MitHzz4l/Documentation/Backgrounds.tex

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\section{Backgrounds}\label{sec:BG}
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This section reviews our evaluation of background in the $4\ell$ analysis.  We discuss expected yields and the predicted $m(4\ell)$ shapes used in the limit and sensitivity calculations of Section~\ref{sec:Extraction}.  We estimate diboson backgrounds with Monte Carlo.  Our estimates of instrumental and jet backgrounds are data-driven.

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\subsection{Diboson Backgrounds}\label{sec:DiB}
%_________________________________________________________________
We use the $ZZ$, $WZ$ and $Z\gamma$ MC samples listed in Table~\ref{tab:MC} to estimate yields and $m(4\ell)$ shapes for these backgrounds.  We correct the acceptances from simulation using the procedures described in Section~\ref{sec:Signal}.  Background yields are determined from the $\alpha_{C}$, luminosity and cross sections from Table~\ref{tab:MC}.  Table~\ref{tab:MCBG} lists the $4.7\rm~fb^{-1}$ expectations for diboson backgrounds.  Figure~\ref{fig:MCshapes} shows the corresponding $m(4\ell)$ distributions.  The contribution from $WZ$ is included in this plot but is too small to be visible.

%-------------------------------------------------
\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.5\linewidth]{figs/dibosonExpectedM4L.png}
\caption{Expected Diboson $m(4\ell)$ Distributions for $4.7\rm~fb^{-1}$.}
\label{fig:MCshapes}
\end{center}
\end{figure}
%-------------------------------------------------

%-------------------------------------------------
\begin{table}[htb]
\begin{center}
\begin{tabular}{c|c|c|c}
\hline
{\bf Process}   & $4e$ & $4\mu$ & $2e2\mu$ \\
\hline
$qq\rightarrow ZZ^{*}$     &  $9.39$             & $11.53$        & $25.05$ \\
$gg\rightarrow ZZ^{*}$     &  $2.00$             & $2.10$         & $4.26$ \\
$WZ$                      &  $0.18$             & $<10^{-4}$     & $0.19$ \\ 
$Z\gamma^{*}$             &  $1.14$             & $<10^{-4}$     & $1.12$ \\ 
\hline
Total Diboson             &  $12.71$            & $13.6301$      & $30.62$ \\
\hline
\end{tabular}
\caption{Expected $4.7\rm~fb^{-1}$ Diboson Yields. {\bf INCLUDE uncertainties from Eff \& Scale}}
\label{tab:MCBG}
\end{center}
\end{table}
%-------------------------------------------------

We consider two sources of systematic uncertainties on diboson background yields.  The first is due to the uncertainty on the efficiency and energy scale-factors, which we propagate from the tables of Section~\ref{sec:Leptons} to the corrected acceptance for each channel. {\bf still have to do this}.  We also propagate PDF uncertainties following standard LHA prescriptions~\cite{LHA}.  We quote the combined uncertainties from these two sources in Table~\ref{tab:MCBG}.

%-------------------------------------------------
\begin{figure}[bht]
\begin{center}
\includegraphics[width=0.5\linewidth]{figs/ewk-shape-mcfm.png}
\caption{Diboson Shape Differences From MCFM Reweighting. }
\label{fig:DiBshapeSys}
\end{center}
\end{figure}
%-------------------------------------------------

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\subsection{Instrumental/Fake Backgrounds}\label{sec:fakes}
%_________________________________________________________________
$Z+jets$ , $Zb\bar{b}/c\bar{c}$ and $t\bar{t}$ backgrounds (collectively, $\ell\ell jj$) contribute to the $4\ell$ signal region when jets in these events are either mismeasured as leptons or produce real leptons through secondary interactions.  These processes are difficult to accurately simulate thus we estimate their contribution from data.  We assess $\ell\ell jj$  backgrounds using the ``fakeable object'' technique~\cite{fakeable}.  For this method we define ``fakerates'' with respect to loosely identified lepton candidates, referred to as ``denominator objects''.  Electron and muon denominator selections are defined in Table~\ref{tab:fo}.

