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+%\section{Systematics Uncertainties on the Background Prediction}
+%\label{sec:systematics}
-<
+\subsection{Uncertainty on the \ttll\ Acceptance}
->
+In this Section we discuss the systematic uncertainty on the BG
->
+prediction.  This prediction is assembled from the event
->
+counts in the peak region of the transverse mass distribution as
->
+well as Monte Carlo
->
+with a number of correction factors, as described previously.
->
+The
->
+final uncertainty on the prediction is built up from the uncertainties in these
->
+individual
->
+components.
->
+The calculation is done for each signal
->
+region,
->
+for electrons and muons separately.
-+
+The choice to normalize to the peak region of $M_T$ has the
-+
+advantage that some uncertainties, e.g., luminosity, cancel.
-+
+It does however introduce complications because it couples
-+
+some of the uncertainties in non-trivial ways.  For example,
-+
+the primary effect of an uncertainty on the rare MC cross-section
-+
+is to introduce an uncertainty in the rare MC background estimate
-+
+which comes entirely from MC.   But this uncertainty also affects,
-+
+for example,
-+
+the $t\bar{t} \to$ dilepton BG estimate because it changes the
-+
+$t\bar{t}$ normalization to the peak region (because some of the
-+
+events in the peak region are from rare processes).  These effects
-+
+are carefully accounted for. The contribution to the overall
-+
+uncertainty from each background source is tabulated in
-+
+Section~\ref{sec:bgunc-bottomline}.
-+
+Here we discuss the uncertainties one-by-one and comment
-+
+on their impact on the overall result, at least to first order.
-+
+Second order effects, such as the one described, are also included.
-+
-+
+\subsection{Statistical uncertainties on the event counts in the $M_T$
-+
+peak regions}
-+
+These vary between 2\% and 20\%, depending on the signal region
-+
+(different
-+
+signal regions have different \met\ requirements, thus they also have
-+
+different $M_T$ regions used as control).
-+
+Since
-+
+the major backgrounds, eg, $t\bar{t}$ are normalized to the peak regions, this
-+
+fractional uncertainty is pretty much carried through all the way to
-+
+the end.  There is also an uncertainty from the finite MC event counts
-+
+in the $M_T$ peak regions.  This is also included, but it is smaller.
-+
-+
+Normalizing to the $M_T$ peak has the distinct advantages that
-+
+uncertainties on luminosity, cross-sections, trigger efficiency,
-+
+lepton ID, cancel out.
-+
+For the low statistics regions with high \met\ requirements, the
-+
+price to pay in terms of event count is that statistical uncertainties start
-+
+to become significant.  In the future we may consider a different
-+
+normalization startegy in the low statistics regions.
-+
-+
+\subsection{Uncertainty from the choice of $M_T$ peak region}
-+
-+
+This choice affects the scale factors of Table~\ref{tab:mtpeaksf}.
-+
+If the $M_T$ peak region is not well modelled, this would introduce an
-+
+uncertainty.
-+
-+
+We have tested this possibility by recalculating the post-veto scale factors for a different
-+
+choice
-+
+of $M_T$ peak region ($40 < M_T < 100$ GeV instead of the default
-+
+$50 < M_T < 80$ GeV).  This is shown in Table~\ref{tab:mtpeaksf2}.
-+
+The two results for the scale factors are very compatible.
-+
+We do not take any systematic uncertainty for this possible effect.
-+
-+
+\begin{table}[!h]
-+
+\begin{center}
-+
+{\footnotesize
-+
+\begin{tabular}{l||c|c|c|c|c|c|c}
-+
+\hline
-+
+Sample              & SRA & SRB & SRC & SRD & SRE & SRF & SRG\\
-+
+\hline
-+
+\hline
-+
+\multicolumn{8}{c}{$50 \leq \mt \leq 80$} \\
-+
+\hline
-+
+$\mu$ pre-veto \mt-SF      & $1.02 \pm 0.02$ & $0.95 \pm 0.03$ & $0.90 \pm 0.05$ & $0.98 \pm 0.08$ & $0.97 \pm 0.13$ & $0.85 \pm 0.18$ & $0.92 \pm 0.31$ \\
-+
+$\mu$ post-veto \mt-SF     & $1.00 \pm 0.02$ & $0.95 \pm 0.03$ & $0.91 \pm 0.05$ & $1.00 \pm 0.09$ & $0.99 \pm 0.13$ & $0.85 \pm 0.18$ & $0.96 \pm 0.31$ \\
-+
+\hline
-+
+$\mu$ veto \mt-SF          & $0.98 \pm 0.01$ & $0.99 \pm 0.01$ & $1.01 \pm 0.02$ & $1.02 \pm 0.04$ & $1.02 \pm 0.06$ & $1.00 \pm 0.09$ & $1.04 \pm 0.11$ \\
-+
+\hline
-+
+\hline
-+
+e pre-veto \mt-SF          & $0.95 \pm 0.02$ & $0.95 \pm 0.03$ & $0.94 \pm 0.06$ & $0.85 \pm 0.09$ & $0.84 \pm 0.13$ & $1.05 \pm 0.23$ & $1.04 \pm 0.33$ \\
-+
+e post-veto \mt-SF         & $0.92 \pm 0.02$ & $0.91 \pm 0.03$ & $0.91 \pm 0.06$ & $0.74 \pm 0.08$ & $0.75 \pm 0.13$ & $0.91 \pm 0.22$ & $1.01 \pm 0.33$ \\
-+
+\hline
-+
+e veto \mt-SF      & $0.97 \pm 0.01$ & $0.96 \pm 0.02$ & $0.97 \pm 0.03$ & $0.87 \pm 0.05$ & $0.89 \pm 0.08$ & $0.86 \pm 0.11$ & $0.97 \pm 0.14$ \\
-+
+\hline
-+
+\hline
-+
+\multicolumn{8}{c}{$40 \leq \mt \leq 100$} \\
-+
+\hline
-+
+$\mu$ pre-veto \mt-SF      & $1.02 \pm 0.01$ & $0.97 \pm 0.02$ & $0.91 \pm 0.05$ & $0.95 \pm 0.06$ & $0.97 \pm 0.10$ & $0.80 \pm 0.14$ & $0.74 \pm 0.22$ \\
-+
+$\mu$ post-veto \mt-SF     & $1.00 \pm 0.01$ & $0.96 \pm 0.02$ & $0.90 \pm 0.04$ & $0.98 \pm 0.07$ & $1.00 \pm 0.11$ & $0.80 \pm 0.15$ & $0.81 \pm 0.24$ \\
-+
+\hline
-+
+$\mu$ veto \mt-SF          & $0.98 \pm 0.01$ & $0.99 \pm 0.01$ & $0.99 \pm 0.02$ & $1.03 \pm 0.03$ & $1.03 \pm 0.05$ & $1.01 \pm 0.08$ & $1.09 \pm 0.09$ \\
-+
+\hline
-+
+\hline
-+
+e pre-veto \mt-SF          & $0.97 \pm 0.01$ & $0.93 \pm 0.02$ & $0.94 \pm 0.04$ & $0.81 \pm 0.06$ & $0.86 \pm 0.10$ & $0.95 \pm 0.17$ & $1.06 \pm 0.26$ \\
-+
+e post-veto \mt-SF         & $0.94 \pm 0.01$ & $0.91 \pm 0.02$ & $0.91 \pm 0.04$ & $0.71 \pm 0.06$ & $0.82 \pm 0.10$ & $0.93 \pm 0.17$ & $1.09 \pm 0.27$ \\
-+
+\hline
-+
+e veto \mt-SF      & $0.97 \pm 0.01$ & $0.98 \pm 0.01$ & $0.97 \pm 0.02$ & $0.88 \pm 0.04$ & $0.95 \pm 0.06$ & $0.98 \pm 0.08$ & $1.03 \pm 0.09$ \\
-+
+\hline
-+
+\end{tabular}}
-+
+\caption{ \mt\ peak Data/MC scale factors. The pre-veto SFs are applied to the
-+
+  \ttdl\ sample, while the post-veto SFs are applied to the single
-+
+  lepton samples. The veto SF is shown for comparison across channels.
