Notes/WZCSA07/AppendixFitTest.tex

\clearpage
\newpage
\appendix
\section{Additional Cross Check on Background Estimation Studies}

In figures~\ref{fig:AllFits}, the fit approximation of the invariant
mass of \Z boson candidate is shown for each channel and for loose and
tight criteria. The fit is performed using an addition of a
convolution of a Gaussian and Breit-Wigner function and a line in
order to fit the background. It has to be noticed that due to a lack
of statistics in chowder soup, all bin with 0 events from chowder have
been modified in order to avoid to have an error at 0. The
corresponding error in the bin with no event correspond to the weight
of each process in Chowder soup. One can see that the errors are
large, and the fit is then not really constraint.


\begin{figure}[hbt]
  \begin{center}
  \scalebox{0.3}{\includegraphics{figs/Fit3eLoose.eps}\includegraphics{figs/Fit3eTight.eps}}\\
  \scalebox{0.3}{\includegraphics{figs/Fit2e1muLoose.eps}\includegraphics{figs/Fit2e1muTight.eps}}\\
  \scalebox{0.3}{\includegraphics{figs/Fit2mu1eLoose.eps}\includegraphics{figs/Fit2mu1eTight.eps}}\\
  \scalebox{0.3}{\includegraphics{figs/Fit3muLoose.eps}\includegraphics{figs/Fit3muTight.eps}}\\
  \caption{Invariante mass of \Z boson candidate for the different samples studied on the left when the lepton pass the loose criteria, on the right when the lepton pass the tight criteria.}
  \label{fig:AllFits}
  \end{center}
\end{figure}


The linear fit will take into account the background with non-genuine
\Z candidate but it will also account for some part of \Z+jets and
$Zb\bar{b}$ background as the gamma$^*$ will populate the side band.
The comparison can be seen in table~\ref{tab:CompFit}.
\begin{table}[h]
\begin{center}
\begin{tabular}{|l|c|c|c|c|c|c|c|} \hline 
                    & \multicolumn{2}{c|}{Background with genuine \Z} & \multicolumn{4}{c|}{Background without
                    genuine \Z boson} \\ 
Channel    & $\Z+jets$ & $\Z b\bar{b}$ &   $t\bar{t}$ & $\W+jets$ & $t\bar{t}$ + $\W+jets$ & Fit result \\ \hline 
$3e$ Loose &7.08067 & 2.86817 & 1.12287 & 0.357018 & 1.47989 & 1.45557$ \pm $2.9589 \\\hline 
$3e$ Tight &1.95631 & 1.20063 & 0.623349 & 0.357018 & 0.980367 & 1.11349$ \pm $2.83365 \\\hline 
$2e1mu$ Loose &3.97174 & 4.73581 & 6.17639 & 0 & 6.17639 & 6.0224$ \pm $4.0679 \\\hline 
$2e1mu$ Tight &0 & 0.0889355 & 0.734362 & 0 & 0.734362 & 0.97086$ \pm $2.80976 \\\hline  
$2mu1e$ Loose &10.1004 & 2.93487 & 0.79839 & 0 & 0.79839 & 1.55994$ \pm $3.1279 \\\hline 
$2mu1e$ Tight &1.81221 & 1.28956 & 0.648954 & 0 & 0.648954 & 0.979719$ \pm $2.67068 \\\hline 
$3mu$ Loose &4.54662 & 4.17997 & 5.87059 & 0 & 5.87059 & 3.07779$ \pm $3.50566 \\\hline 
$3mu$ Tight &0.144028 & 0.28904 & 0.324477 & 0 & 0.324477 & 0.470637$ \pm $2.46181 \\\hline 
\end{tabular}
\end{center}
\caption{Comparison between Monte Carlo truth information and the results of the fit for the background without genuine \Z boson. Number of events are obtained in the invariant mass range between 81 and 101 GeV. The ``Loose'' and ``Tight'' selection criteria applied for third lepton considered. 
}
\label{tab:CompFit}
\end{table}


Nevertheless in association with the matrix method the background is
well estimated as one can see in table~\ref{tab:FinalXC}.The corresponding figure can be
seen~\ref{fig:FinalMatrix3e}~\ref{fig:FinalMatrix2e1mu}~\ref{fig:FinalMatrix2mu1e}~\ref{fig:FinalMatrix3mu}
for $3e$, $2e1\mu$, $2\mu1e$ and $3\mu$ channels respectively.

