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\section{Background Estimation Techniques} |
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\label{sec:bkg} |
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In this section we describe the techniques used to estimate the SM backgrounds in our signal regions defined by requirements of large \MET. |
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The SM backgrounds fall into 3 categories: |
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The SM backgrounds fall into three categories: |
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\begin{itemize} |
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\item \zjets: this is the dominant background after performing the preselection. The \MET\ in \zjets\ events is estimated with the |
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\item \zjets: this is the dominant background after the preselection. The \MET\ in \zjets\ events is estimated with the |
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``\MET\ templates'' technique described in Sec.~\ref{sec:bkg_zjets}; |
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\item Flavor-symmetric (FS) backgrounds: this category includes processes which produces 2 leptons of uncorrelated flavor. It is dominated |
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by \ttbar\ but also contains Z$\to\tau\tau$, WW, and single top processes. This is the dominant contribution in the signal regions, and it |
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is estimated using a data control sample of e$\mu$ events; |
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is estimated using a data control sample of e$\mu$ events as described in Sec.~\ref{sec:bkg_fs}; |
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\item WZ and ZZ backgrounds: this background is estimated from MC, after validating the MC modeling of these processes using data control |
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samples with jets and exactly 3 leptons (WZ control sample) and exactly 4 leptons (ZZ control sample). |
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\item Rare SM backgrounds: this background contains rare processes such as $t\bar{t}$V and triple vector boson processes VVV (V=W,Z). |
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This background is estimated from MC. {\bf TODO: add rare MC} |
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samples with jets and exactly 3 leptons (WZ control sample) and exactly 4 leptons (ZZ control sample) as described in Sec.~\ref{sec:bkg_vz}; |
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%\item Rare SM backgrounds: this background contains rare processes such as $t\bar{t}$V and triple vector boson processes VVV (V=W,Z). |
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%This background is estimated from MC as described in Sec.~\ref{sec:bkg_raresm}. {\bf FIXME: add rare MC} |
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\end{itemize} |
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\subsection{Estimating the \zjets\ Background with \MET\ Templates} |
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\label{sec:bkg_zjets} |
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The premise of this data driven technique is that \MET in \zjets\ events |
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The premise of this data driven technique is that \MET\ in \zjets\ events |
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is produced by the hadronic recoil system and {\it not} by the leptons making up the Z. |
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Therefore, the basic idea of the \MET\ template method is to measure the \MET\ distribution in |
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a control sample which has no true MET and the same general attributes regarding |
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To account for kinematic differences between the hadronic systems in the control vs. signal |
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samples, we measure the \MET\ distributions in the \gjets\ sample in bins of the number of jets |
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and the scalar sum of jet transverse energies (\Ht). These \MET distributions are normalized to unit area to form ``MET templates''. |
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The prediction of the MET in each \Z event is the template which corresponds to the \njets\ and |
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\Ht in the \zjets\ event. The prediction for the \Z sample is simply the sum of all such templates. |
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These templates are displayed in App.~\ref{app:templates}. |
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and the scalar sum of jet transverse energies (\Ht). These \MET\ templates are extracted separately from the 5 single photon |
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triggers with thresholds 22, 36, 50, 75, and 90 GeV, so that the templates are effectively binned in photon \pt. |
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All \MET distributions are normalized to unit area to form ``MET templates''. |
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The prediction of the MET in each \Z event is the template which corresponds to the \njets, |
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\Ht, and Z \pt in the \zjets\ event. The prediction for the \Z sample is simply the sum of all such templates. |
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All templates are displayed in App.~\ref{app:templates}. |
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While there is in principle a small contribution from backgrounds other than \zjets\ in the preselection regions, |
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this contribution is only $\approx$3\% ($\approx$2\%) of the total sample in the inclusive search (targeted search), |