-+
+  The raw MC is used for backgrounds from rare processes.
-+
+  The uncertainties are statistical only.
-+
+\label{tab:mtpeaksf2}}
-+
+\end{center}
-+
+\end{table}
-+
-+
-+
+\subsection{Uncertainty on the \wjets\ cross-section and the rare MC cross-sections}
-+
+These are taken as 50\%, uncorrelated.
-+
+The primary effect is to introduce a 50\%
-+
+uncertainty
-+
+on the $W +$ jets and rare BG
-+
+background predictions, respectively.  However they also
-+
+have an effect on the other BGs via the $M_T$ peak normalization
-+
+in a way that tends to reduce the uncertainty.  This is easy
-+
+to understand: if the $W$ cross-section is increased by 50\%, then
-+
+the $W$ background goes up.  But the number of $M_T$ peak events
-+
+attributed to $t\bar{t}$ goes down, and since the $t\bar{t}$ BG is
-+
+scaled to the number of $t\bar{t}$ events in the peak, the $t\bar{t}$
-+
+BG goes down.
-+
-+
+\subsection{Tail-to-peak ratios for lepton +
-+
+  jets top and W events}
-+
+The tail-to-peak ratios $R_{top}$ and $R_{wjet}$ are described in Section~\ref{sec:ttp}.
-+
+The data/MC scale factors are studied in CR1 and CR2 (Sections~\ref{sec:cr1} and~\ref{sec:cr2}).
-+
+Only the scale factor for \wjets, $SFR_{wjet}$, is used, and its
-+
+uncertainty is given in Table~\ref{tab:cr1yields}.
-+
+This uncertainty affects both $R_{wjet}$ and $R_{top}$.
-+
+The additional systematic uncertainty on $R_{top}$ from the variation between optimistic and pessimistic scenarios is given in Section~\ref{sec:ttp}.
-+
-+
-+
+\subsection{Uncertainty on extra jet radiation for dilepton
-+
+  background}
-+
+As discussed in Section~\ref{sec:jetmultiplicity}, the
-+
+jet distribution in
-+
+$t\bar{t} \to$
-+
+dilepton MC is rescaled by the factors $K_3$ and $K_4$ to make
-+
+it agree with the data.  The 3\% uncertainties on $K_3$ and $K_4$
-+
+comes from data/MC statistics.  This
-+
+results directly in a 3\% uncertainty on the dilepton background, which is by far
-+
+the most important one.
-+
-+
+\subsection{Uncertainty from MC statistics}
-+
+This affects mostly the \ttll\ background estimate, which is taken
-+
+from
-+
+Monte Carlo with appropriate correction factors.  This uncertainty
-+
+is negligible in the low \met\ signal regions, and grows to about
-+
+\% in SRG.
-+
-+
-+
+\subsection{Uncertainty on the \ttll\ Background}
-+
+\label{sec:ttdilbkgunc}
+The \ttbar\ background prediction is obtained from MC, with corrections
+derived from control samples in data. The uncertainty associated with
-<
+the theoretical modeling of the \ttbar\ production and decay is
-<
+estimated by comparing the background predictions obtained using
->
+the \ttbar\ background is derived from the level of closure of the
->
+background prediction in CR4 (Table~\ref{tab:cr4yields}) and
->
+CR5 (Table~\ref{tab:cr5yields}). The results from these control region
->
+checks are shown in Figure~\ref{fig:ttdlunc}. The uncertainties assigned
->
+to the \ttdl\ background prediction based on these tests are
->
+\% (SRA), 10\% (SRB), 15\% (SRC), 25\% (SRD), 40\% (SRE-G).
->
->
+\begin{figure}[hbt]
->
+  \begin{center}
->
+        \includegraphics[width=0.6\linewidth]{plots/ttdilepton_uncertainty.pdf}
->
+        \caption{
->
+          \label{fig:ttdlunc}%\protect
->
+          Results of the comparison of yields in the \mt\ tail comparing the MC prediction (after
->
+          applying SFs) to data for CR4 and CR5 for all the signal
->
+          region requirements considered (A-G). The bands indicate the
->
+          systematic uncertainties assigned based on these tests,
->
+          ranging from $5\%$ for SRA to $40\%$ for SRE-G.}
->
+      \end{center}
->
+\end{figure}
->
->
->
+\subsubsection{Check of the uncertainty on the \ttll\ Background}
->
->
+We check that the systematic uncertainty assigned to the \ttll\ background prediction
->
+covers the uncertainty associated with
->
+the theoretical modeling of the \ttbar\ production and decay
->
+by comparing the background predictions obtained using
+alternative MC samples. It should be noted that the full analysis is
+performed with the alternative samples under consideration,
+including the derivation of the various data-to-MC scale factors.
+\begin{itemize}
+\item Top mass: The alternative values for the top mass differ
-<
+  from the central value by $5~\GeV$: $m_{\mathrm{top}} = 178.5~\GeV$ and $m_{\mathrm{top}}
->
+  from the central value by $6~\GeV$: $m_{\mathrm{top}} = 178.5~\GeV$ and $m_{\mathrm{top}}
+  = 166.5~\GeV$.
+\item Jet-parton matching scale: This corresponds to variations in the
+  scale at which the Matrix Element partons from Madgraph are matched
+  value for the scale used is $Q^2 = m_{\mathrm{top}}^2 +
+  \sum_{\mathrm{jets}} \pt^2$.
+\item Alternative generators: Samples produced with different
-<
+  generators include MC@NLO and Powheg (NLO generators) and
-<
+  Pythia (LO). It may also be noted that MC@NLO uses Herwig6 for the
-<
+  hadronisation, while POWHEG uses Pythia6.
->
+  generators, Powheg (our default) and Madgraph.
+\item Modeling of taus: The alternative sample does not include
-<
+  Tauola and is otherwise identical to the Powheg sample.
->
+  Tauola and is otherwise identical to the Powheg sample.
->
+  This effect was studied earlier using 7~TeV samples and found to be negligible.
