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# Line 1 | Line 1
1 + \clearpage
2 + \newpage
3   \appendix
4   \section{Additional Cross Check on Background Estimation Studies}
5  
6 < In figures~\ref{fig:AllFits}, the fit approximation of the invariant
6 > In Figure~\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 < order to fit the background.
10 > order to fit the background. It has to be noticed that due to a lack
11 > of statistics in chowder soup, all bins 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 constrained.
16  
17  
18   \begin{figure}[hbt]
# Line 14 | Line 21 | order to fit the background.
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.}
24 >  \caption{Invariant 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}
# Line 30 | Line 37 | The comparison can be seen in table~\ref
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 < $3e$ Loose & 7.1 & 2.8 & 1.1 & 0.4 & 1.5& 4.3 $\pm$ 1.8 \\ \hline
41 < $3e$ Tight & 1.9 & 1.2 & 0.6 & 0.4 & 1.0 & 3.2 $\pm$ 1.5 \\ \hline  
42 < $2e1\mu$ Loose  & 4.0 & 4.7 & 5.3 & 0.0 & 5.3 & 17.3 $\pm$ 3.8\\ \hline
43 < $2e1\mu$ Tight  & 0.0 & 0.1 & 0.6 & 0.0 & 0.6 & 2.8 $\pm$ 1.6\\ \hline
44 < $2\mu 1e$ Loose & 10.0 & 2.8 & 0.8 & 0.0 & 0.8 & 4.6 $\pm$ 1.9\\ \hline
45 < $2\mu 1e$ Tight & 1.8 & 1.2 & 0.6 & 0.0 & 0.6 & 3.1 $\pm$ 1.5\\ \hline
46 < $3\mu$ Loose & 4.7 & 4.1 & 5.4 & 0.0 & 5.4 & 8.8 $\pm$ 2.8\\ \hline
47 < $3\mu$ Tight & 0.1 & 0.3 & 0.3 & 0.0 & 0.3 & 1.4 $\pm$ 1.2\\ \hline
40 > $3e$ Loose &7.1 & 2.9 & 1.1 & 0.4 & 1.5 & 1.5$ \pm $3.0 \\\hline
41 > $3e$ Tight &2.0 & 1.2 & 0.6 & 0.4 & 1.0 & 1.1$ \pm $2.8 \\\hline
42 > $2e1mu$ Loose &4.0 & 4.7 & 6.2 & 0.0 & 6.2 & 6.0$ \pm $4.1 \\\hline
43 > $2e1mu$ Tight &0.0 & 0.1 & 0.7 & 0.0 & 0.7 & 1.0$ \pm $2.8 \\\hline  
44 > $2mu1e$ Loose &10.1 & 2.9 & 0.8 & 0.0 & 0.8 & 1.6$ \pm $3.1 \\\hline
45 > $2mu1e$ Tight &1.8 & 1.3 & 0.6 & 0.0 & 0.6 & 1.0$ \pm $2.7 \\\hline
46 > $3mu$ Loose &4.5 & 4.2 & 5.9 & 0.0 & 5.9 & 3.1$ \pm $3.5 \\\hline
47 > $3mu$ Tight &0.1 & 0.3 & 0.3 & 0.0 & 0.3 & 0.5$ \pm $2.5 \\\hline
48   \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.
44 %I AM NOT SURE I UNDERSTAND WHAT IS WRITTEN HERE
45 % 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.
51   }
52   \label{tab:CompFit}
53   \end{table}
54  
55  
56   Nevertheless in association with the matrix method the background is
57 < well estimated as one can see in table~\ref{tab:FinalXC}.
57 > well estimated as one can see in table~\ref{tab:FinalXC}.The corresponding figures can be
58 > seen in Figures~\ref{fig:FinalMatrix3e}, \ref{fig:FinalMatrix2e1mu}, \ref{fig:FinalMatrix2mu1e} and \ref{fig:FinalMatrix3mu}
59 > for $3e$, $2e1\mu$, $2\mu1e$ and $3\mu$ channels respectively.
