| 1 |
|
\section{Non $t\bar{t}$ Backgrounds} |
| 2 |
|
\label{sec:othBG} |
| 3 |
|
|
| 4 |
+ |
\subsection{Dilepton backgrounds from rare SM processes} |
| 5 |
+ |
\label{sec:bgrare} |
| 6 |
|
Backgrounds from divector bosons and single top |
| 7 |
|
can be reliably estimated from Monte Carlo. |
| 8 |
|
They are negligible compared to $t\bar{t}$. |
| 9 |
+ |
|
| 10 |
+ |
|
| 11 |
+ |
\subsection{Drell Yan background} |
| 12 |
+ |
\label{sec:dybg} |
| 13 |
|
|
| 14 |
< |
Backgrounds from Drell Yan are also expected |
| 15 |
< |
to be negligible from MC. However one always |
| 16 |
< |
worries about the modeling of tails of the \met. |
| 17 |
< |
In the context of other dilepton analyses we |
| 18 |
< |
have developed a data driven method to estimate |
| 19 |
< |
the number of Drell Yan events\cite{ref:dy}. |
| 20 |
< |
The method is based on counting the number of |
| 21 |
< |
$Z$ candidates passing the full selection, and |
| 22 |
< |
then scaling by the expected ratio of Drell Yan |
| 23 |
< |
events outside vs. inside the $Z$ mass |
| 24 |
< |
window.\footnote{A correction based on $e\mu$ events |
| 25 |
< |
is also applied.} This ratio is called $R_{out/in}$ |
| 26 |
< |
and is obtained from Monte Carlo. |
| 27 |
< |
|
| 28 |
< |
To estimate the Drell-Yan contribution in the four $ABCD$ |
| 29 |
< |
regions, we count the numbers of $Z \to ee$ and $Z \to \mu\mu$ |
| 30 |
< |
events falling in each region, we subtract off the number |
| 31 |
< |
of $e\mu$ events with $76 < M(e\mu) < 106$ GeV, and |
| 32 |
< |
we multiply the result by $R_{out/in}$ from Monte Carlo. |
| 33 |
< |
The results are summarized in Table~\ref{tab:ABCD-DY}. |
| 34 |
< |
|
| 35 |
< |
\begin{table}[hbt] |
| 36 |
< |
\begin{center} |
| 37 |
< |
\caption{\label{tab:ABCD-DY} Drell-Yan estimations |
| 38 |
< |
in the four |
| 39 |
< |
regions of Figure~\ref{fig:abcdData}. The yields are |
| 40 |
< |
for dileptons with invariant mass consistent with the $Z$. |
| 41 |
< |
The factor |
| 42 |
< |
$R_{out/in}$ is from MC. All uncertainties |
| 43 |
< |
are statistical only. In regions $A$ and $D$ there is no statistics |
| 44 |
< |
in the Monte Carlo to calculate $R_{out/in}$.} |
| 45 |
< |
\begin{tabular}{|l|c|c|c||c|} |
| 46 |
< |
\hline |
| 47 |
< |
Region & $N(ee)+N(\mu\mu)$ & $N(e\mu)$ & $R_{out/in}$ & Estimated DY BG \\ |
| 48 |
< |
\hline |
| 49 |
< |
$A$ & 0 & 0 & ?? & ??$\pm$xx \\ |
| 50 |
< |
$B$ & 5 & 1 & 2.5$\pm$1.0 & 9$\pm$xx \\ |
| 51 |
< |
$C$ & 0 & 0 & 1.$\pm$1. & 0$\pm$xx \\ |
| 52 |
< |
$D$ & 0 & 0 & ?? & 0$\pm$xx \\ |
| 53 |
< |
\hline |
| 54 |
< |
\end{tabular} |
| 55 |
< |
\end{center} |
| 56 |
< |
\end{table} |
| 14 |
> |
%Backgrounds from Drell Yan are also expected |
| 15 |
> |
%to be negligible from MC. However one always |
| 16 |
> |
%worries about the modeling of tails of the \met. |
| 17 |
> |
