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1   \section{Signal extraction}
2 < %\label{sec:gen}
3 < \subsection{Z+jets background fraction}
2 > \label{sec:SignalExt}
3 > 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 > \begin{figure}[!bp]
21 >  \begin{center}
22 >  \scalebox{0.4}{\includegraphics{figs/FitBkg3eTight.eps}}
23 >  \caption{The invariant mass distribution of the $Z$ boson candidate that is fit to a signal
24 >  parameterized as a Gaussian function convoluted with a Breit-Wigner function and
25 >  a background, parameterized as a straight line.}
26 >  \label{fig:ZFit}
27 >  \end{center}
28 > \end{figure}
29 >
30 > \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 > $3e$ Loose & 152.0 & 43.1 & 6.1 & 0 & 6.1& 3.8 $\pm$ 1.1 \\ \hline
37 > $3e$ Tight & 44.9 & 17.1 & 2.7 & 0 & 2.7 & 2.8 $\pm$ 1.0 \\ \hline  
38 > $2\mu 1e$ Loose & 189.6 & 52.6 & 4.7 & 0 & 4.7 & 3.5 $\pm$ 1.1\\ \hline
39 > $2\mu 1e$ Tight & 63.1 & 19.0 & 1.4 & 0 & 1.4 & 1.9 $\pm$ 0.8\\ \hline
40 > $2e1\mu$   & 9.2 & 8.2 & 2.5 & 1.5 & 4.0 & 0.7 $\pm$ 0.5\\ \hline
41 > $3\mu$     & 1.9 & 7.8 & 0.7 & 0 & 0.7 & 0.6 $\pm$ 0.5\\ \hline
42 > \end{tabular}
43 > \end{center}
44 > \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 > %I AM NOT SURE I UNDERSTAND WHAT IS WRITTEN HERE
46 > % 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 > }
48 > \label{tab:FitVsMC}
49 > \end{table}
50 >
51 >
52 > \subsection{Estimation of the background with genuine \Z boson}
53 > \label{sec:D0Matrix}
54 > All of the instrumental background events with real \Z boson come from
55 > $\Z + jets$ 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 > 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 > \label{eq:matrixEq1}
81 > N_{loose} = N_e + N_j.
82 > \end{equation}
83 >
84 > 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 > \label{eq:matrixEq2}
88 > 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 >
98 > \subsubsection{Determination of $\epsilon_{tight}$}
99 >
100 > % 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 >
111 > 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 > and $t\bar{t}$ as background. \Z mass distribution is separated for two cases where
114 > 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 > 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
117 > and straight line for a background model. \Z mass distribution and fit are shown in \ref{fig:tagprobe}.
118 >
119 > Equation for determination of signal efficiency is given as
120 > \begin{equation}
121 > \epsilon_{tight}=\frac{ 2*(N_{TT}-B_{TT}) }{ (N_{TL}-B_{TL})+2*(N_{TT}-B_{TT}) }
122 > \end{equation}
123 >
124 > where $N_{TT}$,$B_{TT}$,$N_{TL}$ and $B_{TL}$ are, respectively, number of signal+background
125 > and background events for ``Tight-Tight'' and ``Loose-Tight'' electron combinations.
126 > %We estimated an efficiency $\epsilon_{tight}=0.99 \pm  0.01$.
127 >
128 > \subsubsection{Determination of $p_{fake}$}
129 >
130 > As the events will be most of the time triggered by the leptons coming
131 > from \Z boson, we assume that the third lepton is unbiased toward the
132 > trigger requirement. Ideally, we need a sample of pure multi-jet events
133 > in order to compute the probability for a jet identified as a loose
134 > electron to be also identified as a tight electron. In selecting such
135 > a sample in data, one has to avoid any bias from the trigger
136 > requirements on the ``Loose'' electron candidate.
137 > %Such sample will not
138 > %exist in data as they will be bias by the trigger requirement.
139 > \begin{figure}[bt]
140 >  \begin{center}
141 >  \scalebox{0.6}{\includegraphics{figs/tight_eff_gumbo.eps}}
142 >  \caption{Fraction of electron candidates passing the ``Tight'' criteria
143 >    in multijet event. No trigger requirement has been applied.{\em NEW PLOT
144 >    WITH TRIGGER REQUIREMENTS TO COME}}
145 >  \label{fig:qcd_efftight_noHLT}
146 >  \end{center}
147 > \end{figure}
148 >
149 > From a sample of multijet events triggered by an ``OR'' of multi-jet
150 > triggers, we select a ``Loose'' electron candidate that are not
151 > matched to any of the trigger objects. We also require the
152 > electron candidate to be separated from the jet that satisfies
153 > the trigger requirement by requiring the candidate to be separated
154 > by at least $\Delta R = 0.2$ from the trigger object.
