Notes/WZCSA07/zjetbackground.tex

\section{Signal extraction}
\label{sec:SignalExt}
We separate backgrounds into two categories: one with a genuine \Z boson
from $\Z+jets$ processes, and the other without a genuine \Z boson from
$t\bar{t}$ and $\W+jet$ production. The latter source can be estimated from
the invariant mass of the \Z boson candidate, where the background events
with no genuine \Z boson should not produce a \Z mass peak and should
be relatively smooth. 

\subsection{Study of the background without a genuine \Z boson}
We estimate the background due to events without a genuine \Z boson from
fitting a \Z candidate invariant mass to a Gaussian function convoluted 
with a Breit-Wigner function. The background is parameterized as a straight
line. An example of a fit for $3e$ category is given in Fig.~\ref{fig:ZFit}.
Both number of signal and background events are calculated for the
invariant mass range between 81 and 101 GeV. In Table~\ref{tab:FitVsMC}
we summarize the number of background events obtained from the fit
and from the Monte Carlo truth information.

\begin{figure}[!bp]
  \begin{center}
  \scalebox{0.4}{\includegraphics{figs/FitBkg3eTight.eps}}
  \caption{The invariant mass distribution of the $Z$ boson candidate that is fitted to a signal
  parameterized as a Gaussian function convoluted with a Breit-Wigner function and
  a background, parameterized as a straight line.}
  \label{fig:ZFit}
  \end{center}
\end{figure}

\begin{table}[!tb]
\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 & 148.6 & 41.8 & 5.4 & 1.2 & 6.6& 4.4 $\pm$ 1.2 \\ \hline
$3e$ Tight & 51.9 & 17.3 & 3.3 & 1.3 & 4.6 & 3.7 $\pm$ 1.1 \\ \hline  
$2\mu 1e$ Loose & 184.3 & 51.2 & 6.3 & 0 & 6.3 & 2.8 $\pm$ 1.0\\ \hline
$2\mu 1e$ Tight & 50.2 & 18.9 & 2.8 & 0 & 2.8 & 4.6 $\pm$ 1.3\\ \hline
$2e1\mu$   & 7.3 & 8.0 & 3.8 & 1.3 & 4.1 & 0.7 $\pm$ 0.5\\ \hline 
$3\mu$     & 1.8 & 7.8 & 1.2 & 0 & 1.2 & 0.5 $\pm$ 0.4\\ \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 $W\rightarrow e\nu$ final state only. 
%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:FitVsMC}
\end{table}


\subsection{Estimation of the background with genuine \Z boson}
\label{sec:D0Matrix}
All of the instrumental background events with real \Z boson come from
$\Z + jets$ processes where one of the jets is misidentified as a
lepton.  The same principle will be used for electron and muon while
the background is coming from differente sources.
The probability to misidentify a jet as a muon is very low in CMS, while that
for the case of electron can be quite high as jets with large electromagnetic
energy fraction can be misidentified as electrons. $\Z+jet$ background
is especially high for \WZ\ signal with $\W\to e\nu$. Thus, it is imperative
to have a reliable estimation of this background from data to avoid
unnecessary systematic uncertainties due to Monte Carlo description of data
in startup conditions. Therefore, in the following we describe the data-driven
estimation of the $\Z+jets$ background for the $\ell^+\ell^- e$ 
categories. A similar study for the remaining $\ell^+\ell^- \mu$ categories 
are in progress. However, as the $\Z+jets$ background is sufficiently small, it is
possible to use Monte Carlo simulation to estimate $\Z+jet$ background with
early data, without incurring significant systematic uncertainty due to data modeling.

