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\vbox{
{\bf TTP93-34}\\
{\bf December 1993}\\
 }
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\begin{large}
HADRON RADIATION IN LEPTONIC $Z$ DECAYS\\[0.3cm]
\end{large}
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\begin{large}
A.H. Hoang, M. Je\.zabek, J.H. K\"uhn and T. Teubner\\[1.0cm]
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\begin{large}
{\bf ERRATUM}\\[1.0cm]
\end{large}
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As a consequence of an error in the FORTRAN code the numerical
values of the predictions for the four fermion (quarks and leptons)
final states have to be slightly modified.\\
Eq.(15) should be modified to
\begin{eqnarray}
\frac{\Gamma_{l\bar l u\bar u}}{\Gamma_{l\bar l}}&amp;=&amp;
4\frac{\Gamma_{l\bar l d\bar d}}{\Gamma_{l\bar l}}=
4\frac{\Gamma_{l\bar l s\bar s}}{\Gamma_{l\bar l}}=2.256\times
10^{-4}\,,\nonumber\\
\frac{\Gamma_{l\bar l c\bar c}}{\Gamma_{l\bar l}}&amp;=&amp;5.259\times
10^{-5}\,,\nonumber\\
\frac{\Gamma_{l\bar l b\bar b}}{\Gamma_{l\bar l}}&amp;=&amp;2.858\times
10^{-6}\,,\nonumber\\
\frac{\Gamma_{l\bar l had}}{\Gamma_{l\bar l}}&amp;=&amp;3.938\times 10^{-4}\,.
\label{equ.14a}
\end{eqnarray}
The relative rates for the four lepton final states quoted after
eq.(16) are modified as follows:\\[0.1cm]
\hspace*{1em} $\Gamma_{e^+e^- l \bar l} / \Gamma_{e^+e^-}$ 
are $3.319 \times 10^{-4}$ for $l=\mu$
and $3.214 \times 10^{-5}$ for $l=\tau$.\\[0.2cm]
The relative rates for secondary QCD radiation of heavy quarks are\\[0.1cm]
\hspace*{1em} $1.545\times 10^{-3}/1.391\times 10^{-3}/1.301\times 10^{-3}$
for $m_b=4.5/4.8/5.0$ GeV,\\
\hspace*{1em} $8.339\times 10^{-3}/7.107\times 10^{-3}/5.729\times 10^{-3}$
for $m_c=1.3/1.5/1.8$ GeV and $\alpha_s=0.12$.
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