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\section{Performance of the Isolation Requirement}
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\label{app:trkvetoperf}
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The last requirement used in the analysis is an isolated track
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veto. This selection criteria rejects events containing a track of $\pt>10~\GeV$
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with relative track isolation $\sum \pt/\pt(trk)$ in a cone of size $R=0.3<0.1$. It may be noted that only tracks consistent with the
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vertex with highest $\sum \pt^2$ are considered in order to
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reduce the impact of spurious tracks, for example from pileup interactions. This requirement has very good
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performance. Figure~\ref{fig:isolvetoroc} shows the
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efficiency for rejecting dilepton events compared to the efficiency
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for selecting single lepton events for various cone sizes and cut
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values. The chosen working point provides a signal efficiency of
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$\epsilon(sig) =92\%$ for a background rejection of $\epsilon(bkg)
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=53\%$ in MC. With "signal" ("background") we are referring to \ttlj\ (\ttll\ ).
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\begin{figure}[hbt]
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\begin{center}
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\includegraphics[width=0.7\linewidth]{plots/roc_ttdl_trkiso_pt10.pdf}
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\caption{
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\label{fig:isolvetoroc}%\protect
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Comparison of the performance in terms of signal (single lepton events) efficiency
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and background (dilepton events) rejection for various cone
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sizes and cut values. The current isolation requirement uses
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a cone of size $\Delta R = 0.3$ and a cut value of 0.1,
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corresponding to $\epsilon(sig) =92\%$ for $\epsilon(bkg)=53\%$.}
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\end{center}
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\end{figure}
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It should be emphasized that the isolated track veto has a different impact on the samples with a single
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lepton (mainly \ttlj\ and \wjets) and that with two leptons (mainly \ttll).
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For the dilepton background, the veto rejects events which have a
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genuine second lepton. Thus the performance may be understood
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as an efficiency $\epsilon_{iso\ trk}$ to identify the isolated track. In the
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case of the single lepton background, the veto rejects events
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which do not have a genuine second lepton, but rather which contain
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a ``fake'' isolated track. The isolated track veto thus effectively scales the
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single lepton sample by (1-$\epsilon_{fake}$), where $\epsilon_{fake}$ is the probability to
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identify an isolated track with \pt $> 10$~\GeV in events which contain no genuine second
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lepton. It is thus necessary to study the isolated track efficiency
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$\epsilon(trk)$ and $\epsilon_{fake}$ in order to fully
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characterize the veto performance.
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The veto efficiency for dilepton events is calculated using
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the tag and probe method in \Z\ events. A good lepton
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satisfying the full ID and isolation criteria and matched to a
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trigger object serves as the tag. The probe is defined as a track with
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$\pt>10~\GeV$ that has opposite charge to the tag and has an invariant
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mass with the probe consistent with the \Z\ mass.
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%{\bf Fix me: fkw does not understand why you refer to \pt $>$ 10~\GeV here, given that in the very next paragraph you state that
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%this is measured via the absolute track isolation, implying, but not explicitly stating, that a much higher \pt\ threshold is used to get a clean Z signal. ???}
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The variable used to study the performance of the veto is the absolute track isolation,
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since it removes the dependence of the isolation variable on the \pt\ of the
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object under consideration. This is particularly useful because the
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underlying \pt\ distribution is different for second leptons in
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\ttll\ events compared to \Z\ events, particularly due to the presence of $\tau$s
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that have softer decay products. As shown in Figure~\ref{fig:absiso}, the absolute
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isolation is consistent between $\Z+4$ jet events and \ttll\ events,
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including leptons from \W\ and $\tau$ decays. This supports the notion
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that the isolation, defined as the energy surrounding the object under
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consideration, depends only on the environment of the object and not
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on the object itself. The isolation is thus sensitive to the ambient
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pileup and jet activity in the event, which is uncorrelated with
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the lepton \pt. It is thus justified to use tag and probe in
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$\Z+4$ jet events, where the jet activity is similar to \ttll\
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events in our \njets\ $>$ 4 signal region, in order to estimate the performance of the isolation
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requirement for the various leptonic categories of \ttll\ events.
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\begin{figure}[hbt]
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\begin{center}
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\includegraphics[width=0.5\linewidth]{plots/pfabsiso_njets4_log.png}%
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\includegraphics[width=0.5\linewidth]{plots/pfabsiso_njets4_clean_log.png}
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\caption{
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\label{fig:absiso}%\protect
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Comparison of absolute track isolation for track probes in
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$\Z+4$ jet and \ttll\ events for different lepton types. The
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isolation variables agree across samples, except for single
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prong $\tau$s, that tend to be slightly less isolated
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(left). The agreement across isolation distributions is
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recovered after removing single prong $\tau$ events produced
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in association with $\pi^0$s from the sample (right).}
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\end{center}
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\end{figure}
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%It may be noted that tracks from single prong $\tau$ decays are
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%slightly less isolated compared to electrons and muons. The reason is that single
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%prong $\tau$s can have $\pi^0$ associated with the single charged
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%track. These decay into $\gamma$s that in turn convert $\gamma\to e^+e^-$ and spoil the
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%isolation. As also shown in Figure~\ref{fig:absiso},
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%the isolation distribution for charged tracks from $\tau$ decays that
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%are not produced in association with $\pi^0$s are consistent with that
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%from $\E$s and $\M$s. Since events from single prong
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%$\tau$ decays produced in association with $\pi^0$s comprise a small
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%fraction of the total sample, the isolation measured for leptons is used
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%for all single prong $\tau$ events. A systematic uncertainty is
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%assigned to account for the difference in the underlying
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%isolation distribution for this sample.
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