremath{\alpha}}_{W}}^{3})$ in the $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ theory. The expression for the decay rate was derived and numerical integration over the phase space was performed. The heavy fermion was taken to be the top quark or any of the hypothetical fourth-generation quarks and leptons. For heavy-fermion mass ${M}_{h}l{M}_{W}$, the approximation of real-intermediate-$W$ production and subsequent decay was good to only about a factor of 2.5. All branching ratios are at most \ensuremath{\sim}${10}^{\ensuremath{-}7}$ (times a possibly small Kobayashi-Maskawa factor in the fourth-generation case), and decrease with increasing ${M}_{h}$.
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