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 &2.8 & 2.9 & 0.8 & 0.1 & 0.9 & 1.0$ \pm $2.7 \\\hline 
$3e$ Tight &0.8 & 1.2 & 0.4 & 0.1 & 0.5 & 0.7$ \pm $2.5 \\\hline 
$2e1\mu$ Loose &1.3 & 4.7 & 4.5 & 0 & 4.5 & 4.2$ \pm $3.7 \\\hline 
$2e1\mu$ Tight &0.0 & 0.1 & 0.5 & 0 & 0.5 & 0.6$ \pm $2.5 \\\hline 
$2\mu1e$ Loose &4.1 & 2.9 & 0.5 & 0 & 0.5 & 0.9$ \pm $2.7 \\\hline 
$2\mu1e$ Tight &0.8 & 1.3 & 0.4 & 0 & 0.4 & 0.6$ \pm $2.4 \\\hline 
$3\mu$ Loose &1.9 & 4.2 & 4.1 & 0 & 4.1 & 2.3$ \pm $3.3 \\\hline 
$3\mu$ Tight &0.1 & 0.3 & 0.2 & 0 & 0.2 & 0.4$ \pm $2.4 \\\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_{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 &12.2$\pm$1.1 &8.7$\pm$0.6 &12.8$\pm$1.0 &11.1$\pm$0.7\\
$N^{non genuine Z}$ (Fit)&0.7$\pm$2.5 &0.6$\pm$2.5 &0.6$\pm$2.4 &0.4$\pm$2.4\\
$N^{genuine Z}$ (matrix method)& 3.2$\pm$1.8 &0.7$\pm$0.9 &4.6$\pm$2.1 &0.9$\pm$1.1\\\hline 
$N^{WZ}$ & 8.3$\pm$3.2 &7.4$\pm$2.8 &7.6$\pm$3.3 &9.8$\pm$2.7\\\hline 
\WZ from MC &7.9&8.0& 8.9 &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{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 &16.4 & 12.7 & 1.1 & 0.1 & 1.2 & 2.8$ \pm $3.4 \\\hline 
$3e$ Tight &4.9 & 5.0 & 0.5 & 0.1 & 0.7 & 1.7$ \pm $2.9 \\\hline 
$2e1\mu$ Loose &15.8 & 78.9 & 9.0 & 0 & 9.0 & 11.6$ \pm $4.9 \\\hline 
$2e1\mu$ Tight &0.3 & 2.0 & 0.7 & 0 & 0.7 & 1.0$ \pm $2.8 \\\hline 
$2\mu1e$ Loose &20.4 & 15.4 & 1.3 & 0 & 1.3 & 2.9$ \pm $3.5 \\\hline 
$2\mu1e$ Tight &5.8 & 5.6 & 0.5 & 0 & 0.5 & 1.7$ \pm $3.0 \\\hline 
$3\mu$ Loose &16.8 & 84.9 & 8.5 & 0 & 8.5 & 7.1$ \pm $4.4 \\\hline 
$3\mu$ Tight &0.3 & 2.3 & 0.2 & 0 & 0.2 & 0.7$ \pm $2.8 \\\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:	1.4
Committed:	Sun Jul 27 17:53:05 2008 UTC (16 years, 9 months ago) by beaucero
Content type:	application/x-tex
Branch:	MAIN
Changes since 1.3:	+104 -28 lines
Log Message:	Steph Appendix
#	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	1.2	$3e$ Loose &2.8 & 2.9 & 0.8 & 0.1 & 0.9 & 1.0$ \pm $2.7 \\\hline
41			$3e$ Tight &0.8 & 1.2 & 0.4 & 0.1 & 0.5 & 0.7$ \pm $2.5 \\\hline
42			$2e1\mu$ Loose &1.3 & 4.7 & 4.5 & 0 & 4.5 & 4.2$ \pm $3.7 \\\hline
43			$2e1\mu$ Tight &0.0 & 0.1 & 0.5 & 0 & 0.5 & 0.6$ \pm $2.5 \\\hline
44			$2\mu1e$ Loose &4.1 & 2.9 & 0.5 & 0 & 0.5 & 0.9$ \pm $2.7 \\\hline
45			$2\mu1e$ Tight &0.8 & 1.3 & 0.4 & 0 & 0.4 & 0.6$ \pm $2.4 \\\hline
46			$3\mu$ Loose &1.9 & 4.2 & 4.1 & 0 & 4.1 & 2.3$ \pm $3.3 \\\hline
47			$3\mu$ Tight &0.1 & 0.3 & 0.2 & 0 & 0.2 & 0.4$ \pm $2.4 \\\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$\\ \hline
65			%$N_{Loose}$ - ZZ -Zgamma &19.7$\pm$1.1 &22.9$\pm$0.7 &22.9$\pm$1.1 &25.6$\pm$0.8 \\
66			%$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\\
67			$N$ - ZZ -Zgamma &12.2$\pm$1.1 &8.7$\pm$0.6 &12.8$\pm$1.0 &11.1$\pm$0.7\\
68	beaucero	1.2	$N^{non genuine Z}$ (Fit)&0.7$\pm$2.5 &0.6$\pm$2.5 &0.6$\pm$2.4 &0.4$\pm$2.4\\
69			$N^{genuine Z}$ (matrix method)& 3.2$\pm$1.8 &0.7$\pm$0.9 &4.6$\pm$2.1 &0.9$\pm$1.1\\\hline
70			$N^{WZ}$ & 8.3$\pm$3.2 &7.4$\pm$2.8 &7.6$\pm$3.3 &9.8$\pm$2.7\\\hline
71	beaucero	1.1	\WZ from MC &7.9&8.0& 8.9 &10.1\\