\begin{table}[h]
  \begin{center}
\begin{tabular}{lcccc} \hline \hline 
 & 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline 
$N$ - ZZ -Zgamma &12.4437$\pm$0.992046 &8.69811$\pm$0&13.1255$\pm$0.937399&10.5715$\pm$0\\ \hline
$N^{non genuine Z}$ (Fit)&1.11349$\pm$2.83365&0.97086$\pm$2.80976&0.979719$\pm$2.67068&0.470637$\pm$2.46181\\ \hline
$N^{genuine Z}$ (matrix method)&3.21939 $\pm$1.78953&0.948261 $\pm$1.05074&4.63515 $\pm$2.11436&0.945652 $\pm$1.13388\\ \hline
$N^{WZ}$ & 8.23222 $\pm$3.53155&7.74985 $\pm$3.15299 &7.55297 $\pm$3.54442&9.62584 $\pm$2.75094\\ \hline
\WZ from MC &7.9&8.1& 9.0 &10.1\\

\hline
\end{tabular}

\caption{Expected number of selected events for an integrated luminosity of 300
 pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.}
\label{tab:FinalXC}
\end{center}
\end{table}


\begin{table}[h]
  \begin{center}
\begin{tabular}{lcccc} \hline \hline 
 & 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline 
$N$ - ZZ -Zgamma &19.9098$\pm$1.00886&23.5941$\pm$0.00420358&23.3592$\pm$0.95001&25.5227$\pm$0.00420358\\ \hline
$N^{non genuine Z}$ (Fit)&1.45557$\pm$2.9589&6.0224$\pm$4.0679&1.55994$\pm$3.1279&3.07779$\pm$3.50566\\ \hline
$N^{genuine Z}$ (matrix method)&10.0606 $\pm$6.75575&15.8043 $\pm$8.41727)&14.4848 $\pm$6.80421&15.7609 $\pm$5.70923\\ \hline
$N^{WZ}$ & 8.84029 $\pm$7.51757&7.78552 $\pm$11.1206&7.92435 $\pm$7.64947&9.75762 $\pm$7.37277\\ \hline
\WZ from MC &8.1&9.0& 9.2 &11.3\\

\hline
\end{tabular}

\caption{Loose Sample: Expected number of selected events for an integrated luminosity of 300
 pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.}
\label{tab:FinalXCLoose}
\end{center}
\end{table}

\begin{figure}[hbt]
  \begin{center}
  \scalebox{0.8}{\includegraphics{figs/MatrixMethod3eLooseTightZmassMWtCut.eps}}
  \caption{Result of Matrix Method application for $3e$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.}
  \label{fig:FinalMatrix3e}
  \end{center}
\end{figure}

\begin{figure}[hbt]
  \begin{center}
  \scalebox{0.8}{\includegraphics{figs/MatrixMethod2e1muLooseTightZmassMWtCut.eps}}
  \caption{Result of Matrix Method application for $2e1\mu$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.}
  \label{fig:FinalMatrix2e1mu}
  \end{center}
\end{figure}

\begin{figure}[hbt]
  \begin{center}
  \scalebox{0.8}{\includegraphics{figs/MatrixMethod2mu1eLooseTightZmassMWtCut.eps}}
  \caption{Result of Matrix Method application for $2\mu1e$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.}
  \label{fig:FinalMatrix2mu1e}
  \end{center}
\end{figure}

\begin{figure}[hbt]
  \begin{center}
  \scalebox{0.8}{\includegraphics{figs/MatrixMethod3muLooseTightZmassMWtCut.eps}}
  \caption{Result of Matrix Method application for $3\mu$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.}
  \label{fig:FinalMatrix3mu}
  \end{center}
\end{figure}