+\item The PDF uncertainty is estimated following the PDF4LHC
-<
+  recommendations[CITE]. The events are reweighted using alternative
->
+  recommendations. The events are reweighted using alternative
+  PDF sets for CT10 and MSTW2008 and the uncertainties for each are derived using the
-<
+  alternative eigenvector variations and the ``master equation''. In
-<
+  addition, the NNPDF2.1 set with 100 replicas. The central value is
->
+  alternative eigenvector variations and the ``master equation''.
->
+  The NNPDF2.1 set with 100 replicas is also used. The central value is
+  determined from the mean and the uncertainty is derived from the
+  $1\sigma$ range. The overall uncertainty is derived from the envelope of the
-<
+  alternative predictions and their uncertainties.
-<
+\end{itemize}
-<
->
+  alternative predictions and their uncertainties.
->
+  This effect was studied earlier using 7~TeV samples and found to be negligible.
->
+  \end{itemize}
+\begin{figure}[hbt]
+  \begin{center}
-<
+        \includegraphics[width=0.8\linewidth]{plots/n_dl_syst_comp.png}
->
+        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRA.pdf}%
->
+        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRB.pdf}
->
+        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRC.pdf}%
->
+        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRD.pdf}
->
+        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRE.pdf}
+        \caption{
-<
+          \label{fig:ttllsyst}%\protect
->
+          \label{fig:ttllsyst}\protect
+          Comparison of the \ttll\ central prediction with those using
+          alternative MC samples. The blue band corresponds to the
+          total statistical error for all data and MC samples. The
+          alternative sample predictions are indicated by the
+          datapoints. The uncertainties on the alternative predictions
+          correspond to the uncorrelated statistical uncertainty from
-<
+          the size of the alternative sample only.}
->
+          the size of the alternative sample only.  Note the
->
+          suppressed vertical scales.}
+      \end{center}
+    \end{figure}
-+
+\begin{table}[!h]
-+
+\begin{center}
-+
+{\footnotesize
-+
+\begin{tabular}{l||c|c|c|c|c|c|c}
-+
+\hline
-+
+$\Delta/N$  [\%] & Madgraph & Mass Up & Mass Down & Scale Up & Scale Down &
-+
+Match Up & Match Down \\
-+
+\hline
-+
+\hline
-+
+SRA      & $2$ & $2$ & $5$ & $12$ & $7$ & $0$ & $2$  \\
-+
+\hline
-+
+SRB      & $6$ & $0$ & $6$ & $5$ & $12$ & $5$ & $6$  \\
-+
+\hline
-+
+% SRC    & $10$ & $3$ & $2$ & $12$ & $14$ & $16$ & $4$  \\
-+
+% \hline
-+
+% SRD    & $10$ & $6$ & $6$ & $21$ & $15$ & $19$ & $0$  \\
-+
+% \hline
-+
+% SRE    & $6$ & $17$ & $15$ & $2$ & $12$ & $17$ & $8$  \\
-+
+\hline
-+
+\end{tabular}}
-+
+\caption{ Relative difference in \ttdl\ predictions for alternative MC
-+
+  samples in
-+
+the higher statistics regions SRA and SRB.  These differences
-+
+are based on the central values of the predictions.  For a fuller
-+
+picture
-+
+of the situation, including statistical uncertainites, see Fig.~\ref{fig:ttllsyst}.
-+
+\label{tab:fracdiff}}
-+
+\end{center}
-+
+\end{table}
-+
-+
-+
+In Fig.~\ref{fig:ttllsyst} we compare the alternate MC \ttll\ background predictions
-+
+for regions A through E.  We can make the following observations based
-+
+on this Figure.
-+
-+
+\begin{itemize}
-+
+\item In the tighter signal regions we are running out of
-+
+  statistics.
-+
+\item Within the limited statistics, there is no evidence that the
-+
+  situation changes as we go from signal region A to signal region E.
-+
+%Therefore, we assess a systematic based on the relatively high
-+
+%statistics
-+
+%test in signal region A, and apply the same systematic uncertainty
-+
+%to all other regions.
-+
+\item In signal regions B and above, the uncertainties assigned in Section~\ref{sec:ttdilbkgunc}
-+
+fully cover the alternative MC variations.
-+
+\item In order to fully (as opposed as 1$\sigma$) cover the
-+
+alternative MC variations in region A we would have to take a
-+
+systematic
-+
+uncertainty of $\approx 10\%$ instead of $5\%$.  This would be driven by the
-+
+scale up/scale down variations, see Table~\ref{tab:fracdiff}.
-+
+\end{itemize}
-+
-+
+\begin{table}[!ht]
-+
+\begin{center}
-+
+\begin{tabular}{l|c|c}
-+
+\hline
-+
+            Sample
-+
+            &                K3   & K4\\
-+
+\hline
-+
+\hline
-+
+Powheg     & $1.01 \pm 0.03$ & $0.93 \pm 0.04$ \\
-+
+Madgraph  & $1.01 \pm 0.04$ & $0.92 \pm 0.04$ \\
-+
+Mass Up    & $1.00 \pm 0.04$ & $0.92 \pm 0.04$ \\
-+
+Mass Down    & $1.06 \pm 0.04$ & $0.99 \pm 0.05$ \\
-+
+Scale Up    & $1.14 \pm 0.04$ & $1.23 \pm 0.06$ \\
-+
+Scale Down    & $0.89 \pm 0.03$ & $0.74 \pm 0.03$ \\
-+
+Match Up    & $1.02 \pm 0.04$ & $0.97 \pm 0.04$ \\
-+
+Match Down    & $1.02 \pm 0.04$ & $0.91 \pm 0.04$ \\
-+
+\hline
-+
+\end{tabular}
-+
+\caption{$\met>100$ GeV: Data/MC scale factors used to account for differences in the
-+
+  fraction of events with additional hard jets from radiation in
-+
+  \ttll\ events. \label{tab:njetskfactors_met100}}
-+
+\end{center}
-+
+\end{table}
-+
-+
-+
+However, we have two pieces of information indicating that the
-+
+scale up/scale down variations are inconsistent with the data.
-+
+These are described below.
-+
-+
+The first piece of information is that the jet multiplicity in the scale
-+
+up/scale down sample is the most inconsistent with the data.  This is shown
-+
+in Table~\ref{tab:njetskfactors_met100}, where we tabulate the
-+
+$K_3$ and $K_4$ factors of Section~\ref{sec:jetmultiplicity} for
-+
+different \ttbar\ MC samples.  The data/MC disagreement in the $N_{jets}$
-+
+distribution
-+
+for the scale up/scale down samples is also shown in Fig.~\ref{fig:dileptonnjets_scaleup}
-+
+and~\ref{fig:dileptonnjets_scaledw}.  This should be compared with the
-+
+equivalent $N_{jets}$ plots for the default Powheg MC, see
-+
+Fig.~\ref{fig:dileptonnjets}, which agrees much better with data.
