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%\clearpage
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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 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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``\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 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 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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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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fake MET as in \zjets\ events. We thus use a sample of \gjets\ events, since both \zjets\
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and \gjets\ events consist of a well-measured object recoiling against hadronic jets.
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For selecting photon-like objects, the very loose photon selection described in Sec.~\ref{sec:phosel} is used.
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It is not essential for the photon sample to have high purity. For our purposes, selecting jets with predominantly
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electromagnetic energy deposition in a good fiducial volume suffices to ensure that
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they are well measured and do not contribute to fake \MET. The \gjets\ events are selected with a suite of
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single photon triggers with \pt thresholds varying from 22--90 GeV. The events are weighted by the trigger prescale
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such that \gjets\ events evenly sample the conditions over the full period of data taking.
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There remains a small difference in the PU conditions in the \gjets\ vs. \zjets\ samples due to the different
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dependencies of the $\gamma$ vs. Z isolation efficiencies on PU. To account for this, we reweight the \gjets\ samples
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to match the distribution of reconstructed primary vertices in the \zjets\ sample.
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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\ 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$2\%) of the total sample in the inclusive search (targeted search),
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as shown in Table~\ref{table:zyields_2j} (Table~\ref{table:zyields_2j_targeted}), and is therefore negligible compared to the total
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background uncertainty.
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\subsection{Estimating the Flavor-Symmetric Background with e$\mu$ Events}
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\label{sec:bkg_fs}
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In this subsection we describe the background estimate for the FS background. Since this background produces equal rates of same-flavor (SF)
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ee and $\mu\mu$ lepton pairs as opposite-flavor (OF) e$\mu$ lepton pairs, the OF yield can be used to estimate the SF yield, after
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correcting for the different electron vs. muon offline selection efficiencies and the different efficiencies for the ee, $\mu\mu$, and e$\mu$ triggers.
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An important quantity needed to translate from the OF yield to a prediction for the background in the SF final state is the ratio
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$R_{\mu e} = \epsilon_\mu / \epsilon_e$, where $\epsilon_\mu$ ($\epsilon_e$) indicates the offline muon (electron) selection efficiency.
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This quantity can be extracted from data using the observed Z$\to\mu\mu$ and Z$\to$ee yields in the preselection region, after correcting
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for the different trigger efficiencies.
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Hence we define:
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\begin{itemize}
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\item $N_{ee}^{\rm{trig}} = \epsilon_{ee}^{\rm{trig}}N_{ee}^{\rm{offline}}$,
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\item $N_{\mu\mu}^{\rm{trig}} = \epsilon_{\mu\mu}^{\rm{trig}}N_{\mu\mu}^{\rm{offline}}$,
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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 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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R_{\mu e} = \sqrt{\frac{N_{\mu\mu}^{\rm{offline}}}{N_{ee}^{\rm{offline}}}} = \sqrt{\frac{N_{\mu\mu}^{\rm{trig}}/\epsilon_{\mu\mu}^{\rm{trig}}}{N_{ee}^{\rm{trig}}/\epsilon_{ee}^{\rm{trig}}}}
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= \sqrt{\frac{80367/0.88}{54426/0.95}} = 1.26\pm0.07.
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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 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 $N_{ee}^{\rm{predicted}} = \frac {N_{e\mu}^{\rm{trig}}} {\epsilon_{e\mu}^{\rm{trig}}} \frac {\epsilon_{ee}^{\rm{trig}}} {2 R_{\mu e}}
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= \frac{N_{e\mu}^{\rm{trig}}}{0.92}\frac{0.95}{2\times1.26} = (0.41\pm0.05) \times N_{e\mu}^{\rm{trig}}$ ,
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\item $N_{\mu\mu}^{\rm{predicted}} = \frac {N_{e\mu}^{\rm{trig}}} {\epsilon_{e\mu}^{\rm{trig}}} \frac {\epsilon_{\mu\mu}^{\rm{trig}} R_{\mu e}} {2}
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= \frac {N_{e\mu}^{\rm{trig}}} {0.95} \frac {0.88 \times 1.26}{2} = (0.58\pm0.07) \times N_{e\mu}^{\rm{trig}}$,
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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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\begin{itemize}
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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 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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we display the value of $K$ in data and simulation, for a variety of \MET\ requirements, for the inclusive analysis. Based on this we chose $K=0.14\pm0.02$
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for all \MET\ regions except for \MET\ $>$ 300 GeV. For this region the statistical precision is reduced, so that we inflate the uncertainty and chose $K=0.14\pm0.08$.