72
73			\hline
74			\end{tabular}
75
76			\caption{Expected number of selected events for an integrated luminosity of 300
77			pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.}
78			\label{tab:FinalXC}
79			\end{center}
80			\end{table}
81
82	beaucero	1.4	\begin{figure}[hbt]
83			\begin{center}
84			\scalebox{0.8}{\includegraphics{figs/MatrixMethod3eLooseTightZmassMWtCut.eps}}
85			\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.}
86			\label{fig:FinalMatrix3e}
87			\end{center}
88			\end{figure}
89
90			\begin{figure}[hbt]
91			\begin{center}
92			\scalebox{0.8}{\includegraphics{figs/MatrixMethod2e1muLooseTightZmassMWtCut.eps}}
93			\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.}
94			\label{fig:FinalMatrix2e1mu}
95			\end{center}
96			\end{figure}
97
98			\begin{figure}[hbt]
99			\begin{center}
100			\scalebox{0.8}{\includegraphics{figs/MatrixMethod2mu1eLooseTightZmassMWtCut.eps}}
101			\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.}
102			\label{fig:FinalMatrix2mu1e}
103			\end{center}
104			\end{figure}
105	beaucero	1.2
106	beaucero	1.4	\begin{figure}[hbt]
107			\begin{center}
108			\scalebox{0.8}{\includegraphics{figs/MatrixMethod3muLooseTightZmassMWtCut.eps}}
109			\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.}
110			\label{fig:FinalMatrix3mu}
111			\end{center}
112			\end{figure}
113	beaucero	1.2
114
115
116			Check on Without MWtCut Samples~\ref{tab:FitNoMWt} (Linear Fit):
117			\begin{table}[h]
118			\begin{center}
119			\begin{tabular}{\|l\|c\|c\|c\|c\|c\|c\|c\|} \hline
120			& \multicolumn{2}{c\|}{Background with genuine \Z} & \multicolumn{4}{c\|}{Background without
121			genuine \Z boson} \\
122			Channel & $\Z+jets$ & $\Z b\bar{b}$ & $t\bar{t}$ & $\W+jets$ & $t\bar{t}$ + $\W+jets$ & Fit result \\ \hline
123			$3e$ Loose &16.4 & 12.7 & 1.1 & 0.1 & 1.2 & 2.8$ \pm $3.4 \\\hline
124			$3e$ Tight &4.9 & 5.0 & 0.5 & 0.1 & 0.7 & 1.7$ \pm $2.9 \\\hline
125			$2e1\mu$ Loose &15.8 & 78.9 & 9.0 & 0 & 9.0 & 11.6$ \pm $4.9 \\\hline
126			$2e1\mu$ Tight &0.3 & 2.0 & 0.7 & 0 & 0.7 & 1.0$ \pm $2.8 \\\hline
127			$2\mu1e$ Loose &20.4 & 15.4 & 1.3 & 0 & 1.3 & 2.9$ \pm $3.5 \\\hline
128			$2\mu1e$ Tight &5.8 & 5.6 & 0.5 & 0 & 0.5 & 1.7$ \pm $3.0 \\\hline
129			$3\mu$ Loose &16.8 & 84.9 & 8.5 & 0 & 8.5 & 7.1$ \pm $4.4 \\\hline
130			$3\mu$ Tight &0.3 & 2.3 & 0.2 & 0 & 0.2 & 0.7$ \pm $2.8 \\\hline
131			\end{tabular}
132			\end{center}
133			\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.
134			%I AM NOT SURE I UNDERSTAND WHAT IS WRITTEN HERE
135			% 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.
136			}
137			\label{tab:FitNoMWt}
138			\end{table}
139
140
141	beaucero	1.4	In table~\ref{tab:FinalNoMWtCut}, the final results are presented if
142			we remove the cut on the W transverse mass. Everthing is still in
143			perfect agreement... The corresponding figure can be
144			seen~\ref{fig:FinalMatrix3eNoWtCut}~\ref{fig:FinalMatrix2e1muNoWtCut}~\ref{fig:FinalMatrix2mu1eNoWtCut}~\ref{fig:FinalMatrix3muNoWtCut}
145			for $3e$, $2e1\mu$, $2\mu1e$ and $3\mu$ channels respectively.
