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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 four 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 the preselection. The \MET\ in \zjets\ events is estimated with the |
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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) 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 TODO: add rare MC} |
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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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\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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\end{itemize} |
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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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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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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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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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\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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{\bf TODO: list samples, yields in preselection region, and show \MET\ distribution} |
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%{\bf TODO: list samples, yields in preselection region, and show \MET\ distribution} |