%-------------------------------------------------
\begin{table}[htb]
\begin{center}
\begin{tabular}{c|c|c|c}
\hline
\multicolumn{2}{c|}{{\bf Electron}}                    & \multicolumn{2}{|c}{{\bf Muon}}  \\
\hline
{\bf Variable}               & {\bf Requirement}              & {\bf Variable}   & {\bf Requirement}          \\
\hline
$E_{T}$   &  $> 7\rm~GeV$            &             $p_{T}$                & $> 5\rm~GeV$            \\
$|dz|$    &   $< 0.1\rm~cm$          &             type                   & $\rm Global~||~Tracker$  \\
$|\eta|$  & $< 2.5\rm~$              &             $|d_{0}|$              & $< 2\rm~mm$             \\
$H/E$     &    $< 0.12(0.1) EB(EE)$  &            $Iso^{pf}_{0.3}$       & $< 3\times p_{T}$        \\
$iso_{PF}~(p_{T}<20)$ & $<1.0$                 &                                  ~                      & ~                        \\  
$iso_{PF}~(p_{T}>20)$ & $<1.15(1.2)~EB(EE)$    &                                  ~                      & ~                        \\  
\hline
\end{tabular}
\caption{Denominator Object Definitions}\label{tab:fo}
\end{center}
\end{table}
%-------------------------------------------------

We calculate the fakerates ($\epsilon_{FR}(p_{T},\eta)$) in samples of events that pass single lepton triggers: \verb|HLT_Ele8| for electrons, \verb|HLT_Mu8| or \verb|HLT_Mu13| for muons.  In both channels we reduce contamination from $W\rightarrow \ell\nu$ and $Z/\gamma^{*}\rightarrow\ell\ell$ by vetoing events with $MET > 20\rm~GeV$, or with $m_{T} > 35\rm~GeV$ or with two or more denominator objects of $p_{T} > 10\rm~GeV$.  We enrich the samples in background by selecting only those denominator objects opposite to  ($\Delta R(\eta,\phi) > 1.0$) a reconstructed $p_{T} > 35\rm~GeV$ jet.  Figure~\ref{fig:FR} shows the electron and muon fakerates obtained from this procedure as a function of $p_{T}$. 

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\begin{figure}[tbp]
\begin{center}
\includegraphics[width=0.45\linewidth]{figs/bdt-medium-frpt.png}
\includegraphics[width=0.45\linewidth]{figs/frMu.png}
\caption{ Muon and Electron Fake Rates.}
\label{fig:FR} 
\end{center}
\end{figure}
%-------------------------------------------------

We estimate $\ell\ell jj$ backgrounds in the signal region by applying the $\epsilon_{FR}$ in events that contain a good $Z1$.  First, we select denominator objects that fail identification/isolation to prevent bias from real leptons.  Next, we loop over pairs of the denominator objects, weight each leg with $\epsilon_{FR}(p_{T},\eta)/(1-\epsilon_{FR}(p_{T},\eta))$  and apply the $Z2$ kinematic requirements ($12\rm~GeV < m(Z2) < 120$).  The denominator in the weight term accounts for the fact that the we only consider candidates that fail full lepton selection.  Weighted pairs that pass the $Z2$ kinematic selection are summed to obtain an estimate of the $\ell\ell jj$ background.  

Table~\ref{tab:fakes} presents $\ell\ell jj$ background estimates for the $4.7\rm~fb^{-1}$ dataset.  We maximize the statistical power of the small $Z1 + \ge 2\rm~denominator$ sample by integrating over the flavor of the $Z1$ leptons and then dividing the $Z1$-inclusive prediction between the $4\ell_{e,\mu}$ and $2\ell_{e,\mu}2\ell_{\mu,e}$ channels.  The division is performed by assuming equal $ee$ and $\mu\mu$ $Z1$ branching ratios and using an acceptance factor ($=\sim 1$), measured from inclusive $Z\rightarrow ee,\mu\mu$ yields {\bf need to double check this. 1 seems strange}) to account for efficiency differences in the detection of electrons and muons.