\subsubsection{$\Z+jets$ background fraction}
To estimate the fraction of the $\Z+jets$ events in data
we apply a method, commonly referred to as ``matrix'' method.
The idea of a method is to apply ``Loose'' identification criteria
on the third lepton after \Z boson candidate is identified
and count the number of the observed events, $N_{loose}$.
These events contain events with real electrons $N_{e}$
and events with misidentified jets $N_j$:
\begin{equation}
\label{eq:matrixEq1}
N_{loose} = N_e + N_j.
\end{equation}

If we are to apply ``Tight'' selection on the third lepton, the number
of the observed events $N_{tight}$ would change as following
\begin{equation}
\label{eq:matrixEq2}
N_{tight} = \epsilon_{tight} N_e + p_{fake} N_j,
\end{equation}
where $\epsilon_{tight}$ and $p_{fake}$ are efficiency of ``Tight''
criteria with respect to ``Loose'' requirements for electrons and
misidentified jets, respectively. As $N_{loose}$ and $N_{tight}$
are directly observable, to extract the number of $Z+jet$ events
in the final sample, one needs to measure $\epsilon_{tight}$
and $p_{fake}$ in control data samples. Two possible ways
to estimate these values are given below.

\subsubsection{Determination of $\epsilon_{tight}$}

% UNDEERSTAND THIS FIT: THIS CANNOT BE SHOWN AS IT IS!!!
%\begin{figure}[bt]
%  \begin{center}
%  \scalebox{0.8}{\includegraphics{figs/tag_probe_fit.eps}}
%  \caption{Invariant mass of the \Z boson candidate for ``Tight-Tight'' (a)
%  and ``Tight-Loose'' (b) electron selections fitted to a Gaussian with
%  bifurcated Breit-Wigner functions.}
%  \label{fig:tagprobe}
%  \end{center}
%\end{figure}

To estimate the $\epsilon_{tight}$ we apply ``tag-and-probe'' method
using $\Z \to e^+e^-$ from \Z+jets Chowder sample, including  \W+jets 
and $t\bar{t}$ as background. \Z mass distribution is separated for two cases where
electrons from \Z decay either both pass ``Tigh'' selection (``Tight-Tight'' case), or only 
one passes the ``Tight'' selection, while the other electron passes ``Loose'' but not ``Tight'' 
selection (``Tight-Loose'' case). 
%To estimate signal in the selected \Z candidate invariant mass distribution, we fit it to a Gaussisan with bifurcated Breit-Wigner function as a signal
%and straight line for a background model. \Z mass distribution and fit are shown in \ref{fig:tagprobe}.

Equation for determination of signal efficiency is given as
\begin{equation}
\epsilon_{tight}=\frac{ 2*(N_{TT}-B_{TT}) }{ (N_{TL}-B_{TL})+2*(N_{TT}-B_{TT}) }
\end{equation}

where $N_{TT}$,$B_{TT}$,$N_{TL}$ and $B_{TL}$ are, respectively, number of signal+background
and background events for ``Tight-Tight'' and ``Loose-Tight'' electron combinations.
We estimated an efficiency $\epsilon_{tight}=0.98 \pm  0.01$.
 
\subsubsection{Determination of $p_{fake}$}

As the events will be most of the time triggered by the leptons coming
from \Z boson, we assume that the third lepton is unbiased toward the
trigger requirement. Ideally, we need a sample of pure multi-jet events
in order to compute the probability for a jet identified as a loose
electron to be also identified as a tight electron. In selecting such
a sample in data, one has to avoid any bias from the trigger 
requirements on the ``Loose'' electron candidate.
%Such sample will not
%exist in data as they will be bias by the trigger requirement.
\begin{figure}[bt]
  \begin{center}
  \scalebox{0.6}{\includegraphics{figs/tight_eff_gumbo.eps}}
  \caption{Fraction of electron candidates passing the ``Tight'' criteria
    in multijet event. No trigger requirement has been applied.{\em NEW PLOT
    WITH TRIGGER REQUIREMENTS TO COME}}
  \label{fig:qcd_efftight_noHLT}
  \end{center}
\end{figure}

\begin{figure}[!bt]
  \begin{center}
  \scalebox{0.6}{\includegraphics{figs/p0_p_fake_mu_fit.eps}}
  \caption{Determination of $p_{fake}$ for muons. Top plot: $p_t$ spectrum
    of muons passing the ``Loose'' and ``Tight'' criteria in $b\bar{b}$ events
    accepted by electron triggers; bottom plot: 
    fraction of muon candidates passing the ``Tight'' criteria. A constant fit
    is overlayed.}
  \label{fig:mu_pfake}
  \end{center}
\end{figure}