60  
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 < $N^{non genuine Z}$ (Fit)&3.2$\pm$1.5 &2.8$\pm$1.6 &3.1$\pm$1.5 &1.4$\pm$1.2\\
69 < $N^{genuine Z}$ (matrix method)& 2.8$\pm$1.5 &0.4$\pm$1.1 &4.2$\pm$1.7 &3.7$\pm$1.7\\\hline
63 < $N^{WZ}$ & 6.2$\pm$2.4 &5.5$\pm$2.0 &5.5$\pm$2.5 &6.0$\pm$2.2\\\hline
64 < \WZ from MC &7.9&8.0& 8.9 &10.1\\
65 > $N$ - ZZ -Zgamma &12.4$\pm$1.0 &8.7$\pm$0.0&13.1$\pm$0.9&10.6$\pm$0.0\\ \hline
66 > $N^{non genuine Z}$ (Fit)&1.1$\pm$2.8&1.0$\pm$2.8&1.0$\pm$2.7&0.5$\pm$2.5\\ \hline
67 > $N^{genuine Z}$ (matrix method)&3.2 $\pm$1.8&0.9 $\pm$1.1&4.6 $\pm$2.1&0.9 $\pm$1.1\\ \hline
68 > $N^{WZ}$ & 8.2$\pm$3.5&7.7 $\pm$3.2 &7.6$\pm$3.5&9.6 $\pm$2.8\\ \hline
69 > \WZ from MC &7.9&8.1& 9.0 &10.1\\
70  
71   \hline
72   \end{tabular}
# Line 72 | Line 77 | $N^{WZ}$ & 6.2$\pm$2.4 &5.5$\pm$2.0 &5.5
77   \end{center}
78   \end{table}
79  
80 +
81 + \begin{table}[h]
82 +  \begin{center}
83 + \begin{tabular}{lcccc} \hline \hline
84 + & 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline
85 + $N$ - ZZ -Zgamma &19.9$\pm$1.0&23.6$\pm$0.0&23.4$\pm$1.0&25.5$\pm$0.0\\ \hline
86 + $N^{non genuine Z}$ (Fit)&1.5$\pm$3.0&6.0$\pm$4.1&1.6$\pm$3.1&3.1$\pm$3.5\\ \hline
87 + $N^{genuine Z}$ (matrix method)&10.1 $\pm$6.8&15.8 $\pm$8.4&14.5 $\pm$6.8&15.8 $\pm$5.7\\ \hline
88 + $N^{WZ}$ & 8.8$\pm$7.5&7.8$\pm$11.1&7.9$\pm$7.6&9.8 $\pm$7.4\\ \hline
89 + \WZ from MC &8.1&9.0& 9.2 &11.3\\
90 +
91 + \hline
92 + \end{tabular}
93 +
94 + \caption{Loose Sample: Expected number of selected events for an integrated luminosity of 300
95 + pb$^{-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 + \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 Invariant 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 Invariant 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 Invariant 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 +
124 + \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 Invariant 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 +
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 + $3e$ Loose &44.6 & 12.7 & 1.6 & 0.4 & 2.0 & 6.6$\pm$4.2 \\\hline
142 + $3e$ Tight &13.9 & 5.0 & 0.8 & 0.4 & 1.2 & 3.8$\pm$3.5 \\\hline
143 + $2e1mu$ Loose &41.5 & 78.9 & 12.6 & 0 & 12.6 & 16.9$\pm$5.5 \\\hline
144 + $2e1mu$ Tight &1.0 & 2.0 & 0.9 & 0 & 0.9 & 1.5$\pm$3.2 \\\hline
145 + $2mu1e$ Loose &56.3 & 15.4 & 1.9 & 0 & 1.9 & 6.9$\pm$4.4 \\\hline
146 + $2mu1e$ Tight &17.3 & 5.6 & 0.8 & 0 & 0.8 & 4.1$\pm$2.5 \\\hline
147 + $3mu$ Loose &43.7 & 84.9 & 12.0 & 0 & 12.0 & 11.0$\pm$5.0 \\\hline
148 + $3mu$ Tight &0.8 & 2.3 & 0.3 & 0 & 0.3 & 0.8$\pm$2.8 \\\hline
149 + \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 + 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 figures can be
162 + seen in Figures~\ref{fig:FinalMatrix3eNoWtCut}, \ref{fig:FinalMatrix2e1muNoWtCut},
163 + \ref{fig:FinalMatrix2mu1eNoWtCut} and  \ref{fig:FinalMatrix3muNoWtCut}
164 + for $3e$, $2e1\mu$, $2\mu1e$ and $3\mu$ channels respectively.