%In the context of other dilepton analyses we |
| 18 |
> |
%have developed a data driven method to estimate |
| 19 |
> |
%the number of Drell Yan events\cite{ref:dy}. |
| 20 |
> |
%The method is based on counting the number of |
| 21 |
> |
%$Z$ candidates passing the full selection, and |
| 22 |
> |
%then scaling by the expected ratio of Drell Yan |
| 23 |
> |
%events outside vs. inside the $Z$ mass |
| 24 |
> |
%window.\footnote{A correction based on $e\mu$ events |
| 25 |
> |
%is also applied.} This ratio is called $R_{out/in}$ |
| 26 |
> |
%and is obtained from Monte Carlo. |
| 27 |
> |
|
| 28 |
> |
%To estimate the Drell-Yan contribution in the four $ABCD$ |
| 29 |
> |
%regions, we count the numbers of $Z \to ee$ and $Z \to \mu\mu$ |
| 30 |
> |
%events falling in each region, we subtract off the number |
| 31 |
> |
%of $e\mu$ events with $76 < M(e\mu) < 106$ GeV, and |
| 32 |
> |
%we multiply the result by $R_{out/in}$ from Monte Carlo. |
| 33 |
> |
%The results are summarized in Table~\ref{tab:ABCD-DY}. |
| 34 |
> |
|
| 35 |
> |
%\begin{table}[hbt] |
| 36 |
> |
%\begin{center} |
| 37 |
> |
%\caption{\label{tab:ABCD-DY} Drell-Yan estimations |
| 38 |
> |
%in the four |
| 39 |
> |
%regions of Figure~\ref{fig:abcdData}. The yields are |
| 40 |
> |
%for dileptons with invariant mass consistent with the $Z$. |
| 41 |
> |
%The factor |
| 42 |
> |
%$R_{out/in}$ is from MC. All uncertainties |
| 43 |
> |
%are statistical only. In regions $A$ and $D$ there is no statistics |
| 44 |
> |
%in the Monte Carlo to calculate $R_{out/in}$.} |
| 45 |
> |
%\begin{tabular}{|l|c|c|c||c|} |
| 46 |
> |
%\hline |
| 47 |
> |
%Region & $N(ee)+N(\mu\mu)$ & $N(e\mu)$ & $R_{out/in}$ & Estimated DY BG \\ |
| 48 |
> |
%\hline |
| 49 |
> |
%$A$ & 0 & 0 & ?? & ??$\pm$xx \\ |
| 50 |
> |
%$B$ & 5 & 1 & 2.5$\pm$1.0 & 9$\pm$xx \\ |
| 51 |
> |
%$C$ & 0 & 0 & 1.$\pm$1. & 0$\pm$xx \\ |
| 52 |
> |
%$D$ & 0 & 0 & ?? & 0$\pm$xx \\ |
| 53 |
> |
%\hline |
| 54 |
> |
%\end{tabular} |
| 55 |
> |
%\end{center} |
| 56 |
> |
%\end{table} |
| 57 |
|
|
| 58 |
|
|
| 59 |
|
|
| 68 |
|
events can have a significant effect on the data driven background |
| 69 |
|
prediction based on $P_T(\ell\ell)$. This is taken into account, |
| 70 |
|
based on MC expectations, |
| 71 |
< |
by the $K_{\rm{fudge}}$ factor describes in that Section. |
| 72 |
< |
As a cross-check, we use the same Drell Yan background |
| 73 |
< |
estimation method described above to estimated the |
| 74 |
< |
number of DY events in the regions $A'B'C'D'$. |
| 75 |
< |
The region $A'$ is defined in the same way as the region $A$ |
| 76 |
< |
except that the $\met/\sqrt{\rm SumJetPt}$ requirement is |
| 77 |
< |
replaced by a $P_T(\ell\ell)/\sqrt{\rm SumJetPt}$ requirement. |
| 78 |
< |
The regions B', |
| 79 |
< |
C', and D' are defined in a similar way. The results are |
| 80 |
< |