From a sample of multijet events triggered by an ``OR'' of multi-jet
triggers, we select a ``Loose'' electron candidate that are not
matched to any of the trigger objects. We also require the
electron candidate to be separated from the jet that satisfies
the trigger requirement by requiring the candidate to be separated
%by at least $\Delta R = 0.2$ 
from the trigger object.
This allows us to obtain an unbiased sample of multijet events
where an electron candidate is likely to be either a converted
photon or a misidentified jet. The $p_{fake}$ function of $p_T$
and $\eta$ is simply obtained by dividing the $p_T$ and $\eta$
distributions for the electron candidate that satisfied ``Simple Tight''
electron identification requirements to that for electron candidates
that satisfied ``Simple Loose''. We estimate the $p_{fake}=0.32 \pm 0.1$ for
electrons.


For muons, a similar procedure has been applied. Since the bulk
of background muons is coming from heavy quark decays, we select
a $b\bar{b}$ sample as control sample. As an exercise, we selected
electron-triggered events on a $b\bar{b}$ Monte Carlo sample, 
required one ``loose electron'' in the event and looked for
for muon candidates that are not close to the electron candidate,
and determined $p_{fake}$ on this sample of muons. The $p_t$ spectrum
for ``loose'' and ``tight'' muons and their ratio is shown in 
Figure~\ref{fig:mu_pfake}. The factor $p_{fake}$ for muons estimated
in this way amounts to $0.08 \pm 0.01$.


\subsubsection{Background determination results}

Using the values of $\epsilon_{tight}$ and $p_{fake}$ obtained 
from the methods described in the previous sections, we estimated
the backgrounds from genuine Z decays by solving equations 
(\ref{eq:matrixEq1}) and (\ref{eq:matrixEq2}) for $N_j$. The estimated
background through this method is shown in Figure~\ref{fig:CrossCheckBkg}.
\begin{figure}[!bt]
  \begin{center}
  \scalebox{0.55}{\includegraphics{figs/Matrix2mu1e.eps}}\scalebox{0.27}{\includegraphics{figs/Matrix3mu.eps}}
  \caption{Comparison of the background obtained by adding monte carlo information from $Z+jets$, $Z+b\bar{b}$, $t\bar{t}$ and $W+jets$ process and the one using the successively fitting estimation and the matrix estimation. Invariante mass distribution of the two leptons is shown when for the $2\mu1e$ channel a) loose selection is applied, b) tight selection is applied on the third lepton and c) for the $3\mu$ channel when a tight selection is applied on the third lepton.
A constant value as been used for the $p_{fake}$ variable.Errors are only statistical.
}
  \label{fig:CrossCheckBkg}
  \end{center}
\end{figure}