Check on Without MWtCut Samples~\ref{tab:FitNoMWt} (Linear Fit):
\begin{table}[h]
\begin{center}
\begin{tabular}{|l|c|c|c|c|c|c|c|} \hline 
                    & \multicolumn{2}{c|}{Background with genuine \Z} & \multicolumn{4}{c|}{Background without
                    genuine \Z boson} \\ 
Channel    & $\Z+jets$ & $\Z b\bar{b}$ &   $t\bar{t}$ & $\W+jets$ & $t\bar{t}$ + $\W+jets$ & Fit result \\ \hline 
$3e$ Loose &44.5748 & 12.6511 & 1.62239 & 0.357018 & 1.9794 & 6.81271$ \pm $5.60783 \\\hline 
$3e$ Tight &13.8877 & 5.04709 & 0.79839 & 0.357018 & 1.15541 & 3.76484$ \pm $7.74145 \\\hline 
$2e1mu$ Loose &41.5198 & 78.9304 & 12.6155 & 0 & 12.6155 & 16.1879$ \pm $5.12531 \\\hline 
$2e1mu$ Tight &0.993801 & 1.97881 & 0.883798 & 0 & 0.883798 & 1.63388$ \pm $2.94792 \\\hline 
$2mu1e$ Loose &56.2794 & 15.3858 & 1.89565 & 0 & 1.89565 & 7.24906$ \pm $5.77249 \\\hline 
$2mu1e$ Tight &17.2942 & 5.55847 & 0.79839 & 0 & 0.79839 & 4.53933$ \pm $7.00846 \\\hline 
$3mu$ Loose &43.6972 & 84.8891 & 11.9976 & 0 & 11.9976 & 11.1603$ \pm $3.36046 \\\hline 
$3mu$ Tight &0.806562 & 2.31232 & 0.324477 & 0 & 0.324477 & 0.836361$ \pm $2.47575 \\\hline 
\end{tabular}
\end{center}
\caption{Comparison between Monte Carlo truth information and the results of the fit for the background without genuine \Z boson. Number of events are obtained in the invariant mass range between 81 and 101 GeV. The ``Loose'' and ``Tight'' selection criteria applied for third lepton considered. 
%I AM NOT SURE I UNDERSTAND WHAT IS WRITTEN HERE
% One has to consider that this study as been perform on a smaller sample than the other part of the analysis a 10\% statistics error as to be counted until the study is performed on the whole samples.
}
\label{tab:FitNoMWt}
\end{table}


In table~\ref{tab:FinalNoMWtCut}, the final results are presented if
we remove the cut on the W transverse mass. Everthing is still in
perfect agreement... The corresponding figure can be
seen~\ref{fig:FinalMatrix3eNoWtCut}~\ref{fig:FinalMatrix2e1muNoWtCut}~\ref{fig:FinalMatrix2mu1eNoWtCut}~\ref{fig:FinalMatrix3muNoWtCut}
for $3e$, $2e1\mu$, $2\mu1e$ and $3\mu$ channels respectively.

\begin{table}[h]
  \begin{center}
\begin{tabular}{lcccc} \hline \hline 
 & 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline 
%$N_{Loose}$ - ZZ -Zgamma &19.7$\pm$1.1 &22.9$\pm$0.7 &22.9$\pm$1.1 &25.6$\pm$0.8 \\
%$N_{Loose} ^{non genuine Z}$ (Fit) &1.0$\pm$1.5  &11.2$\pm$5.5 &3.1$\pm$2.4 &  4.8$\pm$3.7\\
$N$ - ZZ -Zgamma &21.9$\pm$5.4 &15.2$\pm$1.0 &24.9$\pm$4.4 &17.8$\pm$1.3\\
$N^{non genuine Z}$ (Fit)&1.7$\pm$2.9 &1.0$\pm$2.8 &1.7$\pm$3.0 &0.7$\pm$2.8\\
$N^{genuine Z}$ (matrix method)& 8.4$\pm$3.5 &5.7$\pm$4.7 &11.2$\pm$4.3 &6.4$\pm$5.3\\\hline 
$N^{WZ}$ & 11.8$\pm$7.0 &8.5$\pm$5.6 &12.0$\pm$6.8 &10.7$\pm$6.1\\\hline 
\WZ from MC &11.6&12.3& 13.1 &14.9\\

\hline
\end{tabular}

\caption{Expected number of selected events for an integrated luminosity of 300
 pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.}
\label{tab:FinalNoMWtCut}
\end{center}
\end{table}

\begin{figure}[hbt]
  \begin{center}
  \scalebox{0.8}{\includegraphics{figs/MatrixMethod3eLooseTightZmassNoCutMWt.eps}}
  \caption{Before M$_T$(W) criteria: Result of Matrix Method application for $3e$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.}
  \label{fig:FinalMatrix3eNoWtCut}
  \end{center}
\end{figure}