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as shown in Table~\ref{table:zyields_2j} (Table~\ref{table:zyields_2j_targeted}, and is therefore negligible compared to the total |
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as shown in Table~\ref{table:zyields_2j} (Table~\ref{table:zyields_2j_targeted}), and is therefore negligible compared to the total |
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background uncertainty. |
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\subsection{Estimating the Flavor-Symmetric Background with e$\mu$ Events} |
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\item $N_{e\mu}^{\rm{trig}} = \epsilon_{e\mu}^{\rm{trig}}N_{e\mu}^{\rm{offline}}$. |
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\end{itemize} |
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Here $N_{\ell\ell}^{\rm{trig}}$ denotes the number of selected events in the $\ell\ell$ channel passing the offline and trigger selection |
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(in other words, the number of recorded events), $\epsilon_{\ell\ell}^{\rm{trig}}$ is the trigger efficiency, and |
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$N_{e\mu}^{\rm{offline}}$ is the number of events that would have passed the offline selection if the trigger had an efficiency of 100\%. |
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Here $N_{\ell\ell}^{\rm{trig}}$ denotes the number of selected Z events in the $\ell\ell$ channel passing the offline and trigger selection |
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(in other words, the number of recorded and selected events), $\epsilon_{\ell\ell}^{\rm{trig}}$ is the trigger efficiency, and |
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$N_{\ell\ell}^{\rm{offline}}$ is the number of events that would have passed the offline selection if the trigger had an efficiency of 100\%. |
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Thus we calculate the quantity: |
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\begin{equation} |
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\end{equation} |
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Here we have used the Z$\to\mu\mu$ and Z$\to$ee yields from Table~\ref{table:zyields_2j} and the trigger efficiencies quoted in Sec.~\ref{sec:datasets}. |
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The indicated uncertainty is due to the 3\% uncertainties in the trigger efficiencies. {\bf TODO: check for variation w.r.t. lepton \pt}. |
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The indicated uncertainty is due to the 3\% uncertainties in the trigger efficiencies. %{\bf FIXME: check for variation w.r.t. lepton \pt}. |
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The predicted yields in the ee and $\mu\mu$ final states are calculated from the observed e$\mu$ yield as |
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\begin{itemize} |
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\item $N_{ee}^{\rm{predicted}} = \frac {N_{e\mu}^{\rm{trig}}} {\epsilon_{e\mu}^{\rm{trig}}} \frac {\epsilon_{ee}^{\rm{trig}}} {2 R_{\mu e}} |
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= \frac{N_{e\mu}^{\rm{trig}}}{0.92}\frac{0.95}{2\times1.26} = (0.41\pm0.04) \times N_{e\mu}^{\rm{trig}}$ , |
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= \frac{N_{e\mu}^{\rm{trig}}}{0.92}\frac{0.95}{2\times1.26} = (0.41\pm0.05) \times N_{e\mu}^{\rm{trig}}$ , |
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\item $N_{\mu\mu}^{\rm{predicted}} = \frac {N_{e\mu}^{\rm{trig}}} {\epsilon_{e\mu}^{\rm{trig}}} \frac {\epsilon_{\mu\mu}^{\rm{trig}} R_{\mu e}} {2} |
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= \frac {N_{e\mu}^{\rm{trig}}} {0.95} \frac {0.88 \times 1.26}{2} = (0.58\pm0.06) \times N_{e\mu}^{\rm{trig}}$, |
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= \frac {N_{e\mu}^{\rm{trig}}} {0.95} \frac {0.88 \times 1.26}{2} = (0.58\pm0.07) \times N_{e\mu}^{\rm{trig}}$, |
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\end{itemize} |
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and the predicted yield in the combined ee and $\mu\mu$ channel is simply the sum of these two predictions: |
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\item $N_{ee+\mu\mu}^{\rm{predicted}} = (0.99\pm0.06)\times N_{e\mu}^{\rm{trig}}$. |
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\end{itemize} |
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Note that the relative uncertainty in the combined ee and $\mu\mu$ prediction is smaller than the those for the individual ee and $\mu\mu$ predictions |
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because the uncertainty in $R_{\mu e}$ cancels when summing the ee and $\mu\mu$ predictions. {\bf N.B. these uncertainties are preliminary}. |
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Note that the relative uncertainty in the combined ee and $\mu\mu$ prediction is smaller than those for the individual ee and $\mu\mu$ predictions |
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because the uncertainty in $R_{\mu e}$ cancels when summing the ee and $\mu\mu$ predictions. %{\bf N.B. these uncertainties are preliminary}. |
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To improve the statistical precision of the FS background estimate, we remove the requirement that the e$\mu$ lepton pair falls in the Z mass window. |
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Instead we scale the e$\mu$ yield by $K$, the efficiency for e$\mu$ events to satisfy the Z mass requirement, extracted from simulation. In Fig.~\ref{fig:K_incl} |
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The efficiency for e$\mu$ events to satisfy the dilepton mass requirement, $K$, in data and simulation for inclusive \MET\ intervals (left) and |
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exclusive \MET\ intervals (right) for the inclusive analysis. Based on this we chose $K=0.14\pm0.02$ for all \MET\ regions except \MET\ $>$ 300 GeV, |