Revision:	1.21
Committed:	Sat Jun 28 01:19:57 2008 UTC (16 years, 10 months ago) by vuko
Content type:	application/x-tex
Branch:	MAIN
CVS Tags:	draft0
Changes since 1.20:	+7 -5 lines
Log Message:	final edit before draft0
#	User	Rev	Content
1	smorovic	1.1	\section{Signal extraction}
2	beaucero	1.6	\label{sec:SignalExt}
3	ymaravin	1.10	We separate backgrounds into two categories: one with a genuine \Z boson
4			from $\Z+jets$ processes, and the other without a genuine \Z boson from
5			$t\bar{t}$ and $\W+jet$ production. The latter source can be estimated from
6			the invariant mass of the \Z boson candidate, where the background events
7			with no genuine \Z boson should not produce a \Z mass peak and should
8			be relatively smooth.
9
10			\subsection{Study of the background without a genuine \Z boson}
11			We estimate the background due to events without a genuine \Z boson from
12			fitting a \Z candidate invariant mass to a Gaussian function convoluted
13			with a Breit-Wigner function. The background is parameterized as a straight
14			line. An example of a fit for $3e$ category is given in Fig.~\ref{fig:ZFit}.
15			Both number of signal and background events are calculated for the
16			invariant mass range between 81 and 101 GeV. In Table~\ref{tab:FitVsMC}
17			we summarize the number of background events obtained from the fit
18			and from the Monte Carlo truth information.
19
20	beaucero	1.8	\begin{figure}[!bp]
21			\begin{center}
22			\scalebox{0.4}{\includegraphics{figs/FitBkg3eTight.eps}}
23	vuko	1.21	\caption{The invariant mass distribution of the $Z$ boson candidate that is fitted to a signal
24	ymaravin	1.10	parameterized as a Gaussian function convoluted with a Breit-Wigner function and
25			a background, parameterized as a straight line.}
26	beaucero	1.8	\label{fig:ZFit}
27			\end{center}
28			\end{figure}
29
30	beaucero	1.12	\begin{table}[!tb]
31			\begin{center}
32			\begin{tabular}{\|l\|c\|c\|c\|c\|c\|c\|c\|} \hline
33			& \multicolumn{2}{c\|}{Background with genuine \Z} & \multicolumn{4}{c\|}{Background without
34			genuine \Z boson} \\
35			Channel & $\Z+jets$ & $\Z b\bar{b}$ & $t\bar{t}$ & $\W+jets$ & $t\bar{t}$ + $\W+jets$ & Fit result \\ \hline
36	beaucero	1.15	$3e$ Loose & 148.6 & 41.8 & 5.4 & 1.2 & 6.6& 4.4 $\pm$ 1.2 \\ \hline
37			$3e$ Tight & 51.9 & 17.3 & 3.3 & 1.3 & 4.6 & 3.7 $\pm$ 1.1 \\ \hline
38			$2\mu 1e$ Loose & 184.3 & 51.2 & 6.3 & 0 & 6.3 & 2.8 $\pm$ 1.0\\ \hline
39			$2\mu 1e$ Tight & 50.2 & 18.9 & 2.8 & 0 & 2.8 & 4.6 $\pm$ 1.3\\ \hline
40			$2e1\mu$ & 7.3 & 8.0 & 3.8 & 1.3 & 4.1 & 0.7 $\pm$ 0.5\\ \hline
41			$3\mu$ & 1.8 & 7.8 & 1.2 & 0 & 1.2 & 0.5 $\pm$ 0.4\\ \hline
42	beaucero	1.12	\end{tabular}
43			\end{center}
44	beaucero	1.13	\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 $W\rightarrow e\nu$ final state only.
45	ymaravin	1.10	%I AM NOT SURE I UNDERSTAND WHAT IS WRITTEN HERE
46	beaucero	1.13	% 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.
47	beaucero	1.8	}
48	beaucero	1.12	\label{tab:FitVsMC}
49			\end{table}
50	beaucero	1.8
51
52	ymaravin	1.10	\subsection{Estimation of the background with genuine \Z boson}
53	beaucero	1.8	\label{sec:D0Matrix}
54	ymaravin	1.10	All of the instrumental background events with real \Z boson come from
55	beaucero	1.13	$\Z + jets$ processes where one of the jets is misidentified as a
56			lepton. The same principle will be used for electron and muon while
57			the background is coming from differente sources.
58	ymaravin	1.10	The probability to misidentify a jet as a muon is very low in CMS, while that
59			for the case of electron can be quite high as jets with large electromagnetic
60			energy fraction can be misidentified as electrons. $\Z+jet$ background
61			is especially high for \WZ\ signal with $\W\to e\nu$. Thus, it is imperative
62			to have a reliable estimation of this background from data to avoid
63			unnecessary systematic uncertainties due to Monte Carlo description of data
64			in startup conditions. Therefore, in the following we describe the data-driven
65			estimation of the $\Z+jets$ background for the $\ell^+\ell^- e$
