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\section{Non $t\bar{t}$ Backgrounds}
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\label{sec:othBG}
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\subsection{Dilepton backgrounds from rare SM processes}
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\label{sec:bgrare}
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Backgrounds from divector bosons and single top
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can be reliably estimated from Monte Carlo.
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They are negligible compared to $t\bar{t}$.
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\subsection{Drell Yan background}
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\label{sec:dybg}
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%Backgrounds from Drell Yan are also expected
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%to be negligible from MC. However one always
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%worries about the modeling of tails of the \met.
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%In the context of other dilepton analyses we
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%have developed a data driven method to estimate
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%the number of Drell Yan events\cite{ref:dy}.
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%The method is based on counting the number of
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%$Z$ candidates passing the full selection, and
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%then scaling by the expected ratio of Drell Yan
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%events outside vs. inside the $Z$ mass
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%window.\footnote{A correction based on $e\mu$ events
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%is also applied.} This ratio is called $R_{out/in}$
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%and is obtained from Monte Carlo.
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%To estimate the Drell-Yan contribution in the four $ABCD$
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%regions, we count the numbers of $Z \to ee$ and $Z \to \mu\mu$
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%events falling in each region, we subtract off the number
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%of $e\mu$ events with $76 < M(e\mu) < 106$ GeV, and
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%we multiply the result by $R_{out/in}$ from Monte Carlo.
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%The results are summarized in Table~\ref{tab:ABCD-DY}.
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%\begin{table}[hbt]
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%\begin{center}
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%\caption{\label{tab:ABCD-DY} Drell-Yan estimations
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%in the four
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%regions of Figure~\ref{fig:abcdData}. The yields are
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%for dileptons with invariant mass consistent with the $Z$.
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%The factor
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%$R_{out/in}$ is from MC. All uncertainties
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%are statistical only. In regions $A$ and $D$ there is no statistics
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%in the Monte Carlo to calculate $R_{out/in}$.}
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%\begin{tabular}{|l|c|c|c||c|}
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%\hline
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%Region & $N(ee)+N(\mu\mu)$ & $N(e\mu)$ & $R_{out/in}$ & Estimated DY BG \\
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%\hline
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%$A$ & 0 & 0 & ?? & ??$\pm$xx \\
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%$B$ & 5 & 1 & 2.5$\pm$1.0 & 9$\pm$xx \\
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%$C$ & 0 & 0 & 1.$\pm$1. & 0$\pm$xx \\
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%$D$ & 0 & 0 & ?? & 0$\pm$xx \\
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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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%When find no dilepton events with invariant mass
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%consistent with the $Z$ in the signal region.
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%Using the value of 0.1 for the ratio described above, this
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%means that the Drell Yan background in our signal
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%region is $< 0.23\%$ events at the 90\% confidence level.
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%{\color{red} (If we find 1 event this will need to be adjusted)}.
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As discussed in Section~\ref{sec:victory}, residual Drell-Yan
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events can have a significant effect on the data driven background
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prediction based on $P_T(\ell\ell)$. This is taken into account,
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based on MC expectations,
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by the $K_C$ factor described in that Section.
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As a cross-check, we use a separate data driven method to
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estimate the impact of Drell Yan events on the
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background prediction based on $P_T(\ell\ell)$.
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In this method\cite{ref:top} we count the number
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of $Z$ candidates\footnote{$e^+e^-$ and $\mu^+\mu^-$
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with invariant mass between 76 and 106 GeV.}
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passing the same selection as
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region $D$ except that the $\met/\sqrt{\rm SumJetPt}$ requirement is
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replaced by a $P_T(\ell\ell)/\sqrt{\rm SumJetPt}$ requirement
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(we call this the ``region $D'$ selection'').
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We subtract off the number of $e\mu$ events with
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invariant mass in the $Z$ passing the region $D'$ selection.
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Finally, we multiply the result by ratio $R_{out/in}$ derived
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from Monte Carlo as the ratio of Drell-Yan events
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outside/inside the $Z$ mass window
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in the $D'$ region.
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We find $N^{D'}(ee+\mu\mu)=2$, $N^{D'}(e\mu)=0$,
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$R^{D'}_{out/in}=0.18\pm0.16$ (stat.).
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Thus we estimate the number of Drell Yan events in region $D'$ to
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be $0.36\pm 0.36$.
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We also perform the DY estimate in the region $A'$. Here we find
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$N^{A'}(ee+\mu\mu)=5$, $N^{A'}(e\mu)=0$,
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$R^{D'}_{out/in}=0.50\pm0.43$ (stat.), giving an estimated
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number of Drell Yan events in region $A'$ to
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be $2.5 \pm 2.4$.
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This Drell Yan method could also be used to estimate
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the number of DY events in the signal region (region $D$).
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However, there is not enough statistics in the Monte
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Carlo to make a measurement of $R_{out/in}$ in region
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$D$. In any case, no $Z \to \ell\ell$ candidates are
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found in region $D$.