-+
-+
+\begin{figure}[hbt]
-+
+  \begin{center}
-+
+        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_mueg_scaleup.pdf}
-+
+        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_diel_scaleup.pdf}%
-+
+        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_dimu_scaleup.pdf}
-+
+        \caption{
-+
+          \label{fig:dileptonnjets_scaleup}%\protect
-+
+          SCALE UP: Comparison of the jet multiplicity distribution in data and MC for dilepton events in the \E-\M\
-+
+          (top), \E-\E\ (bottom left) and \M-\M\ (bottom right) channels.}
-+
+      \end{center}
-+
+\end{figure}
-+
-+
+\begin{figure}[hbt]
-+
+  \begin{center}
-+
+        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_mueg_scaledw.pdf}
-+
+        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_diel_scaledw.pdf}%
-+
+        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_dimu_scaledw.pdf}
-+
+        \caption{
-+
+          \label{fig:dileptonnjets_scaledw}%\protect
-+
+          SCALE DOWN: Comparison of the jet multiplicity distribution in data and MC for dilepton events in the \E-\M\
-+
+          (top), \E-\E\ (bottom left) and \M-\M\ (bottom right) channels.}
-+
+      \end{center}
-+
+\end{figure}
-+
-+
-+
+\clearpage
-+
-+
+The second piece of information is that we have performed closure
-+
+tests in CR5 using the alternative MC samples.  These are exactly
-+
+the same tests as the one performed in Section~\ref{sec:CR5} on the
-+
+Powheg sample.  As we argued previously, this is a very powerful
-+
+test of the background calculation.
-+
+The results of this test are summarized in Table~\ref{tab:hugecr5yields}.
-+
+Concentrating on the relatively high statistics CR5A region, we see
-+
+for all \ttbar\ MC samples except scale up/scale down we obtain
-+
+closure within 1$\sigma$.  The scale up/scale down tests closes
-+
+worse, only within 2$\sigma$.  This again is evidence that the
-+
+scale up/scale down variations are in disagreement with the data.
-+
-+
+\input{hugeCR5Table.tex}
-+
-+
+Based on the two observations above, we argue that the MC
-+
+scale up/scale down variations are too extreme.  We feel that
-+
+a reasonable choice would be to take one-half of the scale up/scale
-+
+down variations in our MC.  This factor of 1/2 would then bring
-+
+the discrepancy in the closure test of
-+
+Table~\ref{tab:hugecr5yields} for the scale up/scale down variations
-+
+from about 2$\sigma$ to about 1$\sigma$.
-+
-+
+Then, going back to Table~\ref{tab:fracdiff}, and reducing the scale
-+
+up/scale
-+
+down variations by a factor 2, we can see that a systematic
-+
+uncertainty
-+
+of 5\% covers the range of reasonable variations from different MC
-+
+models in SRA and SRB.
-+
+%The alternative MC models indicate that a 6\% systematic uncertainty
-+
+%covers the range of reasonable variations.
-+
+Note that this 5\% is also consistent with the level at which we are
-+
+able to test the closure of the method with alternative samples in CR5 for the high statistics
-+
+regions (Table~\ref{tab:hugecr5yields}).
-+
+The range of reasonable variations obtained with the alternative
-+
+samples are consistent with the uncertainties assigned for
-+
+the \ttll\ background based on the closure of the background
-+
+predictions and data in CR4 and CR5.
-+
-+
-+
-+
-+
-+
+%\begin{table}[!h]
-+
+%\begin{center}
-+
+%{\footnotesize
-+
+%\begin{tabular}{l||c||c|c|c|c|c|c|c}
-+
+%\hline
-+
+%Sample              & Powheg & Madgraph & Mass Up & Mass Down & Scale
-+
+%Up & Scale Down &
-+
+%Match Up & Match Down \\
-+
+%\hline
-+
+%\hline
-+
+%SRA     & $579 \pm 10$ & $569 \pm 16$ & $591 \pm 18$ & $610 \pm 22$ & $651 \pm 22$ & $537 \pm 16$ & $578 \pm 18$ & $570 \pm 17$  \\
-+
+%\hline
-+
+%SRB     & $328 \pm 7$ & $307 \pm 11$ & $329 \pm 13$ & $348 \pm 15$ & $344 \pm 15$ & $287 \pm 10$ & $313 \pm 13$ & $307 \pm 12$  \\
-+
+%\hline
-+
+%SRC     & $111 \pm 4$ & $99 \pm 5$ & $107 \pm 7$ & $113 \pm 8$ & $124 \pm 8$ & $95 \pm 6$ & $93 \pm 6$ & $106 \pm 6$  \\
-+
+%\hline
-+
+%SRD     & $39 \pm 2$ & $35 \pm 3$ & $41 \pm 4$ & $41 \pm 5$ & $47 \pm 5$ & $33 \pm 3$ & $31 \pm 3$ & $39 \pm 4$  \\
-+
+%\hline
-+
+%SRE     & $14 \pm 1$ & $15 \pm 2$ & $17 \pm 3$ & $12 \pm 3$ & $15 \pm 3$ & $13 \pm 2$ & $12 \pm 2$ & $16 \pm 2$  \\
-+
+%\hline
-+
+%\end{tabular}}
-+
+%\caption{ \ttdl\ predictions for alternative MC samples. The uncertainties are statistical only.
-+
+%\label{tab:ttdlalt}}
-+
+%\end{center}
-+
+%\end{table}
-+
-+
-+
-+
-+
+%\begin{table}[!h]
-+
+%\begin{center}
-+
+%{\footnotesize
-+
+%\begin{tabular}{l||c|c|c|c|c|c|c}
-+
+%\hline
-+
+%$N \sigma$     & Madgraph & Mass Up & Mass Down & Scale Up & Scale Down &
-+
+%Match Up & Match Down \\
-+
+%\hline
-+
+%\hline
-+
+%SRA     & $0.38$ & $0.42$ & $1.02$ & $2.34$ & $1.58$ & $0.01$ & $0.33$  \\
-+
+%\hline
-+
+%SRB     & $1.17$ & $0.07$ & $0.98$ & $0.76$ & $2.29$ & $0.78$ & $1.11$  \\
-+
+%\hline
-+
+%SRC     & $1.33$ & $0.37$ & $0.26$ & $1.24$ & $1.82$ & $1.97$ & $0.54$  \\
-+
+%\hline
-+
+%SRD     & $0.82$ & $0.46$ & $0.38$ & $1.32$ & $1.27$ & $1.47$ & $0.00$  \\
-+
+%\hline
-+
+%SRE     & $0.32$ & $0.75$ & $0.66$ & $0.07$ & $0.66$ & $0.83$ & $0.38$  \\
-+
+%\hline
-+
+%\end{tabular}}
-+
+%\caption{ N $\sigma$ difference in \ttdl\ predictions for alternative MC samples.