66			categories. A similar study for the remaining $\ell^+\ell^- \mu$ categories
67			are in progress. However, as the $\Z+jets$ background is sufficiently small, it is
68			possible to use Monte Carlo simulation to estimate $\Z+jet$ background with
69			early data, without incurring significant systematic uncertainty due to data modeling.
70
71			\subsubsection{$\Z+jets$ background fraction}
72			To estimate the fraction of the $\Z+jets$ events in data
73			we apply a method, commonly referred to as ``matrix'' method.
74			The idea of a method is to apply ``Loose'' identification criteria
75			on the third lepton after \Z boson candidate is identified
76			and count the number of the observed events, $N_{loose}$.
77			These events contain events with real electrons $N_{e}$
78			and events with misidentified jets $N_j$:
79			\begin{equation}
80	vuko	1.21	\label{eq:matrixEq1}
81	ymaravin	1.10	N_{loose} = N_e + N_j.
82			\end{equation}
83	beaucero	1.4
84	ymaravin	1.10	If we are to apply ``Tight'' selection on the third lepton, the number
85			of the observed events $N_{tight}$ would change as following
86			\begin{equation}
87	vuko	1.21	\label{eq:matrixEq2}
88	ymaravin	1.10	N_{tight} = \epsilon_{tight} N_e + p_{fake} N_j,
89			\end{equation}
90			where $\epsilon_{tight}$ and $p_{fake}$ are efficiency of ``Tight''
91			criteria with respect to ``Loose'' requirements for electrons and
92			misidentified jets, respectively. As $N_{loose}$ and $N_{tight}$
93			are directly observable, to extract the number of $Z+jet$ events
94			in the final sample, one needs to measure $\epsilon_{tight}$
95			and $p_{fake}$ in control data samples. Two possible ways
96			to estimate these values are given below.
97	smorovic	1.1
98	beaucero	1.8	\subsubsection{Determination of $\epsilon_{tight}$}
99	smorovic	1.9
100	vuko	1.11	% UNDEERSTAND THIS FIT: THIS CANNOT BE SHOWN AS IT IS!!!
101			%\begin{figure}[bt]
102			% \begin{center}
103			% \scalebox{0.8}{\includegraphics{figs/tag_probe_fit.eps}}
104			% \caption{Invariant mass of the \Z boson candidate for ``Tight-Tight'' (a)
105			% and ``Tight-Loose'' (b) electron selections fitted to a Gaussian with
106			% bifurcated Breit-Wigner functions.}
107			% \label{fig:tagprobe}
108			% \end{center}
109			%\end{figure}
110	smorovic	1.9
111	ymaravin	1.10	To estimate the $\epsilon_{tight}$ we apply ``tag-and-probe'' method
112			using $\Z \to e^+e^-$ from \Z+jets Chowder sample, including \W+jets
113	smorovic	1.9	and $t\bar{t}$ as background. \Z mass distribution is separated for two cases where
114	ymaravin	1.10	electrons from \Z decay either both pass ``Tigh'' selection (``Tight-Tight'' case), or only
115			one passes the ``Tight'' selection, while the other electron passes ``Loose'' but not ``Tight''
116	beaucero	1.16	selection (``Tight-Loose'' case).
117			%To estimate signal in the selected \Z candidate invariant mass distribution, we fit it to a Gaussisan with bifurcated Breit-Wigner function as a signal
118			%and straight line for a background model. \Z mass distribution and fit are shown in \ref{fig:tagprobe}.
119	smorovic	1.9
120			Equation for determination of signal efficiency is given as
121			\begin{equation}
122			\epsilon_{tight}=\frac{ 2(N_{TT}-B_{TT}) }{ (N_{TL}-B_{TL})+2(N_{TT}-B_{TT}) }
123			\end{equation}
124
125	ymaravin	1.10	where $N_{TT}$,$B_{TT}$,$N_{TL}$ and $B_{TL}$ are, respectively, number of signal+background
126			and background events for ``Tight-Tight'' and ``Loose-Tight'' electron combinations.
127	beaucero	1.16	We estimated an efficiency $\epsilon_{tight}=0.98 \pm 0.01$.
128	smorovic	1.9
129	ymaravin	1.10	\subsubsection{Determination of $p_{fake}$}
130
131			As the events will be most of the time triggered by the leptons coming
132			from \Z boson, we assume that the third lepton is unbiased toward the
133			trigger requirement. Ideally, we need a sample of pure multi-jet events
134			in order to compute the probability for a jet identified as a loose
135			electron to be also identified as a tight electron. In selecting such
136			a sample in data, one has to avoid any bias from the trigger