%-------------------------------------------------
\begin{table}[htb]
\begin{center}
\begin{tabular}{c|c}
\hline
\multicolumn{2}{c}{Z1-Inclusive $\ell\ell jj$ Yields} \\
\hline
$Z1 + \mu\mu$      & $0.057 \pm X$ \\
$Z1 + ee$          & $1.8   \pm 1$     \\
\hline
\multicolumn{2}{c}{Per-Channel $\ell\ell jj$ Yields} \\
\hline 
$4\mu$      & $0.044 \pm X$ \\
$4e$        & $0.4 \pm 0.3$     \\
$2e2\mu$    & $(0.013 + 1.4) \pm 0.9$     \\
\hline
\end{tabular}
\caption{Expected $\ell\ell jj$ Events.}
\label{tab:fakes}
\end{center}
\end{table}
%-------------------------------------------------

It is difficult to predict $m(4\ell)$ and kinematic shapes for $\ell\ell jj$ background with the limited number of events containing a good $Z1$ and two failing denominator objects.  Loosening the denominator and $Z1,2$ selections in data helps, however these requirements must not be made so loose that background from the control region no longer resemble those of the signal region.  For this reason we instead estimate $\ell\ell jjs$ shapes by applying a loose selection in $Z+jets$ and $t\bar{t}$ MC events.  Figure~\ref{fig:fakeshapes} shows the cross section normalized $m(4\ell)$ distributions from these processes.

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\begin{figure}[tbp]
\begin{center}
\includegraphics[width=0.45\linewidth]{figs/muFakeShape-4m.png}
\caption{ Predicted $m(4\ell)$ Distributions for $\ell\ell jj$ Events. {\bf this is an old data-driven plot.  Put the MC one here.}}
\label{fig:fakeshapes}
\end{center}
\end{figure}
%-------------------------------------------------

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\subsubsection{Cross Check and Systematics: Light Flavor }\label{sec:lflavor}
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We cross-check our procedures by predicting the number of fake leptons in independent control regions that are enriched in light flavor.  We require one $p_{T} > 25\rm~GeV$ lepton candidate that passes our nominal lepton selection and $1+$ same-sign, same-flavor denominator objects.  This selection produces a sample of nearly pure background, of which the primary component is $W+jet$ with a jet faking a lepton.  Smaller multi-jet backgrounds consist of both light and heavy flavor and contain at least two jets that both fake leptons.  We reduce heavy flavor contributions by requiring $|\sigma(IP_{3D})/IP_{3D} < 3|$ for all denominator objects and $MET > 25\rm~GeV$.  

Relative abundances for muon-channel events passing these selections are determined by fitting the resulting $m_{T}$ distribution with a same-sign MC template for $W+jets$ and a Rayleigh distribution for multi-jets.  The fit result (Figure~\ref{fig:ssMuon}, left) indicates that $W+jets$ constitutes $\sim95\%$ of the sample for $m_{T} > 45\rm~GeV$.

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\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.45\linewidth]{figs/ssMuMT.png}
\includegraphics[width=0.45\linewidth]{figs/mufakes_mZ1.png}
\caption{Sample Composition and Fakerate Predictions for Same-sign Muon Events.}\label{fig:ssMuon} 
\end{center}
\end{figure}
%-------------------------------------------------

Next, we attempt to predict the number of events containing two identified and isolated same-sign muons by applying our fakerates to denominator objects in the sample.  We loop over all fakeable objects, weight each with the appropriate $\epsilon_{FR}(p_{T},\eta)$ and sum.  The expected and observed $m(\ell\ell)$ distributions are shown in the rightmost plot of Figure~\ref{fig:ssMuon}.  The shape of the predicted distribution agrees with the observation, however the yield is under-predicted by $12.3\%$.  We round up to $13\%$ and take this difference as a systematic uncertainty on the muon fakerate.   

For electrons, in order to isolate a pure sample of W+jets where the jet fakes an electron, a cross-flavor same-sign sample was chosen with a well-identified muon satisfying $iso_{PF}/P_{T} < 0.025$ and $p_{T}>25$. This region also contains Z+jets and dijet backgrounds. The W+jets and Z+jets components are represented by templates from Monte Carlo while the dijet is modelled by a Rayleigh distribution. The three are fitted to the observed same-sign events on the left of Figure~\ref{fig:ssEle}. The region with $MET>30~GeV$ is enriched in W+jets, so is chosen to test closure in the mass spectrum. The center of the same figure shows this observation compared to the fake prediction computed in the same way as in the muon case, and shows an overall under-prediction of $4\%$. The right of this figure shows that the observed shape discrepancy comes from an under-prediction of $33\%$ for $p_{T}<20$ and an over-prediction of $20\%$ for $p_{T}>20$. We thus take an overall systematic of $33\%$ on the fake prediction.

An additional cross-check of the electron fake rates was performed on a sample of single-Z plus one fakeable object in both data and $Z+jets$ monte carlo. The largest observed discrepancy between observation and fake rate prediction of these four estimates was $20\%$, well within the systematic used above.