\begin{figure}[hbt]
  \begin{center}
  \scalebox{0.8}{\includegraphics{figs/MatrixMethod2e1muLooseTightZmassNoCutMWt.eps}}
  \caption{Before M$_T$(W) criteria: Result of Matrix Method application for $2e1\mu$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.}
  \label{fig:FinalMatrix2e1muNoWtCut}
  \end{center}
\end{figure}

\begin{figure}[hbt]
  \begin{center}
  \scalebox{0.8}{\includegraphics{figs/MatrixMethod2mu1eLooseTightZmassNoCutMWt.eps}}
  \caption{Before M$_T$(W) criteria: Result of Matrix Method application for $2\mu1e$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.}
  \label{fig:FinalMatrix2mu1eNoWtCut}
  \end{center}
\end{figure}

\begin{figure}[hbt]
  \begin{center}
  \scalebox{0.8}{\includegraphics{figs/MatrixMethod3muLooseTightZmassNoCutMWt.eps}}
  \caption{Before M$_T$(W) criteria: Result of Matrix Method application for $3\mu$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.}
  \label{fig:FinalMatrix3muNoWtCut}
  \end{center}
\end{figure}


TO BE REMOVE??? ONLY USEFUL FOR MUONS PART???
Check on Loosy Samples~\ref{tab:FitLoosy} (Linear Fit):
\begin{table}[h]
\begin{center}
\begin{tabular}{|l|c|c|c|c|c|c|c|} \hline 
                    & \multicolumn{2}{c|}{Background with genuine \Z} & \multicolumn{4}{c|}{Background without
                    genuine \Z boson} \\ 
Channel    & $\Z+jets$ & $\Z b\bar{b}$ &   $t\bar{t}$ & $\W+jets$ & $t\bar{t}$ + $\W+jets$ & Fit result \\ \hline 
$3e$ Loose &17.4 & 14.1 & 1.2 & 0.1 & 1.3 & 4.0$ \pm $3.6 \\\hline 
$3e$ Tight &5.3 & 5.8 & 0.7 & 0.1 & 0.8 & 2.7$ \pm $3.2 \\\hline 
$2e1\mu$ Loose &16.5 & 83.1 & 10.0 & 0 & 10.0 & 13.1$ \pm $5.0 \\\hline 
$2e1\mu$ Tight &0.3 & 2.0 & 1.0 & 0 & 1.0 & 1.3$ \pm $3.0 \\\hline 
$2\mu1e$ Loose &27.5 & 20.1 & 15.0 & 0.2 & 15.3 & 23.7$ \pm $5.5 \\ \hline 
$2\mu1e$ Tight &7.7 & 6.9 & 13.2 & 0.1 & 13.3 & 19.7$ \pm $5.2 \\ \hline 
$3\mu$ Loose &33.4 & 138.2 & 45.8 & 0.7 & 46.4 & 48.7$ \pm $6.7 \\\hline 
$3\mu$ Tight &8.9 & 25.2 & 19.7 & 0.2 & 19.9 & 23.5$ \pm $5.5 \\\hline 
\end{tabular}
\end{center}
\caption{Comparison between Monte Carlo truth information and the results of the fit for the background without genuine \Z boson. Number of events are obtained in the invariant mass range between 81 and 101 GeV. The ``Loose'' and ``Tight'' selection criteria applied for third lepton considered. 
%I AM NOT SURE I UNDERSTAND WHAT IS WRITTEN HERE
% One has to consider that this study as been perform on a smaller sample than the other part of the analysis a 10\% statistics error as to be counted until the study is performed on the whole samples.
}
\label{tab:FitLoosy}
\end{table}
Revision:	1.5
Committed:	Mon Jul 28 13:38:36 2008 UTC (16 years, 9 months ago) by beaucero
Content type:	application/x-tex
Branch:	MAIN
Changes since 1.4:	+41 -23 lines
Log Message:	Steph Modif
#	User	Rev	Content
1	beaucero	1.4	\clearpage
2			\newpage
3	beaucero	1.1	\appendix
4			\section{Additional Cross Check on Background Estimation Studies}
5
6			In figures~\ref{fig:AllFits}, the fit approximation of the invariant
7			mass of \Z boson candidate is shown for each channel and for loose and
8			tight criteria. The fit is performed using an addition of a
9			convolution of a Gaussian and Breit-Wigner function and a line in