146	beaucero	1.2
147			\begin{table}[h]
148			\begin{center}
149			\begin{tabular}{lcccc} \hline \hline
150			& 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline
151			%$N_{Loose}$ - ZZ -Zgamma &19.7$\pm$1.1 &22.9$\pm$0.7 &22.9$\pm$1.1 &25.6$\pm$0.8 \\
152			%$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\\
153	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\\
154	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\\
155	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
156			$N^{WZ}$ & 11.8$\pm$7.0 &8.5$\pm$5.6 &12.0$\pm$6.8 &10.7$\pm$6.1\\\hline
157			\WZ from MC &11.6&12.3& 13.1 &14.9\\
158	beaucero	1.2
159			\hline
160			\end{tabular}
161
162			\caption{Expected number of selected events for an integrated luminosity of 300
163			pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.}
164	beaucero	1.3	\label{tab:FinalNoMWtCut}
165	beaucero	1.2	\end{center}
166			\end{table}
167	beaucero	1.4
168			\begin{figure}[hbt]
169			\begin{center}
170			\scalebox{0.8}{\includegraphics{figs/MatrixMethod3eLooseTightZmassNoCutMWt.eps}}
171			\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.}
172			\label{fig:FinalMatrix3eNoWtCut}
173			\end{center}
174			\end{figure}
175
176			\begin{figure}[hbt]
177			\begin{center}
178			\scalebox{0.8}{\includegraphics{figs/MatrixMethod2e1muLooseTightZmassNoCutMWt.eps}}
179			\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.}
180			\label{fig:FinalMatrix2e1muNoWtCut}
181			\end{center}
182			\end{figure}
183
184			\begin{figure}[hbt]
185			\begin{center}
186			\scalebox{0.8}{\includegraphics{figs/MatrixMethod2mu1eLooseTightZmassNoCutMWt.eps}}
187			\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.}
188			\label{fig:FinalMatrix2mu1eNoWtCut}
189			\end{center}
190			\end{figure}
191
192			\begin{figure}[hbt]
193			\begin{center}
194			\scalebox{0.8}{\includegraphics{figs/MatrixMethod3muLooseTightZmassNoCutMWt.eps}}
195			\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.}
196			\label{fig:FinalMatrix3muNoWtCut}
197			\end{center}
198			\end{figure}
199
200
201			TO BE REMOVE??? ONLY USEFUL FOR MUONS PART???
202			Check on Loosy Samples~\ref{tab:FitLoosy} (Linear Fit):
203			\begin{table}[h]
204			\begin{center}
205			\begin{tabular}{\|l\|c\|c\|c\|c\|c\|c\|c\|} \hline
206			& \multicolumn{2}{c\|}{Background with genuine \Z} & \multicolumn{4}{c\|}{Background without
207			genuine \Z boson} \\
208			Channel & $\Z+jets$ & $\Z b\bar{b}$ & $t\bar{t}$ & $\W+jets$ & $t\bar{t}$ + $\W+jets$ & Fit result \\ \hline
209			$3e$ Loose &17.4 & 14.1 & 1.2 & 0.1 & 1.3 & 4.0$ \pm $3.6 \\\hline
210			$3e$ Tight &5.3 & 5.8 & 0.7 & 0.1 & 0.8 & 2.7$ \pm $3.2 \\\hline
211			$2e1\mu$ Loose &16.5 & 83.1 & 10.0 & 0 & 10.0 & 13.1$ \pm $5.0 \\\hline
212			$2e1\mu$ Tight &0.3 & 2.0 & 1.0 & 0 & 1.0 & 1.3$ \pm $3.0 \\\hline
213			$2\mu1e$ Loose &27.5 & 20.1 & 15.0 & 0.2 & 15.3 & 23.7$ \pm $5.5 \\ \hline
214			$2\mu1e$ Tight &7.7 & 6.9 & 13.2 & 0.1 & 13.3 & 19.7$ \pm $5.2 \\ \hline
215			$3\mu$ Loose &33.4 & 138.2 & 45.8 & 0.7 & 46.4 & 48.7$ \pm $6.7 \\\hline
216			$3\mu$ Tight &8.9 & 25.2 & 19.7 & 0.2 & 19.9 & 23.5$ \pm $5.5 \\\hline
217			\end{tabular}
218			\end{center}
219			\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.
220			%I AM NOT SURE I UNDERSTAND WHAT IS WRITTEN HERE
221			% 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.
222			}
223			\label{tab:FitLoosy}
224			\end{table}