%-------------------------------------------------
\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.45\linewidth]{figs/ssEleMET.png}
\includegraphics[width=0.45\linewidth]{figs/ssEleMZ1.png}
\caption{ Sample Composition and Fakerate Predictions for Same-sign Electron Events.}
\label{fig:ssEle}
\end{center}
\end{figure}
%-------------------------------------------------

Table summarizes the results of this section.  We take $13\%$ ($15\%$) as the systematic uncertainty on the muon (electron) fakerate to account for potential biases in our prediction due to differences in light flavor composition.

%-------------------------------------------------
\begin{table}[tbh]
\begin{center}
\begin{tabular}{c|c|c|c}
\hline
{\bf Channel}                   & {\bf Observed} & {\bf Predicted}  & {\bf Systematic}     \\
\hline
${\rm same~sign}~\mu\mu$        & $336$    & $299.2$   & $13\%$\\
${\rm same~sign}~ee (total) $   & $5333$   & $5132$    & $33\%$ \\
${\rm same~sign}~ee (p_{T}<20)$ & $2783$   & $1993$    & $33\%$ \\
${\rm same~sign}~ee (p_{T}>20)$ & $2550$   & $3138$    & $20\%$ \\
\hline
\end{tabular}
\caption{Same-sign Control Yields and Systematic Uncertainty.}
\label{tab:ssfakes}
\end{center}
\end{table}
%-------------------------------------------------

%_________________________________________________________________
\subsubsection{Cross Check and Systematics : Heavy Flavor }\label{sec:hflavor}
%_________________________________________________________________
Backgrounds from $t\bar{t}$ and $Zb\bar{b}/c\bar{c}$ involve real leptons from heavy flavor decays.  As with light flavor, a difference in the fraction of heavy flavor in the fakerate and prediction samples can lead to errors in signal region background estimation.  We assess the impact of heavy flavor composition differences by applying our fakerate in a sample of relatively pure $Zb\bar{b}/c\bar{c}$ and $t\bar{t}$.

The control region consists of events that contain a pair of leptons passing the $Z1$ selection and at least two additional denominator objects with $\sigma(IP_{3D})/IP_{3D} > 3$, of which at least one has $\sigma(IP_{3D})/IP_{3D} > 5$ .  Denominators are defined according to the requirements of Table~\ref{tab:fo}.  We make no requirement on denominator charge or flavor.  The leftmost plot of Figure~\ref{fig:ZHF} compares the observed $m(Z1)$ distributions for events passing this selection in data with cross section normalized predictions from MC.  We observe $153$ events and predict $154.9 \pm 4.2$ with $Zb\bar{b}$ and $t\bar{t}$ MC, which confirms that the data sample is indeed dominated by heavy flavor.

Next, we require the denominator objects to additionally pass the more stringent lepton ID and isolation criteria used in our nominal Z2 selection.  Of the $107$ ($214$) electron (muon) denominators in the sample $17$ ($11$) satisfy the selection requirements.  We then weight the denominators with the appropriate electron and muon fakerates and predict $21.1$ ($20.3$) electrons (muons).  We assign an additional $20\%$ ($46\%$) systematic uncertainty on the electron (muon) fakerates from the difference between observation and prediction.

%We estimate $0.81 \pm 0.21$ events from MC and observe 2.  Electron and muon fakerates are then applied to the denominator objects in the original $71$ events and, following the procedures described in Section~\ref{sec:lflavor}, we predict $0.84 \pm 0.10$ events.  Given the consistent results, we assign no additional systematic uncertainty on our predicted  $\ell\ell jj$ background yields.

%We then reinstate the $\sigma_{IP_{3D}}/IP_{3D} < 4$ cut and estimate $2.5 \pm 0.4$ events in the signal region from the $Zb\bar{b}$ and $t\bar{t}$ MC.  We take this prediction as an estimate of the heavy flavor contribution to our overall $\ell\ell jj$ background esimtate of $XXX$.  We assign a s sysmatic uncertainty on the estimated fraction Considering the We assignconsider th

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\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.45\linewidth]{figs/HFmZ1.png}
\includegraphics[width=0.45\linewidth]{figs/HFm4l.png}
\caption{$m(Z1)$ and $m(4\ell)$ in the Heavy Flavor control region.}\label{fig:ZHF} 
\end{center}
\end{figure}
%-------------------------------------------------

%We determine a shape for heavy flavor background in the signal region from the distribution of $m(4\ell)$ from the $Z1 + 2\times$ denominator events.  The rightmost plot of Figure~\ref{fig:ZHF} compares the $m(4\ell)$ distributions for this selection in data and (cross-section normalized) simulation.  We fit both distributions with Landaus and compare the normalized PDFs in Figure~\ref{fig:HFshape}.  