summarized in Table~\ref{tab:ABCD-DYptll}. |
| 81 |
< |
|
| 82 |
< |
\begin{table}[hbt] |
| 83 |
< |
\begin{center} |
| 84 |
< |
\caption{\label{tab:ABCD-DYptll} Drell-Yan estimations |
| 85 |
< |
in the four |
| 86 |
< |
regions $A'B'C'D'$ defined in the text. The yields are |
| 87 |
< |
for dileptons with invariant mass consistent with the $Z$. |
| 88 |
< |
The factor |
| 89 |
< |
$R_{out/in}$ is from MC. All uncertainties |
| 90 |
< |
are statistical only.} |
| 91 |
< |
\begin{tabular}{|l|c|c|c||c|} |
| 92 |
< |
\hline |
| 93 |
< |
Region & $N(ee)+N(\mu\mu)$ & $N(e\mu)$ & $R_{out/in}$ & Estimated DY BG \\ |
| 94 |
< |
\hline |
| 95 |
< |
$A'$ & 3 & 0 & 0.7$\pm$0.3 & 2.1$\pm$xx \\ |
| 96 |
< |
$B'$ & 3 & 0 & 2.5$\pm$2.1 & 7.5$\pm$xx \\ |
| 97 |
< |
$C'$ & 0 & 0 & 0.1$\pm$0.1 & 0$\pm$xx \\ |
| 98 |
< |
$D'$ & 1 & 0 & 0.4$\pm$0.3 & 0.4$\pm$xx \\ |
| 99 |
< |
\hline |
| 100 |
< |
\end{tabular} |
| 101 |
< |
\end{center} |
| 102 |
< |
\end{table} |
| 71 |
> |
by the $K_C$ factor described in that Section. |
| 72 |
> |
As a cross-check, we use a separate data driven method to |
| 73 |
> |
estimate the impact of Drell Yan events on the |
| 74 |
> |
background prediction based on $P_T(\ell\ell)$. |
| 75 |
> |
In this method\cite{ref:top} we count the number |
| 76 |
> |
of $Z$ candidates\footnote{$e^+e^-$ and $\mu^+\mu^-$ |
| 77 |
> |
with invariant mass between 76 and 106 GeV.} |
| 78 |
> |
passing the same selection as |
| 79 |
> |
region $D$ except that the $\met/\sqrt{\rm SumJetPt}$ requirement is |
| 80 |
> |
replaced by a $P_T(\ell\ell)/\sqrt{\rm SumJetPt}$ requirement |
| 81 |
> |
(we call this the ``region $D'$ selection''). |
| 82 |
> |
We subtract off the number of $e\mu$ events with |
| 83 |
> |
invariant mass in the $Z$ passing the region $D'$ selection. |
| 84 |
> |
Finally, we multiply the result by ratio $R_{out/in}$ derived |
| 85 |
> |
from Monte Carlo as the ratio of Drell-Yan events |
| 86 |
> |
outside/inside the $Z$ mass window |
| 87 |
> |
in the $D'$ region. |
| 88 |
> |
|
| 89 |
> |
We find $N^{D'}(ee+\mu\mu)=2$, $N^{D'}(e\mu)=0$, |
| 90 |
> |
$R^{D'}_{out/in}=0.18\pm0.16$ (stat.). |
| 91 |
> |
Thus we estimate the number of Drell Yan events in region $D'$ to |
| 92 |
> |
be $0.36\pm 0.36$. |
| 93 |
> |
|
| 94 |
> |
We also perform the DY estimate in the region $A'$. Here we find |
| 95 |
> |
$N^{A'}(ee+\mu\mu)=5$, $N^{A'}(e\mu)=0$, |
| 96 |
> |
$R^{D'}_{out/in}=0.50\pm0.43$ (stat.), giving an estimated |
| 97 |
> |
number of Drell Yan events in region $A'$ to |
| 98 |
> |
be $2.5 \pm 2.4$. |
| 99 |
> |
|
| 100 |
> |
|
| 101 |
> |
This Drell Yan method could also be used to estimate |
| 102 |
> |
the number of DY events in the signal region (region $D$). |
| 103 |
> |
However, there is not enough statistics in the Monte |
| 104 |
> |
Carlo to make a measurement of $R_{out/in}$ in region |
