%Title: Final-State Interactions in e^+e^- \to t\bar t \to bl^+\nu\bar bW^-        Near Top Quark Threshold
%Author: M. Peter and Y. Sumino
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\begin{document}

\begin{titlepage}
\title{Final-State Interactions in
$e^+e^- \to t\bar{t} \to bl^+\nu\bar{b}W^-$\\
Near Top Quark Threshold\footnote{
Contributed paper to 
XVIII International Symposium on Lepton-Photon Interactions, 
Hamburg, Germany, 28 July - 1 August 1997.
\\
$\rule[0mm]{5mm}{0mm}^\dagger$On 
leave of absence from Department of Physics, Tohoku University,
Sendai 980-77, Japan.
}
}
\author{ \\
M. Peter and Y. Sumino\footnote{}
\\
\\
{\normalsize \it Institut f\"ur Theoretische Teilchenphysik,
Universit\"at Karlsruhe,}\\
{\normalsize \it D-76128 Karlsruhe, Germany}}
\date{}
\maketitle
\thispagestyle{empty}
\vspace{-4.0truein}
\begin{flushright}
{\bf TTP 97-23}\\
{\bf June 1997}
\end{flushright}
%
\vspace{3.0truein}
\vspace{4cm}
\begin{abstract}
\noindent
{\small
We calculate final-state interaction
corrections to the energy-angular distribution of $l^+$ in semi-leptonic
top quark decay, where the parent top quark is
produced via $e^+e^- \to t\bar{t}$ near threshold.
These are the corrections due to gluon exchange between
$t$ and $\bar{b}$ ($\bar{t}$ and $b$) and between
$b$ and $\bar{b}$.
Combining with previously known other corrections, we explicitly
write down the $l^+$ energy-angular distribution 
including full ${\cal O}(\alpha_s)={\cal O}(\beta )$ corrections
near threshold.
Numerical analyses of the final-state interaction corrections
are presented.
We find that they deform the $l^+$ distribution 
typically at 10\% level.
Also we elucidate mechanisms of the various effects of the final-state
interactions.
We find that all qualitative features of the numerical results can be
understood from intuitive pictures.
The natures that $\bar{b}$ is emitted preferrably in the parent
$\bar{t}$'s spin direction and that there is attractive force between
$\bar{b}$ and $\bar{t}$ generate:
shift of $|\vc{p}_t|$-distribution, 
forward-backward asymmetry of $t$, 
modification of the top-quark polarization vector,
and energy-angle-correlated deformation of $l^+$ distributions.
}
\end{abstract}
\end{titlepage}
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