%-------------------------------------------------
%\begin{figure}[htbp]
%\begin{center}
%\includegraphics[width=0.5\linewidth]{figs/HFshape.png}
%\caption{$m(4\ell)$ shapes in the Heavy Flavor control region.}\label{fig:HFshape} 
%\end{center}
%\end{figure}
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%_________________________________________________________________
\subsection{Cross Check and Systematics: $WZ$  }
%_________________________________________________________________
The estimate of $WZ$ background in Table~\ref{tab:MCBG} is entirely MC-based.  In addition to the leptons from $W$ and $Z$ decay, an additional ``fake'' lepton is needed for this process to contribute in the $4\ell$ signal region.  We cross-check MC predictions with an estimate obtained from the fakeable object method.  

We begin by requiring three fully selected leptons (two from the $Z1$ plus one additional) and $1+$ denominator objects.  We then perform a single loop to associate the denominator objects with the third lepton.  As before, we weight the denominators with $\epsilon_{FR}(p_{T},\eta)/(1-\epsilon_{FR}(p_{T},\eta))$, apply opposite-sign, same-flavor and kinematic selections and sum.  The additional, identified lepton with which the denominators are paired is either a fake (from $Z+jets$) or a real lepton (from $WZ$, $Z\gamma$, or $ZZ$ where one of the leptons is not reconstructed).  In order to extract the $WZ$ component of the measurement, we need to subtract off the $3\ell$ contribution predicted by MC for $ZZ$ and $Z\gamma$, as well as the double-fake estimate described in Section~\ref{sec:fakes}.  The latter is double-counted when performing a single denominator loop.

The single loop fake prediction is shown in Figure~\ref{fig:ssElepredict}.

\begin{eqnarray}
 N(WZ) &=& \ell\ell\ell~\Sigma_{i=0}^{Nd}~\frac{\epsilon(\eta^{i},p_{T}^{i})}{1-\epsilon(\eta^{i},p_{T}^{i})}   \\
     ~ &-& 2\times \ell\ell~\Sigma_{i=0}^{Nd}\Sigma_{j=i+1}^{Nd}~\frac{\epsilon(\eta^{i},p_{T}^{i})}{1-\epsilon(\eta^{i},p_{T}^{i})}~\frac{\epsilon(\eta^{j},p_{T}^{j})}{1-\epsilon(\eta^{j},p_{T}^{j})} \\
     ~ &-& N(ZZ) 
\end{eqnarray}

Table~\ref{tab:WZfake} lists values for the terms in the equation above.

%-------------------------------------------------
\begin{table}[tbh]
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
            &  $4e$            &         $4\mu$   &       $2e2\mu$ \\
\hline
single loop &  $7.6\pm 1.7$    &         $Z\pm Y$ &       $5.8 + Z\pm 1.6 + Y$ \\
\hline
double loop &  $2.3\pm 0.4$    &         $Z\pm Y$ &       $1.8 +  \pm 0.3 + Y$ \\
\hline
$ZZ$        &  $0.47\pm 0.005$ &         $Z\pm Y$ &       $0.66 + Z\pm 0.01 + Y$ \\
\hline
$Z\gamma$   &  $0.74\pm 0.4$   &         $Z\pm Y$ &       $0.74 + Z\pm 0.5 + Y$ \\
\hline
$WZ$ estimate &  $1.7\pm 1.8$  &         $Z\pm Y$ &       $0.5 + Z\pm 1.7 + Y$ \\
\hline
\end{tabular}
\caption{Data-driven Expected $WZ$ Yields}
\label{tab:WZfake}
\end{center}
\end{table}

%-------------------------------------------------
\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.45\linewidth]{figs/m4l-ele-fake-prediction.png}
\caption{ Four-lepton mass distribution for the single-loop fake prediction. }
\label{fig:ssElepredict}
\end{center}
\end{figure}
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Revision:	1.12
Committed:	Fri Nov 25 20:20:15 2011 UTC (13 years, 5 months ago) by dkralph
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