10	beaucero	1.4	order to fit the background. It has to be noticed that due to a lack
11			of statistics in chowder soup, all bin with 0 events from chowder have
12			been modified in order to avoid to have an error at 0. The
13			corresponding error in the bin with no event correspond to the weight
14			of each process in Chowder soup. One can see that the errors are
15			large, and the fit is then not really constraint.
16	beaucero	1.1
17
18			\begin{figure}[hbt]
19			\begin{center}
20			\scalebox{0.3}{\includegraphics{figs/Fit3eLoose.eps}\includegraphics{figs/Fit3eTight.eps}}\\
21			\scalebox{0.3}{\includegraphics{figs/Fit2e1muLoose.eps}\includegraphics{figs/Fit2e1muTight.eps}}\\
22			\scalebox{0.3}{\includegraphics{figs/Fit2mu1eLoose.eps}\includegraphics{figs/Fit2mu1eTight.eps}}\\
23			\scalebox{0.3}{\includegraphics{figs/Fit3muLoose.eps}\includegraphics{figs/Fit3muTight.eps}}\\
24			\caption{Invariante mass of \Z boson candidate for the different samples studied on the left when the lepton pass the loose criteria, on the right when the lepton pass the tight criteria.}
25			\label{fig:AllFits}
26			\end{center}
27			\end{figure}
28
29
30			The linear fit will take into account the background with non-genuine
31			\Z candidate but it will also account for some part of \Z+jets and
32			$Zb\bar{b}$ background as the gamma$^*$ will populate the side band.
33			The comparison can be seen in table~\ref{tab:CompFit}.
34			\begin{table}[h]
35			\begin{center}
36			\begin{tabular}{\|l\|c\|c\|c\|c\|c\|c\|c\|} \hline
37			& \multicolumn{2}{c\|}{Background with genuine \Z} & \multicolumn{4}{c\|}{Background without
38			genuine \Z boson} \\
39			Channel & $\Z+jets$ & $\Z b\bar{b}$ & $t\bar{t}$ & $\W+jets$ & $t\bar{t}$ + $\W+jets$ & Fit result \\ \hline
40	beaucero	1.5	$3e$ Loose &7.08067 & 2.86817 & 1.12287 & 0.357018 & 1.47989 & 1.45557$ \pm $2.9589 \\\hline
41			$3e$ Tight &1.95631 & 1.20063 & 0.623349 & 0.357018 & 0.980367 & 1.11349$ \pm $2.83365 \\\hline
42			$2e1mu$ Loose &3.97174 & 4.73581 & 6.17639 & 0 & 6.17639 & 6.0224$ \pm $4.0679 \\\hline
43			$2e1mu$ Tight &0 & 0.0889355 & 0.734362 & 0 & 0.734362 & 0.97086$ \pm $2.80976 \\\hline
44			$2mu1e$ Loose &10.1004 & 2.93487 & 0.79839 & 0 & 0.79839 & 1.55994$ \pm $3.1279 \\\hline
45			$2mu1e$ Tight &1.81221 & 1.28956 & 0.648954 & 0 & 0.648954 & 0.979719$ \pm $2.67068 \\\hline
46			$3mu$ Loose &4.54662 & 4.17997 & 5.87059 & 0 & 5.87059 & 3.07779$ \pm $3.50566 \\\hline
47			$3mu$ Tight &0.144028 & 0.28904 & 0.324477 & 0 & 0.324477 & 0.470637$ \pm $2.46181 \\\hline
48	beaucero	1.1	\end{tabular}
49			\end{center}
50			\caption{Comparison between Monte Carlo truth information and the results of the fit for the background without genuine \Z boson. Number of events are obtained in the invariant mass range between 81 and 101 GeV. The ``Loose'' and ``Tight'' selection criteria applied for third lepton considered.
51			}
52			\label{tab:CompFit}
53			\end{table}
54
55
56			Nevertheless in association with the matrix method the background is
57	beaucero	1.4	well estimated as one can see in table~\ref{tab:FinalXC}.The corresponding figure can be
58			seen~\ref{fig:FinalMatrix3e}~\ref{fig:FinalMatrix2e1mu}~\ref{fig:FinalMatrix2mu1e}~\ref{fig:FinalMatrix3mu}
59			for $3e$, $2e1\mu$, $2\mu1e$ and $3\mu$ channels respectively.