-+
+%\label{tab:nsig}}
-+
+%\end{center}
-+
+%\end{table}
-+
-+
-+
+%\begin{table}[!h]
-+
+%\begin{center}
-+
+%\begin{tabular}{l||c|c|c|c}
-+
+%\hline
-+
+%Av. $\Delta$ Evt.     & Alt. Gen. & $\Delta$ Mass & $\Delta$ Scale
-+
+%& $\Delta$ Match \\
-+
+%\hline
-+
+%\hline
-+
+%SRA     & $5.0$ ($1\%$) & $9.6$ ($2\%$) & $56.8$ ($10\%$) & $4.4$ ($1\%$)  \\
-+
+%\hline
-+
+%SRB     & $10.4$ ($3\%$) & $9.6$ ($3\%$) & $28.2$ ($9\%$) & $2.8$ ($1\%$)  \\
-+
+%\hline
-+
+%SRC     & $5.7$ ($5\%$) & $3.1$ ($3\%$) & $14.5$ ($13\%$) & $6.4$ ($6\%$)  \\
-+
+%\hline
-+
+%SRD     & $1.9$ ($5\%$) & $0.1$ ($0\%$) & $6.9$ ($18\%$) & $3.6$ ($9\%$)  \\
-+
+%\hline
-+
+%SRE     & $0.5$ ($3\%$) & $2.3$ ($16\%$) & $1.0$ ($7\%$) & $1.8$ ($12\%$)  \\
-+
+%\hline
-+
+%\end{tabular}
-+
+%\caption{ Av. difference in \ttdl\ events for alternative sample pairs.
-+
+%\label{tab:devt}}
-+
+%\end{center}
-+
+%\end{table}
-+
-+
-+
-+
+\clearpage
+%\end{tabular}
+%\end{center}
+%\end{table}
-+
-+
+\subsection{Uncertainty from the isolated track veto}
-+
+This is the uncertainty associated with how well the isolated track
-+
+veto performance is modeled by the Monte Carlo.  This uncertainty
-+
+only applies to the fraction of dilepton BG events that have
-+
+a second e/$\mu$ or a one prong $\tau \to h$, with
-+
+$P_T > 10$ GeV in $|\eta| < 2.4$.  This fraction is about 1/3, see
-+
+Table~\ref{tab:trueisotrk}.
-+
+The uncertainty for these events
-+
+is 6\% and is obtained from tag-and-probe studies, see Section~\ref{sec:trkveto}.
-+
-+
+\begin{table}[!h]
-+
+\begin{center}
-+
+{\footnotesize
-+
+\begin{tabular}{l||c|c|c|c|c|c|c}
-+
+\hline
-+
+Sample              & SRA & SRB & SRC & SRD & SRE & SRF & SRG \\
-+
+\hline
-+
+\hline
-+
+$\mu$ Frac. \ttdl\ with true iso. trk.   & $0.32 \pm 0.03$ & $0.30 \pm 0.03$ & $0.32 \pm 0.06$ & $0.34 \pm 0.10$ & $0.35 \pm 0.16$ & $0.40 \pm 0.24$ & $0.50 \pm 0.32$  \\
-+
+\hline
-+
+\hline
-+
+e Frac. \ttdl\ with true iso. trk.       & $0.32 \pm 0.03$ & $0.31 \pm 0.04$ & $0.33 \pm 0.06$ & $0.38 \pm 0.11$ & $0.38 \pm 0.19$ & $0.60 \pm 0.31$ & $0.61 \pm 0.45$  \\
-+
+\hline
-+
+\end{tabular}}
-+
+\caption{ Fraction of \ttdl\ events with a true isolated track.
-+
+\label{tab:trueisotrk}}
-+
+\end{center}
-+
+\end{table}
-+
-+
+\subsubsection{Isolated Track Veto: Tag and Probe Studies}
-+
+\label{sec:trkveto}
-+
-+
-+
+In this section we compare the performance of the isolated track veto in data and MC using tag-and-probe studies
-+
+with samples of Z$\to$ee and Z$\to\mu\mu$. The purpose of these studies is to demonstrate that the efficiency
-+
+to satisfy the isolated track veto requirements is well-reproduced in the MC, since if this were not the case
-+
+we would need to apply a data-to-MC scale factor in order to correctly
-+
+predict the \ttll\ background.
-+
-+
+This study
-+
+addresses possible data vs. MC discrepancies for the {\bf efficiency} to identify (and reject) events with a
-+
+second {\bf genuine} lepton (e, $\mu$, or $\tau\to$1-prong). It does not address possible data vs. MC discrepancies
-+
+in the fake rate for rejecting events without a second genuine lepton; this is handled separately in the top normalization
-+
+procedure by scaling the \ttlj\ contribution to match the data in the \mt\ peak after applying the isolated track veto.
-+
-+
+Furthermore, we test the data and MC
-+
+isolated track veto efficiencies for electrons and muons since we are using a Z tag-and-probe technique, but we do not
-+
+directly test the performance for hadronic tracks from $\tau$ decays. The performance for hadronic $\tau$ decay products
-+
+may differ from that of electrons and muons for two reasons. First, the $\tau$ may decay to a hadronic track plus one
-+
+or two $\pi^0$'s, which may decay to $\gamma\gamma$ followed by a photon conversion. As shown in Figure~\ref{fig:absiso},
-+
+the isolation distribution for charged tracks from $\tau$ decays that are not produced in association with $\pi^0$s are
-+
+consistent with that from $\E$s and $\M$s. Since events from single prong $\tau$ decays produced in association with
-+
+$\pi^0$s comprise a small fraction of the total sample, and since the kinematics of $\tau$, $\pi^0$ and $\gamma\to e^+e^-$
-+
+decays are well-understood, we currently demonstrate that the isolation is well-reproduced for electrons and muons only.
-+
+Second, hadronic tracks may undergo nuclear interactions and hence their tracks may not be reconstructed.
-+
+As discussed above, independent studies show that the MC reproduces the hadronic tracking efficiency within 4\%,
-+
+leading to a total background uncertainty of less than 0.5\% (after taking into account the fraction of the total background
-+
+due to hadronic $\tau$ decays with \pt\ $>$ 10 GeV tracks), and we hence regard this effect as negligible.
-+
-+
+The tag-and-probe studies are performed in the full data sample, and compared with the DYJets madgraph sample.
-+
+All events must contain a tag-probe pair (details below) with opposite-sign and satisfying the Z mass requirement 76--106 GeV.
-+
+We compare the distributions of absolute track isolation for probe electrons/muons in data vs. MC. The contributions to
-+
+this isolation sum are from ambient energy in the event from underlying event, pile-up and jet activitiy, and hence do
-+
+not depend on the \pt\ of the probe lepton. We therefore restrict the probe \pt\ to be $>$ 30 GeV in order to suppress
-+
+fake backgrounds with steeply-falling \pt\ spectra. To suppress non-Z backgrounds (in particular \ttbar) we require
-+
+\met\ $<$ 30 GeV and 0 b-tagged events.
-+
+The specific criteria for tags and probes for electrons and muons are:
-+
-+
+%We study the isolated track veto efficiency in bins of \njets.