165 +
166 + \begin{table}[h]
167 +  \begin{center}
168 + \begin{tabular}{lcccc} \hline \hline
169 + & 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline
170 + $N$ - ZZ -Zgamma &36.0$\pm$7.1&15.9$\pm$0.0&40.2$\pm$5.7&18.0$\pm$0.0\\ \hline
171 + $N^{non genuine Z}$ (Fit)&3.8$\pm$3.5&1.5$\pm$3.2&4.1$\pm$2.5&0.8$\pm$2.8\\ \hline
172 + $N^{genuine Z}$ (matrix method)&18.7 $\pm$6.1&8.4 $\pm$6.6&23.4 $\pm$7.5& 8.9 $\pm$7.1\\ \hline
173 + $N^{WZ}$ &10.1 $\pm$8.0&7.6 $\pm$7.5&11.0 $\pm$8.9& 9.1 $\pm$7.6\\ \hline
174 + \WZ from MC &11.6&12.3& 13.3 &14.9\\
175 +
176 + \hline
177 + \end{tabular}
178 +
179 + \caption{Expected number of selected events for an integrated luminosity of 300
180 + pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.}
181 + \label{tab:FinalNoMWtCut}
182 + \end{center}
183 + \end{table}
184 +
185 + \begin{table}[h]
186 +  \begin{center}
187 + \begin{tabular}{lcccc} \hline \hline
188 + & 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline
189 + $N$ - ZZ -Zgamma  &75.3$\pm$7.3&146.6$\pm$0.0&90.4$\pm$5.9&156.9$\pm$0.0\\ \hline
190 + $N^{non genuine Z}$ (Fit)&6.6$\pm$4.2&16.9$\pm$5.5&6.9$\pm$4.4&11.0$\pm$5.0\\ \hline
191 + $N^{genuine Z}$ (matrix method)&58.5 $\pm$14.4&139.2 $\pm$20.3&73.2 $\pm$14.9& 147.7 $\pm$14.7\\ \hline
192 + $N^{WZ}$  &9.5$\pm$16.4&7.4 $\pm$27.0&11.3 $\pm$17.0&  9.2 $\pm$19.0\\\hline
193 + \WZ from MC &12.0&14.2& 13.6 &17.2\\
194 +
195 + \hline
196 + \end{tabular}
197 +
198 + \caption{Loose Sample: Expected number of selected events for an integrated luminosity of 300
199 + pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.}
200 + \label{tab:FinalNoMWtCutLoose}
201 + \end{center}
202 + \end{table}
203 +
204 + \begin{figure}[hbt]
205 +  \begin{center}
206 + <<<<<<< AppendixFitTest.tex
207 +  \scalebox{0.8}{\includegraphics{figs/MatrixMethod3eLooseTightZmassNoCutMWt.eps}}
208 +  \caption{Before M$_T$(W) criteria: Result of Matrix Method application for $3e$ channel for Invariant 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.}
209 + =======
210 +  \scalebox{0.8}{\includegraphics{figs/MatrixMethod3eLooseTightZmassMWtCutNoFit.eps}}
211 +  \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.}
212 + >>>>>>> 1.7
213 +  \label{fig:FinalMatrix3eNoWtCut}
214 +  \end{center}
215 + \end{figure}
216 +
217 + \begin{figure}[hbt]
218 +  \begin{center}
219 + <<<<<<< AppendixFitTest.tex
220 +  \scalebox{0.8}{\includegraphics{figs/MatrixMethod2e1muLooseTightZmassNoCutMWt.eps}}
221 +  \caption{Before M$_T$(W) criteria: Result of Matrix Method application for $2e1\mu$ channel for Invariant 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.}
222 + =======
223 +  \scalebox{0.8}{\includegraphics{figs/MatrixMethod2e1muLooseTightZmassMWtCutNoFit.eps}}
224 +  \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.}
225 + >>>>>>> 1.7
226 +  \label{fig:FinalMatrix2e1muNoWtCut}
227 +  \end{center}
228 + \end{figure}
229 +
230 + \begin{figure}[hbt]
231 +  \begin{center}
232 + <<<<<<< AppendixFitTest.tex
233 +  \scalebox{0.8}{\includegraphics{figs/MatrixMethod2mu1eLooseTightZmassNoCutMWt.eps}}
234 +  \caption{Before M$_T$(W) criteria: Result of Matrix Method application for $2\mu1e$ channel for Invariant 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.}
235 + =======
236 +  \scalebox{0.8}{\includegraphics{figs/MatrixMethod2mu1eLooseTightZmassMWtCutNoFit.eps}}