60	beaucero	1.1
61			\begin{table}[h]
62			\begin{center}
63			\begin{tabular}{lcccc} \hline \hline
64			& 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline
65	beaucero	1.5	$N$ - ZZ -Zgamma &12.4437$\pm$0.992046 &8.69811$\pm$0&13.1255$\pm$0.937399&10.5715$\pm$0\\ \hline
66			$N^{non genuine Z}$ (Fit)&1.11349$\pm$2.83365&0.97086$\pm$2.80976&0.979719$\pm$2.67068&0.470637$\pm$2.46181\\ \hline
67			$N^{genuine Z}$ (matrix method)&3.21939 $\pm$1.78953&0.948261 $\pm$1.05074&4.63515 $\pm$2.11436&0.945652 $\pm$1.13388\\ \hline
68			$N^{WZ}$ & 8.23222 $\pm$3.53155&7.74985 $\pm$3.15299 &7.55297 $\pm$3.54442&9.62584 $\pm$2.75094\\ \hline
69			\WZ from MC &7.9&8.1& 9.0 &10.1\\
70	beaucero	1.1
71			\hline
72			\end{tabular}
73
74			\caption{Expected number of selected events for an integrated luminosity of 300
75			pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.}
76			\label{tab:FinalXC}
77			\end{center}
78			\end{table}
79
80	beaucero	1.5
81			\begin{table}[h]
82			\begin{center}
83			\begin{tabular}{lcccc} \hline \hline
84			& 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline
85			$N$ - ZZ -Zgamma &19.9098$\pm$1.00886&23.5941$\pm$0.00420358&23.3592$\pm$0.95001&25.5227$\pm$0.00420358\\ \hline
86			$N^{non genuine Z}$ (Fit)&1.45557$\pm$2.9589&6.0224$\pm$4.0679&1.55994$\pm$3.1279&3.07779$\pm$3.50566\\ \hline
87			$N^{genuine Z}$ (matrix method)&10.0606 $\pm$6.75575&15.8043 $\pm$8.41727)&14.4848 $\pm$6.80421&15.7609 $\pm$5.70923\\ \hline
88			$N^{WZ}$ & 8.84029 $\pm$7.51757&7.78552 $\pm$11.1206&7.92435 $\pm$7.64947&9.75762 $\pm$7.37277\\ \hline
89			\WZ from MC &8.1&9.0& 9.2 &11.3\\
90
91			\hline
92			\end{tabular}
93
94			\caption{Loose Sample: Expected number of selected events for an integrated luminosity of 300
95			pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.}
96			\label{tab:FinalXCLoose}
97			\end{center}
98			\end{table}
99
100	beaucero	1.4	\begin{figure}[hbt]
101			\begin{center}
102			\scalebox{0.8}{\includegraphics{figs/MatrixMethod3eLooseTightZmassMWtCut.eps}}
103			\caption{Result of Matrix Method application for $3e$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.}
104			\label{fig:FinalMatrix3e}
105			\end{center}
106			\end{figure}
107
108			\begin{figure}[hbt]
109			\begin{center}
110			\scalebox{0.8}{\includegraphics{figs/MatrixMethod2e1muLooseTightZmassMWtCut.eps}}
111			\caption{Result of Matrix Method application for $2e1\mu$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.}
112			\label{fig:FinalMatrix2e1mu}
113			\end{center}
114			\end{figure}
115
116			\begin{figure}[hbt]
117			\begin{center}
118			\scalebox{0.8}{\includegraphics{figs/MatrixMethod2mu1eLooseTightZmassMWtCut.eps}}
119			\caption{Result of Matrix Method application for $2\mu1e$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.}
120			\label{fig:FinalMatrix2mu1e}
121			\end{center}
122			\end{figure}
123	beaucero	1.2
124	beaucero	1.4	\begin{figure}[hbt]
125			\begin{center}
126			\scalebox{0.8}{\includegraphics{figs/MatrixMethod3muLooseTightZmassMWtCut.eps}}
127			\caption{Result of Matrix Method application for $3\mu$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.}
128			\label{fig:FinalMatrix3mu}
129			\end{center}
130			\end{figure}
131	beaucero	1.2
132
133