-+
+%We are interested in events with at least 4 jets to emulate the hadronic activity in our signal sample. However since
-+
+%there are limited statistics for Z + $\geq$4 jet events, we study the isolated track performance in events with
-+
-+
-+
+\begin{itemize}
-+
+  \item{Electrons}
-+
-+
+    \begin{itemize}
-+
+    \item{Tag criteria}
-+
-+
+      \begin{itemize}
-+
+      \item Electron passes full analysis ID/iso selection
-+
+      \item \pt\ $>$ 30 GeV, $|\eta|<2.1$
-+
+      \item Matched to the single electron trigger \verb=HLT_Ele27_WP80_v*=
-+
+      \end{itemize}
-+
-+
+    \item{Probe criteria}
-+
+      \begin{itemize}
-+
+      \item Electron passes full analysis ID selection
-+
+      \item \pt\ $>$ 30 GeV
-+
+      \end{itemize}
-+
+      \end{itemize}
-+
+  \item{Muons}
-+
+    \begin{itemize}
-+
+    \item{Tag criteria}
-+
+      \begin{itemize}
-+
+      \item Muon passes full analysis ID/iso selection
-+
+      \item \pt\ $>$ 30 GeV, $|\eta|<2.1$
-+
+      \item Matched to 1 of the 2 single muon triggers
-+
+        \begin{itemize}
-+
+        \item \verb=HLT_IsoMu30_v*=
-+
+        \item \verb=HLT_IsoMu30_eta2p1_v*=
-+
+        \end{itemize}
-+
+      \end{itemize}
-+
+    \item{Probe criteria}
-+
+      \begin{itemize}
-+
+      \item Muon passes full analysis ID selection
-+
+      \item \pt\ $>$ 30 GeV
-+
+      \end{itemize}
-+
+    \end{itemize}
-+
+\end{itemize}
-+
-+
+The absolute track isolation distributions for passing probes are displayed in Fig.~\ref{fig:tnp}. In general we observe
-+
+good agreement between data and MC. To be more quantitative, we compare the data vs. MC efficiencies to satisfy
-+
+absolute track isolation requirements varying from $>$ 1 GeV to $>$ 5 GeV, as summarized in Table~\ref{tab:isotrk}.
-+
+In the $\geq 0$ and $\geq 1$ jet bins where the efficiencies can be tested with statistical precision, the data and MC
-+
+efficiencies agree within 6\%, and we apply this as a systematic uncertainty on the isolated track veto efficiency.
-+
+For the higher jet multiplicity bins the statistical precision decreases, but we do not observe any evidence for
-+
+a data vs. MC discrepancy in the isolated track veto efficiency.
-+
-+
-+
+%This is because our analysis requirement is relative track isolation $<$ 0.1, and m
-+
+%This requirement is chosen because most of the tracks rejected by the isolated
-+
+%track veto have a \pt\ near the 10 GeV threshold, and our analysis requirement is relative track isolation $<$ 1 GeV.
-+
-+
+\begin{figure}[hbt]
-+
+  \begin{center}
-+
+        \includegraphics[width=0.3\linewidth]{plots/el_tkiso_0j.pdf}%
-+
+        \includegraphics[width=0.3\linewidth]{plots/mu_tkiso_0j.pdf}
-+
+        \includegraphics[width=0.3\linewidth]{plots/el_tkiso_1j.pdf}%
-+
+        \includegraphics[width=0.3\linewidth]{plots/mu_tkiso_1j.pdf}
-+
+        \includegraphics[width=0.3\linewidth]{plots/el_tkiso_2j.pdf}%
-+
+        \includegraphics[width=0.3\linewidth]{plots/mu_tkiso_2j.pdf}
-+
+        \includegraphics[width=0.3\linewidth]{plots/el_tkiso_3j.pdf}%
-+
+        \includegraphics[width=0.3\linewidth]{plots/mu_tkiso_3j.pdf}
-+
+        \includegraphics[width=0.3\linewidth]{plots/el_tkiso_4j.pdf}%
-+
+        \includegraphics[width=0.3\linewidth]{plots/mu_tkiso_4j.pdf}
-+
+        \caption{
-+
+          \label{fig:tnp} Comparison of the absolute track isolation in data vs. MC for electrons (left) and muons (right)
-+
+for events with the \njets\ requirement varied from \njets\ $\geq$ 0 to \njets\ $\geq$ 4.
-+
+}
-+
+      \end{center}
-+
+\end{figure}
-+
-+
+\clearpage
-+
-+
+\begin{table}[!ht]
-+
+\begin{center}
-+
+\begin{tabular}{l|c|c|c|c|c}
-+
-+
+%Electrons:
-+
+%Selection            : ((((((((((abs(tagAndProbeMass-91)<15)&&(qProbe*qTag<0))&&((eventSelection&1)==1))&&(abs(tag->eta())<2.1))&&(tag->pt()>30.0))&&(HLT_Ele27_WP80_tag > 0))&&(met<30))&&(nbl==0))&&((leptonSelection&8)==8))&&(probe->pt()>30))&&(drprobe<0.05)
-+
+%Total MC yields        : 2497277
-+
+%Total DATA yields      : 2649453
-+
+%Muons:
-+
+%Selection            : ((((((((((abs(tagAndProbeMass-91)<15)&&(qProbe*qTag<0))&&((eventSelection&2)==2))&&(abs(tag->eta())<2.1))&&(tag->pt()>30.0))&&(HLT_IsoMu24_tag > 0))&&(met<30))&&(nbl==0))&&((leptonSelection&65536)==65536))&&(probe->pt()>30))&&(drprobe<0.05)
-+
+%Total MC yields        : 3749863
-+
+%Total DATA yields      : 4210022
-+
+%Info in <TCanvas::MakeDefCanvas>:  created default TCanvas with name c1
-+
+%Info in <TCanvas::Print>: pdf file plots/nvtx.pdf has been created
-+
-+
+\hline
-+
+\hline
-+
+e + $\geq$0 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
-+
+\hline
-+
+      data   &  0.098 $\pm$ 0.0002   &  0.036 $\pm$ 0.0001   &  0.016 $\pm$ 0.0001   &  0.009 $\pm$ 0.0001   &  0.006 $\pm$ 0.0000  \\
-+
+        mc   &  0.097 $\pm$ 0.0002   &  0.034 $\pm$ 0.0001   &  0.016 $\pm$ 0.0001   &  0.009 $\pm$ 0.0001   &  0.005 $\pm$ 0.0000  \\
-+
+   data/mc   &     1.00 $\pm$ 0.00   &     1.04 $\pm$ 0.00   &     1.04 $\pm$ 0.01   &     1.03 $\pm$ 0.01   &     1.02 $\pm$ 0.01  \\
-+
-+
+\hline
-+
+\hline
-+
+$\mu$ + $\geq$0 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
-+
+\hline
-+
+      data   &  0.094 $\pm$ 0.0001   &  0.034 $\pm$ 0.0001   &  0.016 $\pm$ 0.0001   &  0.009 $\pm$ 0.0000   &  0.006 $\pm$ 0.0000  \\
-+