237 +  \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.}
238 + >>>>>>> 1.7
239 +  \label{fig:FinalMatrix2mu1eNoWtCut}
240 +  \end{center}
241 + \end{figure}
242 +
243 + \begin{figure}[hbt]
244 +  \begin{center}
245 +  \scalebox{0.8}{\includegraphics{figs/MatrixMethod3muLooseTightZmassNoCutMWt.eps}}
246 +  \caption{Before M$_T$(W) criteria: Result of Matrix Method application for $3\mu$ channel for Invariant 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.}
247 +  \label{fig:FinalMatrix3muNoWtCut}
248 +  \end{center}
249 + \end{figure}
250 +
251 +
252 + WIHTOUT FITTING:
253 + \begin{table}[h]
254 +  \begin{center}
255 + \begin{tabular}{lcccc} \hline \hline
256 + & 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline
257 + $N$ - ZZ -Zgamma &12.4$\pm$1.0 &8.7$\pm$0&13.1$\pm$0.9&10.6$\pm$0.0\\ \hline
258 + $N^{genuine Z}$ (matrix method)&3.2 $\pm$1.6&15.8 $\pm$0.7&4.6 $\pm$1.9&0.9 $\pm$1.1\\ \hline
259 + $N^{WZ}$ &8.2 $\pm$1.6&7.8 $\pm$0.7&7.6 $\pm$1.9&9.6$\pm$1.1\\ \hline
260 + \WZ from MC &7.9&8.1& 9.0 &10.1\\
261 +
262 + \hline
263 + \end{tabular}
264 +
265 + \caption{Expected number of selected events for an integrated luminosity of 300
266 + pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.}
267 + \label{tab:FinalNoFit}
268 + \end{center}
269 + \end{table}
270 +
271 + \begin{table}[h]
272 +  \begin{center}
273 + \begin{tabular}{lcccc} \hline \hline
274 + & 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline
275 + $N$ - ZZ -Zgamma  &19.9$\pm$1.0&23.6$\pm$0.0&23.4$\pm$1.0&25.5$\pm$0.0\\ \hline
276 + $N^{genuine Z}$ (matrix method)&10.1 $\pm$0.6&0.9 $\pm$1.0&14.5 $\pm$0.9&15.8 $\pm$0.7\\ \hline
277 + $N^{WZ}$  &8.8 $\pm$0.6&7.7 $\pm$1.0&7.9 $\pm$0.9&9.8 $\pm$0.7\\ \hline
278 + \WZ from MC &8.1&9.0& 9.2 &11.3\\
279 +
280 + \hline
281 + \end{tabular}
282 +
283 + \caption{Loose Sample: Expected number of selected events for an integrated luminosity of 300
284 + pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.}
285 + \label{tab:FinalNoFitLoose}
286 + \end{center}
287 + \end{table}
288 + \clearpage
289 +
290 + \begin{figure}[hbt]
291 +  \begin{center}
292 +  \scalebox{0.8}{\includegraphics{figs/MatrixMethod3eLooseTightZmassMWtCutNoFit.eps}}
293 +  \caption{No fit line: 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.}
294 +  \label{fig:FinalMatrix3eNoFit}
295 +  \end{center}
296 + \end{figure}
297 +
298 + \begin{figure}[hbt]
299 +  \begin{center}
300 +  \scalebox{0.8}{\includegraphics{figs/MatrixMethod2e1muLooseTightZmassMWtCutNoFit.eps}}
301 +  \caption{No fit line: 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.}
302 +  \label{fig:FinalMatrix2e1muNoFit}
303 +  \end{center}
304 + \end{figure}
305 +
306 + \begin{figure}[hbt]
307 +  \begin{center}
308 +  \scalebox{0.8}{\includegraphics{figs/MatrixMethod2mu1eLooseTightZmassMWtCutNoFit.eps}}
309 +  \caption{No fit line: 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.}
310 +  \label{fig:FinalMatrix2mu1eNoFit}
311 +  \end{center}
312 + \end{figure}
313 +
314 + \begin{figure}[hbt]
315 +  \begin{center}
316 +  \scalebox{0.8}{\includegraphics{figs/MatrixMethod3muLooseTightZmassMWtCutNoFit.eps}}
317 +  \caption{No fit line: 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.}
318 +  \label{fig:FinalMatrix3muNoFit}
319 +  \end{center}
320 + \end{figure}

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