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where we chose $K=0.14\pm0.08$. |
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{\bf plots made with 10\% of \zjets\ MC statistics, to be remade with full statistics} |
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%{\bf FIXME plots made with 10\% of \zjets\ MC statistics, to be remade with full statistics} |
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\label{fig:K_incl} |
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} |
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\end{center} |
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exclusive \MET\ intervals (right) for the targeted analysis, including the b-veto. |
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Based on this we chose $K=0.13\pm0.02$ for the \MET\ regions up to \MET\ $>$ 100 GeV. |
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For higher \MET\ regions we chose $K=0.13\pm0.07$. |
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{\bf plots made with 10\% of \zjets\ MC statistics, to be remade with full statistics} |
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%{\bf FIXME plots made with 10\% of \zjets\ MC statistics, to be remade with full statistics} |
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\label{fig:K_targeted} |
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} |
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\end{center} |
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and we therefore check that the MC does a reasonable job of reproducing the \pt distributions of the |
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leptonically decaying \Z. While the inclusive WZ yields are in reasonable agreement, we observe |
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an excess in data in events with at least 2 jets, corresponding to the jet multiplicity requirement |
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in our preselection. We observe 60 events in data while the MC predicts $34\pm5.2$~(stat)), representing an excess of 78\%, |
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as indicated in Table~\ref{tab:wz2j}. |
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We note some possible causes for this discrepancy: |
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in our preselection. We observe 60 events in data while the MC predicts $34\pm5.2$~(stat), representing an excess of 78\%, |
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as indicated in Table~\ref{tab:wz2j}. We note some possible contributions to this discrepancy: |
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\begin{itemize} |
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yield passing a \MET $>$ 50 GeV requirement is under-estimated in MC and second, because the fake |
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rate is typically under-estimated in the MC. To get a rough idea for how much the excess depends |
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on the \zjets\ yield, if the \zjets\ yield is doubled then the excess is reduced from 78\% to 55\%. |
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{\bf currently using 10\% of \zjets\ MC, and there is 1 event with a weight of about 5, plots and tables to be remade with full \zjets\ stats}. |
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Also note that we are currently using 10\% of the \zjets\ MC sample and there is 1 event with a weight |
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of about 5, so the plots and tables will be remade with full \zjets\ sample. |
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\item The \ttbar\ contribution is under-estimated here because the fake |
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rate is typically under-estimated in the MC. To get a rough idea for how much the excess depends |
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on the \ttbar\ yield, if the \ttbar\ yield is doubled then the excess is reduced from 78\% to 57\%. |
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\item Currently no attempt is made to reject jets from pile-up interactions, which may be responsible |
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for some of this excess. To check this, we increase the jet \pt requirement to 40 GeV which |
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helps to suppress PU jets and observe 39 events in data vs. an MC prediction of $25\pm5.2$~(stat), |
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for some of the excess at large \njets. To check this, we increase the jet \pt threhsold to 40 GeV, which |
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helps to suppress PU jets, and observe 39 events in data vs. an MC prediction of $25\pm5.2$~(stat), |
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decreasing the excess from 78\% to 58\%. In the future this may be improved by explicitly |
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requiring the jets to be consistent with originating from the signal primary vertex. |
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\caption{\label{tab:wz} Data and Monte Carlo yields passing the WZ preselection. } |
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\begin{tabular}{lccccc} |
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\hline |
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+ |
\hline |
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Sample & ee & $\mu\mu$ & e$\mu$ & total \\ |
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\hline |
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WZ & 58.9 $\pm$ 0.7 & 82.2 $\pm$ 0.8 & 4.0 $\pm$ 0.2 &145.1 $\pm$ 1.0 \\ |
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\caption{\label{tab:wz2j} Data and Monte Carlo yields passing the WZ preselection and \njets\ $>$ 2. } |
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\begin{tabular}{lccccc} |
