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Patrick Janot edited Theory.tex
about 9 years ago
Commit id: b00b106c280384c0f29265f09750073271c22e20
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\begin{equation}
{{\rm d}^2\sigma \over {\rm d}x {\rm d}\cos\theta} = {3\pi\beta\alpha^2(s) \over 2s} B_\ell S_\ell(x,\cos\theta),
\end{equation}
where $\beta$ is the top velocity, $s$ is the centre-of-mass energy squared, $\alpha(s)$ is the QED running coupling constant, and $B_\ell$ is the fraction of ${\rm t\bar t}$ events with at least one top quark decaying leptonically (about 44\%). As the non-standard form factors
$\delta(A,B,C,D)_v$ $\delta(A,B,C,D)_v \equiv \delta_i$ are supposedly small, only the terms linear in
$\delta(A,B,C,D)_v \equiv \delta_i$ $\delta_i$ are kept:
\begin{equation}
S(x,\theta) = S^0(x,\theta) + \sum_{i=1}^8 \delta_i f_i(x,\cos\theta),
\end{equation}
where $x$ and $\theta$ are the lepton (reduced) energy and the polar angle, respectively, and $S^0$ is the standard-model contribution. The eight distributions
$f_i(x,\cos\theta)$ ($\equiv f_{A,B,C,D}^{\gamma, Z}$) $f_{A,B,C,D}^{\gamma, Z}(x,\cos\theta) \equiv f_i(x,\cos\theta)$ and the standard model contribution $S^0$ are shown in Fig.~\ref{fig:distributions} at $\sqrt{s} = 360$\,GeV and with no incoming beam polarization.