134			Check on Without MWtCut Samples~\ref{tab:FitNoMWt} (Linear Fit):
135			\begin{table}[h]
136			\begin{center}
137			\begin{tabular}{\|l\|c\|c\|c\|c\|c\|c\|c\|} \hline
138			& \multicolumn{2}{c\|}{Background with genuine \Z} & \multicolumn{4}{c\|}{Background without
139			genuine \Z boson} \\
140			Channel & $\Z+jets$ & $\Z b\bar{b}$ & $t\bar{t}$ & $\W+jets$ & $t\bar{t}$ + $\W+jets$ & Fit result \\ \hline
141	beaucero	1.5	$3e$ Loose &44.5748 & 12.6511 & 1.62239 & 0.357018 & 1.9794 & 6.81271$ \pm $5.60783 \\\hline
142			$3e$ Tight &13.8877 & 5.04709 & 0.79839 & 0.357018 & 1.15541 & 3.76484$ \pm $7.74145 \\\hline
143			$2e1mu$ Loose &41.5198 & 78.9304 & 12.6155 & 0 & 12.6155 & 16.1879$ \pm $5.12531 \\\hline
144			$2e1mu$ Tight &0.993801 & 1.97881 & 0.883798 & 0 & 0.883798 & 1.63388$ \pm $2.94792 \\\hline
145			$2mu1e$ Loose &56.2794 & 15.3858 & 1.89565 & 0 & 1.89565 & 7.24906$ \pm $5.77249 \\\hline
146			$2mu1e$ Tight &17.2942 & 5.55847 & 0.79839 & 0 & 0.79839 & 4.53933$ \pm $7.00846 \\\hline
147			$3mu$ Loose &43.6972 & 84.8891 & 11.9976 & 0 & 11.9976 & 11.1603$ \pm $3.36046 \\\hline
148			$3mu$ Tight &0.806562 & 2.31232 & 0.324477 & 0 & 0.324477 & 0.836361$ \pm $2.47575 \\\hline
149	beaucero	1.2	\end{tabular}
150			\end{center}
151			\caption{Comparison between Monte Carlo truth information and the results of the fit for the background without genuine \Z boson. Number of events are obtained in the invariant mass range between 81 and 101 GeV. The ``Loose'' and ``Tight'' selection criteria applied for third lepton considered.
152			%I AM NOT SURE I UNDERSTAND WHAT IS WRITTEN HERE
153			% One has to consider that this study as been perform on a smaller sample than the other part of the analysis a 10\% statistics error as to be counted until the study is performed on the whole samples.
154			}
155			\label{tab:FitNoMWt}
156			\end{table}
157
158
159	beaucero	1.4	In table~\ref{tab:FinalNoMWtCut}, the final results are presented if
160			we remove the cut on the W transverse mass. Everthing is still in
161			perfect agreement... The corresponding figure can be
162			seen~\ref{fig:FinalMatrix3eNoWtCut}~\ref{fig:FinalMatrix2e1muNoWtCut}~\ref{fig:FinalMatrix2mu1eNoWtCut}~\ref{fig:FinalMatrix3muNoWtCut}
163			for $3e$, $2e1\mu$, $2\mu1e$ and $3\mu$ channels respectively.
164	beaucero	1.2
165			\begin{table}[h]
166			\begin{center}
167			\begin{tabular}{lcccc} \hline \hline
168			& 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline
169			%$N_{Loose}$ - ZZ -Zgamma &19.7$\pm$1.1 &22.9$\pm$0.7 &22.9$\pm$1.1 &25.6$\pm$0.8 \\
170			%$N_{Loose} ^{non genuine Z}$ (Fit) &1.0$\pm$1.5 &11.2$\pm$5.5 &3.1$\pm$2.4 & 4.8$\pm$3.7\\
171	beaucero	1.3	$N$ - ZZ -Zgamma &21.9$\pm$5.4 &15.2$\pm$1.0 &24.9$\pm$4.4 &17.8$\pm$1.3\\
172	beaucero	1.2	$N^{non genuine Z}$ (Fit)&1.7$\pm$2.9 &1.0$\pm$2.8 &1.7$\pm$3.0 &0.7$\pm$2.8\\
173	beaucero	1.3	$N^{genuine Z}$ (matrix method)& 8.4$\pm$3.5 &5.7$\pm$4.7 &11.2$\pm$4.3 &6.4$\pm$5.3\\\hline
174			$N^{WZ}$ & 11.8$\pm$7.0 &8.5$\pm$5.6 &12.0$\pm$6.8 &10.7$\pm$6.1\\\hline
175			\WZ from MC &11.6&12.3& 13.1 &14.9\\
176	beaucero	1.2
177			\hline
178			\end{tabular}
179
180			\caption{Expected number of selected events for an integrated luminosity of 300
181			pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.}