155 > This allows us to obtain an unbiased sample of multijet events
156 > where an electron candidate is likely to be either a converted
157 > photon or a misidentified jet. The $p_{fake}$ function of $p_T$
158 > and $\eta$ is simply obtained by dividing the $p_T$ and $\eta$
159 > distributions for the electron candidate that satisfied ``Simple Tight''
160 > electron identification requirements to that for electron candidates
161 > that satisfied ``Simple Loose''. Such distributions are given
162 > in Fig.~\ref{fig:qcd_zjet_est}.
163  
5 After applying "Official Tight" selection on electron decaying from W, there is still a significant fraction of Z+jets events passing selection, due to two orders of magnitude bigger cross section of the background processes. In this section we describe a method to estimate fake rate coming from Z+jets background, which has a significant contribution in channels where $W^{\pm}$ decays into $e^{pm}$ and neutrino.
6
7 Z bosons from Z+jet events will be with the same efficiency reconstructed with a Z mass between a $\pm 20$ window. Background rate is already reduced after applying "Simple Tight" criteria to the W electron. We first apply selection for W electron to "Tight Loose", while later we apply "Simple Tight" selection to count number of events passing selection in both cases. Number of events are named respectively, $N_l$ and $N_t$.
8
9 $Nl$ contains an unknown numbers of signal and background events, $N_s$ and $N_b$, so number of "Simple Loose" events is $Nl=Ns+Nb$. Applying the "Simple TIght" selection. Number of events passing "Simple Tight: is $N_t=\epsilon_s * N_s + \epsilon_b * N_b$. It is possible to calculate background fraction $N_b/(N_s+N_b)$ if we are able to estimate $\epsilon_s$ and $\epsilon_b$, signal and background efficiency. Their estimation ca be done using control data samples, containing electrons and jet with high purity. Tag and probe method is used to determine signal efficiency $\epsilon_b$. The rate will be derived from $Z \to e^+e^-$ samples. In the following text we describe method used to determine $\epsilon_{B}$.
10
11 \subsection{Method description}
12
13 We apply "Simple Loose" selection on jets from QCD and photon+jet control samples for fake rate estimation of Z+jets jet selected as $W\pm$ electron. The samples used in analysis are CSA07 Gumbo samples, with Pythia ID filtering so that only events from photon+jets, QCD and minimum bias event are used. As the sample contains event classes with different event weight, separated bt $\hat{P_t}$ value and Pythia ID, we calculate weight as $w_i=\frac{\sigma_i}{N_i}$ where $\sigma_i$ and $N_i$ are respective cross section and event number for event class with the same event weight. "Simple Loose" selection is applied to each reconstructed object reco::pixelMatchGsfElectrons. In case of having more than one reconstructed electron objects per event passing selection, we appy the same weight to each. Efficiency, defined as a ratio of number of objects passing "Simple Tight" and "Simple Loose" selection, given as a function of $Pt$ and $\eta$, is showed in plots \ref{fig:qcd_zjet_est}.
14
15 Since the data collected by the CMS is filtered by the trigger, the trigger bias study was done one the Gumbo control sample. After requiring all events to pass a HLT1jet trigger path, which cuts on a 200 GeV Pt treshold of the single jet, there is significant drop of the efficiency in the area of interest, 20-100 GeV, as shown in the plot \ref{fig:qcd_zjet_est}. First assumption, that removing objects within a $0.1 \Delta R$ cone to a HLT Jet object which triggered the HLT1jet path would restore efficiency as seen without trigger requirement, prooved insufficient, with efficiency still being biased in the 20-100 GeV range. We assume that this is due to other jets in the event having similar energy to the triggering jet, so with the leading jet of 200 GeV Pt or higher this effectively removes events with jets from the lower Pt range. New attempt was made to remove all reconstructed electrons  from the selection within the $\Delta R$ cone with any of the jets triggering HLT1jet, HLT2jet, HLT3jet and HLT4jet trigger paths, with respective jet tresholds 200, 150, 85 and 60 GeV. Since the tresholds are lower, we assume to have more events with real jets in low Pt range (50-100 GeV). Resulting efficiency is shown in the plot \ref{fig:qcd_zjet_est}.
164  

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