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\hline |
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Sample & ee & $\mu\mu$ & e$\mu$ & total \\ |
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\hline |
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Sample & ee & $\mu\mu$ & e$\mu$ & total \\ |
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\hline |
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WZ & 9.8 $\pm$ 0.3 & 13.3 $\pm$ 0.3 & 0.6 $\pm$ 0.1 & 23.6 $\pm$ 0.4 \\ |
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\ttbar & 0.2 $\pm$ 0.2 & 2.0 $\pm$ 0.9 & 2.2 $\pm$ 1.2 & 4.4 $\pm$ 1.5 \\ |
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WW & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.1 $\pm$ 0.0 \\ |
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single top & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 \\ |
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\hline |
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tot SM MC & 10.3 $\pm$ 0.3 & 20.8 $\pm$ 5.0 & 2.8 $\pm$ 1.2 & 33.8 $\pm$ 5.2 \\ |
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\hline |
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total SM MC & 10.3 $\pm$ 0.3 & 20.8 $\pm$ 5.0 & 2.8 $\pm$ 1.2 & 33.8 $\pm$ 5.2 \\ |
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data & 23 & 32 & 5 & 60 \\ |
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\hline |
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\hline |
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The data and MC yields passing the above selection are in Table~\ref{tab:zz}. Again we observe an |
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excess in data with respect to the MC prediction (29 observed vs. $17.3\pm0.1$~(stat) MC predicted). |
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After requiring at least 2 jets, we observe 2 events and the MC predicts $1.5\pm0.1$~(stat). |
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Based on this we apply an uncertainty of 80\% to the ZZ background. |
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However, we have recently discovered that we may be using the wrong (too small) cross section for the ZZ sample, |
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and we are in contact with the MC generator group to determine the correct cross section. |
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Based on this we currently apply an uncertainty of 80\% to the ZZ background. |
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\begin{table}[htb] |
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\begin{center} |
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\caption{\label{tab:zz} Data and Monte Carlo yields for the ZZ preselection. } |
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\begin{tabular}{lccccc} |
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\hline |
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Sample & ee & $\mu\mu$ & e$\mu$ & total \\ |
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\hline |
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Sample & ee & $\mu\mu$ & e$\mu$ & total \\ |
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\hline |
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ZZ & 6.6 $\pm$ 0.0 & 9.9 $\pm$ 0.0 & 0.4 $\pm$ 0.0 & 17.0 $\pm$ 0.1 \\ |
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WZ & 0.1 $\pm$ 0.0 & 0.2 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.3 $\pm$ 0.0 \\ |
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single top & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 \\ |
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\hline |
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total SM MC & 6.7 $\pm$ 0.0 & 10.1 $\pm$ 0.1 & 0.5 $\pm$ 0.0 & 17.3 $\pm$ 0.1 \\ |
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\hline |
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data & 13 & 16 & 0 & 29 \\ |
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\hline |
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– |
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\hline |
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\end{tabular} |
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\end{center} |
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\begin{center} |
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\includegraphics[width=1\linewidth]{plots/ZZ.pdf} |
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\caption{\label{fig:zz}\protect |
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Data vs. MC comparisons for the $ZZ$ selection discussed in the text for \lumi. |
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The number of jets, missing transverse energy, and $Z$ boson transverse momentum are displayed. |
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Data vs. MC comparisons for the ZZ selection discussed in the text for \lumi. |
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The number of jets, missing transverse energy, and Z boson transverse momentum are displayed. |
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} |
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\end{center} |
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\end{figure} |
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\subsection{Estimating the Rare SM Backgrounds with MC} |
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\label{sec:bkg_raresm} |
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%\subsection{Estimating the Rare SM Backgrounds with MC} |
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%\label{sec:bkg_raresm} |
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|
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{\bf TODO: list samples, yields in preselection region, and \MET distribution} |
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%{\bf TODO: list samples, yields in preselection region, and show \MET\ distribution} |