+        mc   &  0.093 $\pm$ 0.0001   &  0.033 $\pm$ 0.0001   &  0.015 $\pm$ 0.0001   &  0.009 $\pm$ 0.0000   &  0.006 $\pm$ 0.0000  \\
-+
+   data/mc   &     1.01 $\pm$ 0.00   &     1.03 $\pm$ 0.00   &     1.03 $\pm$ 0.01   &     1.03 $\pm$ 0.01   &     1.02 $\pm$ 0.01  \\
-+
-+
+\hline
-+
+\hline
-+
+e + $\geq$1 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
-+
+\hline
-+
+      data   &  0.110 $\pm$ 0.0005   &  0.044 $\pm$ 0.0003   &  0.022 $\pm$ 0.0002   &  0.014 $\pm$ 0.0002   &  0.009 $\pm$ 0.0002  \\
-+
+        mc   &  0.110 $\pm$ 0.0005   &  0.042 $\pm$ 0.0003   &  0.021 $\pm$ 0.0002   &  0.013 $\pm$ 0.0002   &  0.009 $\pm$ 0.0001  \\
-+
+   data/mc   &     1.00 $\pm$ 0.01   &     1.04 $\pm$ 0.01   &     1.06 $\pm$ 0.02   &     1.08 $\pm$ 0.02   &     1.06 $\pm$ 0.03  \\
-+
-+
+\hline
-+
+\hline
-+
+$\mu$ + $\geq$1 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
-+
+\hline
-+
+      data   &  0.106 $\pm$ 0.0004   &  0.043 $\pm$ 0.0003   &  0.023 $\pm$ 0.0002   &  0.014 $\pm$ 0.0002   &  0.010 $\pm$ 0.0001  \\
-+
+        mc   &  0.106 $\pm$ 0.0004   &  0.042 $\pm$ 0.0003   &  0.021 $\pm$ 0.0002   &  0.013 $\pm$ 0.0002   &  0.009 $\pm$ 0.0001  \\
-+
+   data/mc   &     1.00 $\pm$ 0.01   &     1.04 $\pm$ 0.01   &     1.06 $\pm$ 0.01   &     1.08 $\pm$ 0.02   &     1.07 $\pm$ 0.02  \\
-+
-+
+\hline
-+
+\hline
-+
+e + $\geq$2 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
-+
+\hline
-+
+      data   &  0.117 $\pm$ 0.0012   &  0.050 $\pm$ 0.0008   &  0.026 $\pm$ 0.0006   &  0.017 $\pm$ 0.0005   &  0.012 $\pm$ 0.0004  \\
-+
+        mc   &  0.120 $\pm$ 0.0012   &  0.048 $\pm$ 0.0008   &  0.025 $\pm$ 0.0006   &  0.016 $\pm$ 0.0005   &  0.011 $\pm$ 0.0004  \\
-+
+   data/mc   &     0.97 $\pm$ 0.01   &     1.05 $\pm$ 0.02   &     1.05 $\pm$ 0.03   &     1.07 $\pm$ 0.04   &     1.07 $\pm$ 0.05  \\
-+
-+
+\hline
-+
+\hline
-+
+$\mu$ + $\geq$2 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
-+
+\hline
-+
+      data   &  0.111 $\pm$ 0.0010   &  0.048 $\pm$ 0.0007   &  0.026 $\pm$ 0.0005   &  0.018 $\pm$ 0.0004   &  0.013 $\pm$ 0.0004  \\
-+
+        mc   &  0.115 $\pm$ 0.0010   &  0.048 $\pm$ 0.0006   &  0.025 $\pm$ 0.0005   &  0.016 $\pm$ 0.0004   &  0.012 $\pm$ 0.0003  \\
-+
+   data/mc   &     0.97 $\pm$ 0.01   &     1.01 $\pm$ 0.02   &     1.04 $\pm$ 0.03   &     1.09 $\pm$ 0.04   &     1.09 $\pm$ 0.04  \\
-+
-+
+\hline
-+
+\hline
-+
+e + $\geq$3 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
-+
+\hline
-+
+      data   &  0.123 $\pm$ 0.0031   &  0.058 $\pm$ 0.0022   &  0.034 $\pm$ 0.0017   &  0.023 $\pm$ 0.0014   &  0.017 $\pm$ 0.0012  \\
-+
+        mc   &  0.131 $\pm$ 0.0030   &  0.055 $\pm$ 0.0020   &  0.030 $\pm$ 0.0015   &  0.020 $\pm$ 0.0013   &  0.015 $\pm$ 0.0011  \\
-+
+   data/mc   &     0.94 $\pm$ 0.03   &     1.06 $\pm$ 0.06   &     1.14 $\pm$ 0.08   &     1.16 $\pm$ 0.10   &     1.17 $\pm$ 0.12  \\
-+
-+
+\hline
-+
+\hline
-+
+$\mu$ + $\geq$3 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
-+
+\hline
-+
+      data   &  0.121 $\pm$ 0.0025   &  0.055 $\pm$ 0.0018   &  0.033 $\pm$ 0.0014   &  0.022 $\pm$ 0.0011   &  0.017 $\pm$ 0.0010  \\
-+
+        mc   &  0.120 $\pm$ 0.0024   &  0.052 $\pm$ 0.0016   &  0.029 $\pm$ 0.0012   &  0.019 $\pm$ 0.0010   &  0.014 $\pm$ 0.0009  \\
-+
+   data/mc   &     1.01 $\pm$ 0.03   &     1.06 $\pm$ 0.05   &     1.14 $\pm$ 0.07   &     1.14 $\pm$ 0.08   &     1.16 $\pm$ 0.10  \\
-+
-+
+\hline
-+
+\hline
-+
+e + $\geq$4 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
-+
+\hline
-+
+      data   &  0.129 $\pm$ 0.0080   &  0.070 $\pm$ 0.0061   &  0.044 $\pm$ 0.0049   &  0.031 $\pm$ 0.0042   &  0.021 $\pm$ 0.0034  \\
-+
+        mc   &  0.132 $\pm$ 0.0075   &  0.059 $\pm$ 0.0053   &  0.035 $\pm$ 0.0041   &  0.025 $\pm$ 0.0035   &  0.017 $\pm$ 0.0029  \\
-+
+   data/mc   &     0.98 $\pm$ 0.08   &     1.18 $\pm$ 0.15   &     1.26 $\pm$ 0.20   &     1.24 $\pm$ 0.24   &     1.18 $\pm$ 0.28  \\
-+
-+
+\hline
-+
+\hline
-+
+$\mu$ + $\geq$4 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
-+
+\hline
-+
+      data   &  0.136 $\pm$ 0.0067   &  0.064 $\pm$ 0.0048   &  0.041 $\pm$ 0.0039   &  0.029 $\pm$ 0.0033   &  0.024 $\pm$ 0.0030  \\
-+
+        mc   &  0.130 $\pm$ 0.0063   &  0.065 $\pm$ 0.0046   &  0.035 $\pm$ 0.0034   &  0.020 $\pm$ 0.0026   &  0.013 $\pm$ 0.0022  \\
-+
+   data/mc   &     1.04 $\pm$ 0.07   &     0.99 $\pm$ 0.10   &     1.19 $\pm$ 0.16   &     1.47 $\pm$ 0.25   &     1.81 $\pm$ 0.37  \\
-+
-+
+\hline
-+
+\hline
-+
-+
+\end{tabular}
-+
+\caption{\label{tab:isotrk} Comparison of the data vs. MC efficiencies to satisfy the indicated requirements
-+
+on the absolute track isolation, and the ratio of these two efficiencies. Results are indicated separately for electrons and muons and for various
-+
+jet multiplicity requirements.}
-+
+\end{center}
-+
+\end{table}
-+
-+
+\clearpage
-+
+\subsection{Summary of uncertainties}
-+
+\label{sec:bgunc-bottomline}
-+
-+
+The contribution from each source to the total uncertainty on the background yield is given in Tables~\ref{tab:relativeuncertaintycomponents} and~\ref{tab:uncertaintycomponents} for the relative and absolute uncertainties, respectively. In the low-\met\ regions the dominant uncertainty comes from the top tail-to-peak ratio, $R_{top}$ (Section~\ref{sec:ttp}), while in the high-\met\ regions the \ttll\ systematic uncertainty dominates (Section~\ref{sec:ttdilbkgunc}).