137			requirements on the ``Loose'' electron candidate.
138			%Such sample will not
139			%exist in data as they will be bias by the trigger requirement.
140			\begin{figure}[bt]
141			\begin{center}
142			\scalebox{0.6}{\includegraphics{figs/tight_eff_gumbo.eps}}
143			\caption{Fraction of electron candidates passing the ``Tight'' criteria
144	vuko	1.11	in multijet event. No trigger requirement has been applied.{\em NEW PLOT
145			WITH TRIGGER REQUIREMENTS TO COME}}
146	ymaravin	1.10	\label{fig:qcd_efftight_noHLT}
147			\end{center}
148			\end{figure}
149
150	beaucero	1.18	\begin{figure}[!bt]
151	vuko	1.14	\begin{center}
152			\scalebox{0.6}{\includegraphics{figs/p0_p_fake_mu_fit.eps}}
153			\caption{Determination of $p_{fake}$ for muons. Top plot: $p_t$ spectrum
154			of muons passing the ``Loose'' and ``Tight'' criteria in $b\bar{b}$ events
155			accepted by electron triggers; bottom plot:
156			fraction of muon candidates passing the ``Tight'' criteria. A constant fit
157			is overlayed.}
158			\label{fig:mu_pfake}
159			\end{center}
160			\end{figure}
161
162
163
164	ymaravin	1.10	From a sample of multijet events triggered by an ``OR'' of multi-jet
165			triggers, we select a ``Loose'' electron candidate that are not
166			matched to any of the trigger objects. We also require the
167			electron candidate to be separated from the jet that satisfies
168			the trigger requirement by requiring the candidate to be separated
169	beaucero	1.16	%by at least $\Delta R = 0.2$
170			from the trigger object.
171	ymaravin	1.10	This allows us to obtain an unbiased sample of multijet events
172			where an electron candidate is likely to be either a converted
173			photon or a misidentified jet. The $p_{fake}$ function of $p_T$
174			and $\eta$ is simply obtained by dividing the $p_T$ and $\eta$
175			distributions for the electron candidate that satisfied ``Simple Tight''
176			electron identification requirements to that for electron candidates
177	vuko	1.20	that satisfied ``Simple Loose''. We estimate the $p_{fake}=0.32 \pm 0.1$ for
178			electrons.
179
180
181	vuko	1.17	For muons, a similar procedure has been applied. Since the bulk
182			of background muons is coming from heavy quark decays, we select
183			a $b\bar{b}$ sample as control sample. As an exercise, we selected
184			electron-triggered events on a $b\bar{b}$ Monte Carlo sample,
185			required one ``loose electron'' in the event and looked for
186			for muon candidates that are not close to the electron candidate,
187			and determined $p_{fake}$ on this sample of muons. The $p_t$ spectrum
188			for ``loose'' and ``tight'' muons and their ratio is shown in
189	vuko	1.20	Figure~\ref{fig:mu_pfake}. The factor $p_{fake}$ for muons estimated
190			in this way amounts to $0.08 \pm 0.01$.
191	vuko	1.17
192
193			\subsubsection{Background determination results}
194
195			Using the values of $\epsilon_{tight}$ and $p_{fake}$ obtained
196			from the methods described in the previous sections, we estimated
197			the backgrounds from genuine Z decays by solving equations
198	vuko	1.21	(\ref{eq:matrixEq1}) and (\ref{eq:matrixEq2}) for $N_j$. The estimated
199	beaucero	1.18	background through this method is shown in Figure~\ref{fig:CrossCheckBkg}.
200			\begin{figure}[!bt]
201			\begin{center}
202	beaucero	1.19	\scalebox{0.55}{\includegraphics{figs/Matrix2mu1e.eps}}\scalebox{0.27}{\includegraphics{figs/Matrix3mu.eps}}
203	vuko	1.21	\caption{Comparison of the background obtained by adding monte carlo information from $Z+jets$, $Z+b\bar{b}$, $t\bar{t}$ and $W+jets$ process and the one using the successively fitting estimation and the matrix estimation. Invariante mass distribution of the two leptons is shown when for the $2\mu1e$ channel a) loose selection is applied, b) tight selection is applied on the third lepton and c) for the $3\mu$ channel when a tight selection is applied on the third lepton.
204	beaucero	1.18	A constant value as been used for the $p_{fake}$ variable.Errors are only statistical.
205			}
206			\label{fig:CrossCheckBkg}
207			\end{center}
208			\end{figure}
209	vuko	1.21
210