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\section{\ttd\ Jet Multiplicity Reweighting Procedure Information}
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\label{app:ttdlnj}
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\begin{figure}[hbt]
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\begin{center}
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\includegraphics[width=0.5\linewidth]{plots/ttdl_njets_lepremoval_comp.png}
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\caption{
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\label{fig:dileptonnjets_lepcomp}%\protect
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Comparison of the jet multiplicity distribution for \ttll\
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events in MC in the signal sample before (red) and after
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(blue) applying the lepton-jet overlap removal. Note only
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the first 6 jets are shown.}
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\end{center}
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\end{figure}
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In the signal sample, leptons mis-identified as jets are not rare.
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Figure~\ref{fig:dileptonnjets_lepcomp} shows the MC jet
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multiplicity distribution for \ttll\ events satisfying the full
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selection criteria before and after subtracting leptons mis-identified
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as jets. Approximately a quarter of the sample is comprised of 4-jet
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events that actually correspond to a 2-lepton + 3 jet event where the second
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lepton is counted as a jet. Lepton mis-identification depends strongly
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on the type of second lepton, occuring more frequently in the case of
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hadronic $\tau$s than leptonic objects. According to the \ttll\
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MC, for hadronic $\tau$s, $\sim85\%$ of multi-prong $\tau$s and about half
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the single-prong $\tau$ are mis-identified as jets. In the case of
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leptonic objects, the fractions are smaller, comprising about a third
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of \E/\M\ from a \W\ decay and $<20\%$ for leptonic $\tau$s,
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mainly because of the softness of the decay products.
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The scale factors listed in Table.~\ref{tab:njetskfactors} are applied
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to the ``cleaned'' jet counts in the signal sample (shown in blue in
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Figure~\ref{fig:dileptonnjets_lepcomp}). The impact of applying the
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jet multiplicity scale factors on the \ttll\ is about a $10\%$ reduction in the
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background prediction for the signal region.
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%\begin{itemize}
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%\item Hadronic ($\tau$) objects: most multi-prong $\tau$s and about
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% half single-prong $\tau$s
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%\item Leptonic objects: smaller fraction,
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%\end{itemize}
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%Fraction of various lepton types matched to a jet
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%multi-prong taus ⟹ 85% give additional 30 GeV jet
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%single-prong taus ⟹ ~50% give additional 30 GeV jet
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%leptonic taus ⟹ <20% give additional 30 GeV jet
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%e/mu⟹ ~40% give additional 30 GeV jet
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\begin{figure}[hbt]
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\begin{center}
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\includegraphics[width=0.5\linewidth]{plots/ttdl_njets_presel_3j_comp.png}%
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\includegraphics[width=0.5\linewidth]{plots/ttdl_njets_presel_4j_comp.png}
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\caption{
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\label{fig:dileptonnjets_signalcontrol_comp}%\protect
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Comparison of the number of additional jets from radiation
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in the 3-jet (left) and $\ge4$-jet (right) bins for the control \ttll\
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sample (with two reconstructed leptons) and the signal
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sample (with one reconstructed lepton). The distributions
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show good agreement, indicating that the usage of the
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reconstructed jet multiplicity in one sample to reweight the
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signal sample is indeed justified. {\bf Fix me: Is this before or after the isolated track veto?}}
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\end{center}
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\end{figure}
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Ultimately, the interesting quantity for reweighting is the number of
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additional hard jets from radiation and this information is accessed using the
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number of reconstructed
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jets. Figure~\ref{fig:dileptonnjets_signalcontrol_comp}
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demonstrates in MC that the \ttll\ control sample, i.e. when both leptons are reconstructed,
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can indeed be used to reweight the \ttll\ signal sample, i.e. when one lepton is missed.
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The figure compares the
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number of additional jets from truth matching probed by N
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reconstructed jets, in this case 3 and $\ge4$ jets. In order to do so,
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jets that are truth-matched to the top decay products (the b-quarks
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and additional leptons) are removed. The 3-jet distribution shows
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excellent agreement and the differences in the $\ge4$-jet distribution
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are at most $5\%$. The impact of possible differences in the
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underlying distribution of extra
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jets between the signal and control \ttll\ samples are estimated by
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varying the scale factor contributions by $10\%$ and calculating the
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change in the dilepton prediction. This effect is found to have a
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negligible impact on the prediction, well below $1\%$.
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Other effects that have been examined include the impact of
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additional jets from pileup that may bias the jet multiplicity
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distribution, which is found to be a negligible effect in this dataset. The
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impact of the non-\ttll\ background on the jet fraction scale factors
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has also been studied. In particular, given the large uncertainty on
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the $\dy+HF$ MC prediction, this component has been varied by a factor
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of 2 and the resulting change on the dilepton prediction is $<1\%$. As
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a result, the dominant source of uncertainty is the statistical
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uncertainty, primarily from the two-lepton control sample size, that
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corresponds to a $3\%$ uncertainty on the dilepton prediction.
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The scale factors for the fraction of additional jets in the dilepton
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sample are applied throughout the analysis. It may be noted that this
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scaling is also performed consistently for the alternative \ttbar\
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samples, always reweighting the jet multiplicity distribution to the
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data in the \ttll\ control sample. In this way, effects truly
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arising from using different MC samples and settings can be examined,
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separately from issues related to the modeling of additional jets.
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