| 105 |
> |
$D$. In any case, no $Z \to \ell\ell$ candidates are |
| 106 |
> |
found in region $D$. |
| 107 |
> |
|
| 108 |
> |
|
| 109 |
> |
|
| 110 |
> |
%In the context of other dilepton analyses we |
| 111 |
> |
%have developed a data driven method to estimate |
| 112 |
> |
%the number of Drell Yan events\cite{ref:dy}. |
| 113 |
> |
%The method is based on counting the number of |
| 114 |
> |
%$Z$ candidates passing the full selection, and |
| 115 |
> |
%then scaling by the expected ratio of Drell Yan |
| 116 |
> |
%events outside vs. inside the $Z$ mass |
| 117 |
> |
%window.\footnote{A correction based on $e\mu$ events |
| 118 |
> |
%is also applied.} This ratio is called $R_{out/in}$ |
| 119 |
> |
%and is obtained from Monte Carlo. |
| 120 |
> |
|
| 121 |
> |
|
| 122 |
> |
|
| 123 |
> |
|
| 124 |
> |
%As a cross-check, we use the same Drell Yan background |
| 125 |
> |
%estimation method described above to estimate the |
| 126 |
> |
%number of DY events in the regions $A'B'C'D'$. |
| 127 |
> |
%The region $A'$ is defined in the same way as the region $A$ |
| 128 |
> |
%except that the $\met/\sqrt{\rm SumJetPt}$ requirement is |
| 129 |
> |
%replaced by a $P_T(\ell\ell)/\sqrt{\rm SumJetPt}$ requirement. |
| 130 |
> |
%The regions B', |
| 131 |
> |
%C', and D' are defined in a similar way. The results are |
| 132 |
> |
%summarized in Table~\ref{tab:ABCD-DYptll}. |
| 133 |
> |
|
| 134 |
> |
%\begin{table}[hbt] |
| 135 |
> |
%\begin{center} |
| 136 |
> |
%\caption{\label{tab:ABCD-DYptll} Drell-Yan estimations |
| 137 |
> |
%in the four |
| 138 |
> |
%regions $A'B'C'D'$ defined in the text. The yields are |
| 139 |
> |
%for dileptons with invariant mass consistent with the $Z$. |
| 140 |
> |
%The factor |
| 141 |
> |
%$R_{out/in}$ is from MC. All uncertainties |
| 142 |
> |
%are statistical only.} |
| 143 |
> |
%\begin{tabular}{|l|c|c|c||c|} |
| 144 |
> |
%\hline |
| 145 |
> |
%Region & $N(ee)+N(\mu\mu)$ & $N(e\mu)$ & $R_{out/in}$ & Estimated DY BG \\ |
| 146 |
> |
%\hline |
| 147 |
> |
%$A'$ & 3 & 0 & 0.7$\pm$0.3 & 2.1$\pm$xx \\ |
| 148 |
> |
%$B'$ & 3 & 0 & 2.5$\pm$2.1 & 7.5$\pm$xx \\ |
| 149 |
> |
%$C'$ & 0 & 0 & 0.1$\pm$0.1 & 0$\pm$xx \\ |
| 150 |
> |
%$D'$ & 1 & 0 & 0.4$\pm$0.3 & 0.4$\pm$xx \\ |
| 151 |
> |
%\hline |
| 152 |
> |
%\end{tabular} |
| 153 |
> |
%\end{center} |
| 154 |
> |
%\end{table} |
| 155 |
|
|
| 156 |
|
|
| 157 |
+ |
\subsection{Background from ``fake'' leptons} |
| 158 |
+ |
\label{sec:bgfake} |
| 159 |
+ |
|
| 160 |
|
Finally, we can use the ``Fake Rate'' method\cite{ref:FR} |
| 161 |
|
to predict |
| 162 |
|
the number of events with one fake lepton. We select |
| 168 |
|
associated with electron ID cuts applied in the trigger.} |
| 169 |
|
We then weight each event passing the full selection |
| 170 |
|
by FR/(1-FR) where FR is the ``fake rate'' for the |
| 171 |