182	beaucero	1.3	\label{tab:FinalNoMWtCut}
183	beaucero	1.2	\end{center}
184			\end{table}
185	beaucero	1.4
186			\begin{figure}[hbt]
187			\begin{center}
188			\scalebox{0.8}{\includegraphics{figs/MatrixMethod3eLooseTightZmassNoCutMWt.eps}}
189			\caption{Before M$_T$(W) criteria: Result of Matrix Method application for $3e$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.}
190			\label{fig:FinalMatrix3eNoWtCut}
191			\end{center}
192			\end{figure}
193
194			\begin{figure}[hbt]
195			\begin{center}
196			\scalebox{0.8}{\includegraphics{figs/MatrixMethod2e1muLooseTightZmassNoCutMWt.eps}}
197			\caption{Before M$_T$(W) criteria: Result of Matrix Method application for $2e1\mu$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.}
198			\label{fig:FinalMatrix2e1muNoWtCut}
199			\end{center}
200			\end{figure}
201
202			\begin{figure}[hbt]
203			\begin{center}
204			\scalebox{0.8}{\includegraphics{figs/MatrixMethod2mu1eLooseTightZmassNoCutMWt.eps}}
205			\caption{Before M$_T$(W) criteria: Result of Matrix Method application for $2\mu1e$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.}
206			\label{fig:FinalMatrix2mu1eNoWtCut}
207			\end{center}
208			\end{figure}
209
210			\begin{figure}[hbt]
211			\begin{center}
212			\scalebox{0.8}{\includegraphics{figs/MatrixMethod3muLooseTightZmassNoCutMWt.eps}}
213			\caption{Before M$_T$(W) criteria: Result of Matrix Method application for $3\mu$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.}
214			\label{fig:FinalMatrix3muNoWtCut}
215			\end{center}
216			\end{figure}
217
218
219			TO BE REMOVE??? ONLY USEFUL FOR MUONS PART???
220			Check on Loosy Samples~\ref{tab:FitLoosy} (Linear Fit):
221			\begin{table}[h]
222			\begin{center}
223			\begin{tabular}{\|l\|c\|c\|c\|c\|c\|c\|c\|} \hline
224			& \multicolumn{2}{c\|}{Background with genuine \Z} & \multicolumn{4}{c\|}{Background without
225			genuine \Z boson} \\
226			Channel & $\Z+jets$ & $\Z b\bar{b}$ & $t\bar{t}$ & $\W+jets$ & $t\bar{t}$ + $\W+jets$ & Fit result \\ \hline
227			$3e$ Loose &17.4 & 14.1 & 1.2 & 0.1 & 1.3 & 4.0$ \pm $3.6 \\\hline
228			$3e$ Tight &5.3 & 5.8 & 0.7 & 0.1 & 0.8 & 2.7$ \pm $3.2 \\\hline
229			$2e1\mu$ Loose &16.5 & 83.1 & 10.0 & 0 & 10.0 & 13.1$ \pm $5.0 \\\hline
230			$2e1\mu$ Tight &0.3 & 2.0 & 1.0 & 0 & 1.0 & 1.3$ \pm $3.0 \\\hline
231			$2\mu1e$ Loose &27.5 & 20.1 & 15.0 & 0.2 & 15.3 & 23.7$ \pm $5.5 \\ \hline
232			$2\mu1e$ Tight &7.7 & 6.9 & 13.2 & 0.1 & 13.3 & 19.7$ \pm $5.2 \\ \hline
233			$3\mu$ Loose &33.4 & 138.2 & 45.8 & 0.7 & 46.4 & 48.7$ \pm $6.7 \\\hline
234			$3\mu$ Tight &8.9 & 25.2 & 19.7 & 0.2 & 19.9 & 23.5$ \pm $5.5 \\\hline
235			\end{tabular}
236			\end{center}
237			\caption{Comparison between Monte Carlo truth information and the results of the fit for the background without genuine \Z boson. Number of events are obtained in the invariant mass range between 81 and 101 GeV. The ``Loose'' and ``Tight'' selection criteria applied for third lepton considered.
238			%I AM NOT SURE I UNDERSTAND WHAT IS WRITTEN HERE
239			% One has to consider that this study as been perform on a smaller sample than the other part of the analysis a 10\% statistics error as to be counted until the study is performed on the whole samples.
240			}
241			\label{tab:FitLoosy}
242			\end{table}