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The corresponding plot for the targeted analysis, including the b-veto, is displayed in Fig.~\ref{fig:K_targeted}.
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Based on this we chose $K=0.13\pm0.02$
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for all \MET\ regions up to \MET\ $>$ 100 GeV. For higher \MET\ regions (\MET\ $>$ 150 GeV and above) the statistical precision is reduced,
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so that we inflate the uncertainty and chose $K=0.13\pm0.07$.
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\begin{figure}[!ht]
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\begin{center}
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\begin{tabular}{cc}
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\includegraphics[width=0.4\textwidth]{plots/K_incl.pdf} &
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\includegraphics[width=0.4\textwidth]{plots/K_excl.pdf} \\
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\end{tabular}
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\caption{
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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 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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\end{figure}
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\begin{figure}[!hb]
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\begin{center}
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\begin{tabular}{cc}
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\includegraphics[width=0.4\textwidth]{plots/extractK_inclusive_bveto.pdf} &
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\includegraphics[width=0.4\textwidth]{plots/extractK_exclusive_bveto.pdf} \\
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\end{tabular}
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\caption{
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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 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 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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\end{figure}
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\clearpage
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\subsection{Estimating the WZ and ZZ Background with MC}
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\label{sec:bkg_vz}
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Backgrounds from W($\ell\nu$)Z($\ell\ell$) where the W lepton is not identified or is outside acceptance, and Z($\nu\nu$)Z($\ell\ell$),
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are estimated from simulation. The MC modeling of these processes is validated by comparing the MC predictions with data in control samples
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with exactly 3 leptons (WZ control sample) and exactly 4 leptons (ZZ control sample).
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The relevant WZ and ZZ MC samples are:
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\begin{itemize}
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\footnotesize{
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\item \verb=/WZJetsTo3LNu_TuneZ2_8TeV-madgraph-tauola/Summer12-PU_S7_START52_V9-v2/AODSIM= ($\sigma=1.058$ pb),
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\item \verb=/ZZJetsTo4L_TuneZ2star_8TeV-madgraph-tauola/Summer12-PU_S7_START52_V9-v3/AODSIM= ($\sigma=0.093$ pb),
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}
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\end{itemize}
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The WZJetsTo2L2Q, ZZJetsTo2L2Q, and ZZJetsTo2L2Nu samples are also used in this analysis but their contribution to the 3-lepton and 4-lepton
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control samples is negligible.
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\subsubsection{WZ Validation Studies}
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\label{sec:bkg_wz}
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A pure WZ sample can be selected in data with the requirements:
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\begin{itemize}
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\item Exactly 3 $p_T>20$~GeV leptons passing analysis identication and isolation requirements,
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\item 2 of the 3 leptons must fall in the Z window 81-101 GeV,
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\item \MET $>$ 50 GeV (to suppress DY).
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\end{itemize}
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The data and MC yields passing the above selection are in Table~\ref{tab:wz}.
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The inclusive yields (without any jet requirements) agree within 17\%, which is approximately equal
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to the uncertainty in the measured WZ cross section. A data vs. MC comparison of kinematic
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distributions (jet multiplicity, \MET, Z \pt) is given in Fig.~\ref{fig:wz}. High \MET\
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values in WZ and ZZ events arise from highly boosted W or Z bosons that decay leptonically,
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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}. We note some possible contributions to this discrepancy:
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\begin{itemize}
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\item The \zjets\ contribution is under-estimated here, for 2 reasons: first, because the \zjets\
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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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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 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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\end{itemize}
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Based on these studies we currently assess an uncertainty of 80\% on the WZ yield.