< |
fakeable object. {\color{red} The results are...} |
| 171 |
> |
fakeable object. |
| 172 |
> |
|
| 173 |
> |
We first apply this method to events passing the preselection. |
| 174 |
> |
The raw result is $6.7 \pm 1.7 \pm 3.4$, where the first uncertainty is |
| 175 |
> |
statistical and the second uncertainty is from the 50\% systematic |
| 176 |
> |
uncertainty associated with this method\cite{ref:FR}. This has |
| 177 |
> |
to be corrected for ``signal contamination'', {\em i.e.}, the |
| 178 |
> |
contribution from true dilepton events with one lepton |
| 179 |
> |
failing the selection. This is estimated from Monte Carlo |
| 180 |
> |
to be $2.3 \pm 0.05$, where the uncertainty is from MC statistics |
| 181 |
> |
only. Thus, the estimates number of events with one ``fake'' |
| 182 |
> |
lepton after the preselection is $4.4 \pm 3.8$. |
| 183 |
> |
The Monte Carlo expectation for this contribution can be obtained |
| 184 |
> |
by summing up the $t\bar{t}\rightarrow \mathrm{other}$ and |
| 185 |
> |
$W^{\pm}$ + jets entries from Table~\ref{tab:yields}. This |
| 186 |
> |
result is $2.0 \pm 0.2$ (stat. error only). Thus, this study |
| 187 |
> |
confirms that the contribution of fake leptons to the event sample |
| 188 |
> |
after preselection is small, and consistent with the MC prediction. |
| 189 |
> |
|
| 190 |
> |
We apply the same method to events in the signal region (region D). |
| 191 |
> |
There are no events where one of the leptons passes the full selection and |
| 192 |
> |
the other one fails the full selection but passes the |
| 193 |
> |
``Fakeable Object'' selection. Thus the background estimate |
| 194 |
> |
is $0.0^{+0.4}_{-0.0}$, where the upper uncertainty corresponds (roughly) |
| 195 |
> |
to what we would have calculated if we had found one such event. |
| 196 |
> |
|
| 197 |
> |
We can also apply a similar technique to estimate backgrounds |
| 198 |
> |
with two fake leptons, {\em e.g.}, from QCD events. |
| 199 |
> |
In this case we select events with both |
| 200 |
> |
leptons failing the full selection but passing the |
| 201 |
> |
``Fakeable Object'' selection. For the preselection, the |
| 202 |
> |
result is $0.2 \pm 0.2 \pm 0.2$, where the first uncertainty |
| 203 |
> |
is statistical and the second uncertainty is from the fake rate |
| 204 |
> |
systematics (50\% per lepton, 100\% total). Note that this |
| 205 |
> |
double fake contribution is already included in the $4.4 \pm 3.8$ |
| 206 |
> |
single fake estimate discussed above $-$ in fact, it is double counted. |
| 207 |
> |
Therefore the total fake estimate is $4.0 \pm 3.8$ (single fakes) |
| 208 |
> |
and $0.2 \pm 0.2 \pm 0.2$ (double fakes). |
| 209 |
> |
|
| 210 |
> |
In the signal region (region D), the estimated double fake background |
| 211 |
> |
is $0.00^{+0.04}_{-0.00}$. This is negligible. |