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%In the context of other dilepton analyses we
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%have developed a data driven method to estimate
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%the number of Drell Yan events\cite{ref:dy}.
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%The method is based on counting the number of
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%$Z$ candidates passing the full selection, and
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%then scaling by the expected ratio of Drell Yan
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%events outside vs. inside the $Z$ mass
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%window.\footnote{A correction based on $e\mu$ events
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%is also applied.} This ratio is called $R_{out/in}$
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%and is obtained from Monte Carlo.
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%As a cross-check, we use the same Drell Yan background
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%estimation method described above to estimate the
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%number of DY events in the regions $A'B'C'D'$.
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%The region $A'$ is defined in the same way as the region $A$
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%except that the $\met/\sqrt{\rm SumJetPt}$ requirement is
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%replaced by a $P_T(\ell\ell)/\sqrt{\rm SumJetPt}$ requirement.
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%The regions B',
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%C', and D' are defined in a similar way. The results are
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%summarized in Table~\ref{tab:ABCD-DYptll}.
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%\begin{table}[hbt]
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%\begin{center}
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%\caption{\label{tab:ABCD-DYptll} Drell-Yan estimations
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%in the four
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%regions $A'B'C'D'$ defined in the text. The yields are
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%for dileptons with invariant mass consistent with the $Z$.
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%The factor
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%$R_{out/in}$ is from MC. All uncertainties
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%are statistical only.}
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%\begin{tabular}{|l|c|c|c||c|}
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%\hline
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%Region & $N(ee)+N(\mu\mu)$ & $N(e\mu)$ & $R_{out/in}$ & Estimated DY BG \\
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%\hline
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%$A'$ & 3 & 0 & 0.7$\pm$0.3 & 2.1$\pm$xx \\
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%$B'$ & 3 & 0 & 2.5$\pm$2.1 & 7.5$\pm$xx \\
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%$C'$ & 0 & 0 & 0.1$\pm$0.1 & 0$\pm$xx \\
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%$D'$ & 1 & 0 & 0.4$\pm$0.3 & 0.4$\pm$xx \\
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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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\subsection{Background from ``fake'' leptons}
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\label{sec:bgfake}
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Finally, we can use the ``Fake Rate'' method\cite{ref:FR}
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to predict
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the number of events with one fake lepton. We select
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events where one of the leptons passes the full selection and
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the other one fails the full selection but passes the
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``Fakeable Object'' selection of
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Reference~\cite{ref:FR}.\footnote{For electrons we use
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the V3 fakeable object definition to avoid complications
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associated with electron ID cuts applied in the trigger.}
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We then weight each event passing the full selection
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by FR/(1-FR) where FR is the ``fake rate'' for the
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fakeable object.
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We first apply this method to events passing the preselection.
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The raw result is $6.7 \pm xx \pm 3.4$, where the first uncertainty is
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statistical and the second uncertainty is from the 50\% systematic
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uncertainty associated with this method\cite{ref:FR}. This has
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to be corrected for ``signal contamination'', {\em i.e.}, the
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contribution from true dilepton events with one lepton
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failing the selection. This is estimated from Monte Carlo
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to be $2.3 \pm xx$, where the uncertainty is from MC statistics
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only. Thus, the estimates number of events with one ``fake''
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lepton after the preselection is $4.4 \pm xx$.
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The Monte Carlo expectation for this contribution can be obtained
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by summing up the $t\bar{t}\rightarrow \mathrm{other}$ and
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$W^{\pm}$ + jets entries from Table~\ref{tab:yields}. This
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result is $2.0 \pm 0.2$ (stat. error only). Thus, this study
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confirms that the contribution of fake leptons to the event sample
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after preselection is small, and consistent with the MC prediction.
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We apply the same method to events in the signal region (region D).
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There are no events where one of the leptons passes the full selection and
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the other one fails the full selection but passes the
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``Fakeable Object'' selection. Thus the background estimate
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is $0.0^{+0.4}_{-0.0}$, where the upper uncertainty corresponds (roughly)
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to what we would have calculated if we had found one such event.
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We can also apply a similar technique to estimate backgrounds
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with two fake leptons, {\em e.g.}, from QCD events.
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In this case we select events with both
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leptons failing the full selection but passing the
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``Fakeable Object'' selection. For the preselection, the
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result is $0.2 \pm xx \pm 0.2$, where the first uncertainty
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is statistical and the second uncertainty is from the fake rate
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systematics (50\% per lepton, 100\% total). Note that this
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double fake contribution is already included in the $4.4 \pm xx$
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single fake estimate discussed above $-$ in fact, it is double counted.
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Therefore the total fake estimate is $4.0 \pm xx$ (single fakes)
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and $0.2 \pm xx \pm 0.2$ (double fakes).
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In the signal region (region D), the estimated double fake background
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is $0.00^{+0.04}_{-0.00}$. This is negligible. |