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\begin{table}[htb]
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\begin{center}
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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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\ttbar & 0.6 $\pm$ 0.5 & 4.3 $\pm$ 1.5 & 3.0 $\pm$ 1.2 & 8.0 $\pm$ 2.0 \\
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\zjets & 0.4 $\pm$ 0.4 & 4.9 $\pm$ 4.9 & 0.0 $\pm$ 0.0 & 5.3 $\pm$ 4.9 \\
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ZZ & 1.4 $\pm$ 0.0 & 2.0 $\pm$ 0.0 & 0.1 $\pm$ 0.0 & 3.5 $\pm$ 0.0 \\
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WW & 0.0 $\pm$ 0.0 & 0.2 $\pm$ 0.1 & 0.2 $\pm$ 0.1 & 0.3 $\pm$ 0.1 \\
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single top & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.1 $\pm$ 0.1 \\
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\hline
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total SM MC & 61.3 $\pm$ 0.9 & 93.7 $\pm$ 5.2 & 7.3 $\pm$ 1.3 &162.3 $\pm$ 5.4 \\
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data & 68 & 108 & 14 & 190 \\
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\hline
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\hline
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\end{tabular}
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\end{center}
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\end{table}
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\begin{table}[htb]
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\begin{center}
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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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| 239 |
\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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| 243 |
\ttbar & 0.2 $\pm$ 0.2 & 2.0 $\pm$ 0.9 & 2.2 $\pm$ 1.2 & 4.4 $\pm$ 1.5 \\
|
| 244 |
\zjets & 0.0 $\pm$ 0.0 & 4.9 $\pm$ 4.9 & 0.0 $\pm$ 0.0 & 4.9 $\pm$ 4.9 \\
|
| 245 |
ZZ & 0.3 $\pm$ 0.0 & 0.4 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.7 $\pm$ 0.0 \\
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| 246 |
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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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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| 251 |
\hline
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| 252 |
\hline
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| 253 |
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| 254 |
\end{tabular}
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| 255 |
\end{center}
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\end{table}
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\begin{figure}[tbh]
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| 259 |
\begin{center}
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| 260 |
\includegraphics[width=1\linewidth]{plots/WZ.pdf}
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| 261 |
\caption{\label{fig:wz}\protect
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Data vs. MC comparisons for the WZ 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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| 265 |
\end{center}
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| 266 |
\end{figure}
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| 267 |
|
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\clearpage
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\subsubsection{ZZ Validation Studies}
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\label{sec:bkg_zz}
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| 272 |
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| 273 |
A pure ZZ sample can be selected in data with the requirements:
|
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\begin{itemize}
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\item Exactly 4 $p_T>20$~GeV leptons passing analysis identication and isolation requirements,
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\item 2 of the 4 leptons must fall in the $Z$ window 81-101 GeV.
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\end{itemize}
|
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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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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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| 288 |
\begin{center}
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| 289 |
\caption{\label{tab:zz} Data and Monte Carlo yields for the ZZ preselection. }
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| 290 |
\begin{tabular}{lccccc}
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| 291 |
\hline
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| 292 |
\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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\zjets & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 \\
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\ttbar & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 \\
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WW & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 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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| 302 |
total SM MC & 6.7 $\pm$ 0.0 & 10.1 $\pm$ 0.1 & 0.5 $\pm$ 0.0 & 17.3 $\pm$ 0.1 \\
|
| 303 |
data & 13 & 16 & 0 & 29 \\
|
| 304 |
\hline
|
| 305 |
\hline
|
| 306 |
\end{tabular}
|
| 307 |
\end{center}
|
| 308 |
\end{table}
|
| 309 |
|
| 310 |
\begin{figure}[tbh]
|
| 311 |
\begin{center}
|
| 312 |
\includegraphics[width=1\linewidth]{plots/ZZ.pdf}
|
| 313 |
\caption{\label{fig:zz}\protect
|
| 314 |
Data vs. MC comparisons for the ZZ selection discussed in the text for \lumi.
|
| 315 |
The number of jets, missing transverse energy, and Z boson transverse momentum are displayed.
|
| 316 |
}
|
| 317 |
\end{center}
|
| 318 |
\end{figure}
|
| 319 |
|
| 320 |
|
| 321 |
|
| 322 |
|
| 323 |
%\subsection{Estimating the Rare SM Backgrounds with MC}
|
| 324 |
%\label{sec:bkg_raresm}
|
| 325 |
|
| 326 |
%{\bf TODO: list samples, yields in preselection region, and show \MET\ distribution}
|