-+
-+
+\input{uncertainties_table.tex}
-+
-+
-+
-+
-+
-+
+%Figure.~\ref{fig:reliso} compares the relative track isolation
-+
+%for events with a track with $\pt > 10~\GeV$ in addition to a selected
-+
+%muon for $\Z+4$ jet events and various \ttll\ components. The
-+
+%isolation distributions show significant differences, particularly
-+
+%between the leptons from a \W\ or \Z\ decay and the tracks arising
-+
+%from $\tau$ decays. As can also be seen in the figure, the \pt\
-+
+%distribution for the various categories of tracks is different, where
-+
+%the decay products from $\tau$s are significantly softer. Since the
-+
+%\pt\ enters the denominator of the isolation definition and hence
-+
+%alters the isolation variable...
-+
-+
+%\begin{figure}[hbt]
-+
+%  \begin{center}
-+
+%       \includegraphics[width=0.5\linewidth]{plots/pfiso_njets4_log.png}%
-+
+%       \includegraphics[width=0.5\linewidth]{plots/pfpt_njets4.png}
-+
+%       \caption{
-+
+%         \label{fig:reliso}%\protect
-+
+%          Comparison of relative track isolation variable for PF cand probe in Z+jets and ttbar
-+
+%          Z+Jets and ttbar dilepton have similar isolation distributions
-+
+%          ttbar with leptonic and single prong taus tend to be less
-+
+%          isolated. The difference in the isolation can be attributed
-+
+%          to the different \pt\ distribution of the samples, since
-+
+%          $\tau$ decay products tend to be softer than leptons arising
-+
+%          from \W\ or \Z\ decays.}
-+
+%      \end{center}
-+
+%\end{figure}
-+
-+
+%       \includegraphics[width=0.5\linewidth]{plots/pfabsiso_njets4_log.png}
-+
-+
-+
+%BEGIN SECTION TO WRITE OUT
-+
+%In detail, the procedure to correct the dilepton background is:
-+
-+
+%\begin{itemize}
-+
+%\item Using tag-and-probe studies, we plot the distribution of {\bf absolute} track isolation for identified probe electrons
-+
+%and muons {\bf TODO: need to compare the e vs. $\mu$ track iso distributions, they might differ due to e$\to$e$\gamma$}.
-+
+%\item We verify that the distribution of absolute track isolation does not depend on the \pt\ of the probe lepton.
-+
+%This is due to the fact that this isolation is from ambient PU and jet activity in the event, which is uncorrelated with
-+
+%the lepton \pt {\bf TODO: verify this in data and MC.}.
-+
+%\item Our requirement is {\bf relative} track isolation $<$ 0.1. For a given \ttll\ MC event, we determine the \pt of the 2nd
-+
+%lepton and translate this to find the corresponding requirement on the {\bf absolute} track isolation, which is simply $0.1\times$\pt.
-+
+%\item We measure the efficiency to satisfy this requirement in data and MC, and define a scale-factor $SF_{\epsilon(trk)}$ which
-+
+%is the ratio of the data-to-MC efficiencies. This scale-factor is applied to the \ttll\ MC event.
-+
+%\item {\bf THING 2 we are unsure about: we can measure this SF for electrons and for muons, but we can't measure it for hadronic
-+
+%tracks from $\tau$ decays. Verena has showed that the absolute track isolation distribution in hadronic $\tau$ tracks is harder due
-+
+%to $\pi^0\to\gamma\gamma$ with $\gamma\to e^+e^-$.}
-+
+%\end{itemize}
-+
+%END SECTION TO WRITE OUT
-+
-+
-+
+%{\bf fix me: What you have written in the next paragraph does not
-+
+%explain how $\epsilon_{fake}$ is measured.
-+
+%Why not measure $\epsilon_{fake}$ in the b-veto region?}
-+
-+
+%A measurement of the $\epsilon_{fake}$ in data is non-trivial. However, it is
-+
+%possible to correct for differences in the $\epsilon_{fake}$ between data and MC by
-+
+%applying an additional scale factor for the single lepton background
-+
+%alone, using the sample in the \mt\ peak region. This scale factor is determined after applying the isolated track
-+
+%veto and after subtracting the \ttll\ component, corrected for the
-+
+%isolation efficiency derived previously.
-+
+%As shown in Figure~\ref{fig:vetoeffcomp}, the efficiency for selecting an
-+
+%isolated track in single lepton events is independent of \mt\, so the use of
-+
+%an overall scale factor is justified to estimate the contribution in
-+
+%the \mt\ tail.
-+
+%
-+
+%\begin{figure}[hbt]
-+
+%  \begin{center}
-+
+%       \includegraphics[width=0.5\linewidth]{plots/vetoeff_comp.png}
-+
+%       \caption{
-+
+%         \label{fig:vetoeffcomp}%\protect
-+
+%          Efficiency for selecting an isolated track comparing
-+
+%          single lepton \ttlj\ and dilepton \ttll\ events in MC and
-+
+%          data as a function of \mt. The
-+
+%          efficiencies in \ttlj\ and \ttll\ exhibit no dependence on
-+
+%          \mt\, while the data ranges between the two. This behavior
-+
+%          is expected since the low \mt\ region is predominantly \ttlj, while the
-+
+%          high \mt\ region contains mostly \ttll\ events.}
-+
+%      \end{center}
-+
+%\end{figure}
-+
-+
-+
-+
+% THIS NEEDS TO BE WRITTEN

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Comparing UserCode/benhoob/cmsnotes/StopSearch/systematics.tex (file contents): Revision 1.3 by vimartin, Fri Jun 29 03:00:35 2012 UTC vs. Revision 1.26 by claudioc, Sun Oct 21 03:37:29 2012 UTC

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Comparing UserCode/benhoob/cmsnotes/StopSearch/systematics.tex (file contents):
Revision 1.3 by vimartin, Fri Jun 29 03:00:35 2012 UTC vs.
Revision 1.26 by claudioc, Sun Oct 21 03:37:29 2012 UTC