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\section{Model dependence of the signal acceptance}
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\label{sec:modeldependence}
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The signal acceptance for T2tt events has a significant dependence on the model parameters, particularly the mixing angle of left- and right-handed stops.
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Depending on the choice of mixing angle, the top quarks produced in the decay can have a polarization anywhere between
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$+p_{\chi_1^0}/E_{\chi^0}$ and $-p_{\chi_1^0}/E_{\chi^0}$~\cite{0811.1024}, which for a massless $\chi_1^0$ becomes $\pm 1$.
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For right-handed top quarks, the charged lepton is emitted preferentially in the direction parallel to the top velocity, resulting in larger lepton \pt\ and \mt.
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The default signal MC used in this analysis has unpolarized top quarks. We estimate the impact of the top polarization on our signal acceptance by reweighting
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our signal MC events to match the expected distribution of the charged lepton decay angle ($\theta^{*}$) corresponding to the choice of top polarizations of $\pm 1$.
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The default and reweighted $\cos\theta^{*}$ distributions are shown in Figure~\ref{fig:cosThetaStar}.
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Note that this is only an approximate study, because the angular distribution is in fact triply differential. We attempt to account for the dominant effect.
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\begin{figure}[hbt]
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\begin{center}
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\includegraphics[width=0.325\linewidth]{plots/costheta.pdf}
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\includegraphics[width=0.325\linewidth]{plots/costheta_1p.pdf}
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\includegraphics[width=0.325\linewidth]{plots/costheta_1m.pdf}
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\caption{
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\label{fig:cosThetaStar}\protect
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The default and reweighted $\cos\theta^{*}$ distributions. The $1 \pm \cos\theta^{*}$ weightings correspond to top polarizations of $\pm 1$.}
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\end{center}
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\end{figure}
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We find that reweighting to resemble a top polarization of +1 increases the signal acceptance by approximately 20-25\% relative to the default MC,
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while using a top polarization of -1 decreases the signal acceptance by a similar amount. |
