cmsnotes/StopSearch/eventsel.tex


This analysis uses several different control regions in addition to the signal regions. 
All of these different regions are defined in this section. 
%Figure~\ref{fig:venndiagram} illustrates the relationship between these regions.

\subsection{Single Lepton Selection}

[UPDATE SELECTION]

The single lepton preselection sample is based on the following criteria
\begin{itemize}
\item satisfy the trigger requirement (see
  Table.~\ref{tab:DatasetsData}). Dilepton triggers are used only for the dilepton control region.
\item select events with one high \pt\ electron or muon, requiring
  \begin{itemize}
  \item $\pt>30~\GeVc$ and $|\eta|<2.1$
  \item satisfy the identification and isolation requirements detailed
    in the same-sign SUSY analysis (SUS-11-010) for electrons and the opposite-sign 
    SUSY analysis (SUS-11-011) for muons
  \end{itemize} 
  \item require at least 4 PF jets in the event with $\pt>30~\GeV$
    within $|\eta|<2.5$ out of which at least 1 satisfies the CSV
    medium working point b-tagging requirement
  \item require moderate $\met>50~\GeV$
\end{itemize}

Table~\ref{tab:preselectionyield} shows the yields in data and MC without any corrections for this preselection region.

\begin{table}[!h]
\begin{center}
\begin{tabular}{c|c}
\hline
\hline
\end{tabular}
\caption{  Raw Data and MC predictions without any corrections are shown after preselection. \label{tab:preselectionyield}}
\end{center}
\end{table}

\subsection{Signal Region Selection}

[MOTIVATIONAL BLURB ON MET AND MT, \\
CAN ADD SIGNAL VS. TTBAR MC PLOT \\
ADD SIGNAL YIELDS FOR AVAILABLE POINTS, \\
DISCUSS CHOICE SIG REGIONS]

The signal regions (SRs) are selected to improve the sensitivity for the
single lepton requirements and cover a range of scalar top
scenarios. The \mt\ and \met\ variables are used to define the signal
regions and the requirements are listed in Table~\ref{tab:srdef}. 

\begin{table}[!h]
\begin{center}
\begin{tabular}{l|c|c}
\hline
Signal Region & Minimum \mt\ [GeV] & Minimum \met\ [GeV] \\
\hline
\hline
SRA & 150 & 100 \\
SRB & 120 & 150 \\
SRC & 120 & 200 \\
SRD & 120 & 250 \\
SRE & 120 & 300 \\
\hline
\end{tabular}
\caption{ Signal region definitions based on \mt\ and \met\
  requirements. These requirements are applied in addition to the
  baseline single lepton selection.
\label{tab:srdef}}
\end{center}
\end{table}

Table~\ref{tab:srrawmcyields} shows the expected number of SM
background yields for the SRs. A few stop signal yields for four
values of the parameters are also shown for comparison. The signal
regions with looser requirements are sensitive to lower stop masses
M(\sctop), while those with tighter requirements are more sensitive to
higher M(\sctop). 

\begin{table}[!h]
\begin{center}
\begin{tabular}{l||c|c|c|c}
\hline
Sample              & SRA & SRB & SRC & SRD \\
\hline
\hline
\ttdl\           & $700 \pm 15$& $408 \pm 12$& $134 \pm 7$& $43 \pm 4$ \\
\ttsl\ \& single top (1\Lep)             & $111 \pm 6$& $71 \pm 5$& $15 \pm 2$& $4 \pm 1$ \\
\wjets\                  & $58 \pm 35$& $57 \pm 35$& $29 \pm 26$& $26 \pm 26$ \\
Rare             & $63 \pm 3$& $40 \pm 3$& $17 \pm 2$& $7 \pm 1$ \\
\hline
Total            & $932 \pm 39$& $576 \pm 38$& $195 \pm 27$& $80 \pm 26$ \\
\hline
\end{tabular}
\caption{ Expected SM background contributions, including both muon
  and electron channels. The uncertainties are statistical only. ADD
  SIGNAL POINTS.
\label{tab:srrawmcyields}}
\end{center}
\end{table}

\subsection{Control Region Selection}

[1 PARAGRAPH BLURB RELATING BACKGROUNDS (IN TABLE FROM PREVIOUS SECTION)
TO INTRODUCE CONTROL REGIONS]

Control regions (CRs) are used to validate the background estimation
procedure and derive systematic uncertainties for some
contributions. The CRs are selected to have similar
kinematics to the SRs, but have a different requirement in terms of
number of b-tags and number of leptons, thus enhancing them in
different SM contributions. The four CRs used in this analysis are
summarized in Table~\ref{tab:crdef}.

\begin{table}
\begin{center}
{\small
\begin{tabular}{l|c|c|c}
\hline
Selection       & \multirow{2}{*}{exactly 1 lepton}     & \multirow{2}{*}{exactly 2
        leptons}                & \multirow{2}{*}{1 lepton + isolated
        track}\\
      Criteria & & & \\
\hline
\hline
\multirow{4}{*}{0 b-tags}        
&        CR1) W+Jets dominated:
&        CR2) apply \Z-mass constraint                   
&        CR3) not used \\  
&        
&       $\rightarrow$ Z+Jets dominated: Validate 
&      \\
&      Validate W+Jets \mt\ tail
&        \ttsl\ \mt\ tail comparing 
&        \\  
&
&        data vs. MC ``pseudo-\mt ''
&        \\  
\hline
\multirow{4}{*}{$\ge$ 1 b-tags}          
&       
&       CR4) Apply \Z-mass veto 
&      CR5) \ttdl, \ttlt\ and \\
&     SIGNAL 
&      $\rightarrow$ \ttdl\ dominated: Validate 
&       \ttlf\ dominated:  Validate \\
&     REGION 
&      ``physics'' modelling of \ttdl\     
&      \Tau\  and fake lepton modeling/\\
&
&
&      detector effects in \ttdl\     \\
\hline
\end{tabular}
}
\caption{Summary of signal and control regions.
  \label{tab:crdef}%\protect
}
\end{center}
\end{table}


\subsection{MC Corrections}

[UPDATE SECTION]

\subsubsection{Corrections to Jets and \met}

[UPDATE, ADD FEW MORE DETAILS ON WHAT IS DONE HERE]

The official recommendations from the Jet/MET group are used for 
the data and MC samples. In particular, the jet
energy corrections (JEC) are updated using the official recipe.
L1FastL2L3Residual (L1FastL2L3) corrections are applied for data (MC),
based on the global tags GR\_R\_42\_V23 (DESIGN42\_V17) for
data (MC). In addition, these jet energy corrections are propagated to
the \met\ calculation, following the official prescription for
deriving the Type I corrections. 

Events with anomalous ``rho'' pile-up corrections are excluded from the sample since these 
correspond to events with unphysically large \met\ and \mt\ tail
signal region. In addition, the recommended MET filters are applied. 


\subsubsection{Branching Fraction Correction}

The leptonic branching fraction used in some of the \ttbar\ MC samples
differs from the value listed in the PDG $(10.80 \pm 0.09)\%$. 
Table.~\ref{tab:wlepbf} summarizes the branching fractions used in
the generation of the various \ttbar\ MC samples. 
For \ttbar\ samples with the incorrect leptonic branching fraction, event
weights are applied based on the number of true leptons and the ratio
of the corrected and incorrect branching fractions. 

\begin{table}[!h]
\begin{center}
\begin{tabular}{c|c}
\hline
         \ttbar\ Sample - Event Generator & Leptonic Branching Fraction\\
\hline
\hline
Madgraph   &       0.111\\
MC@NLO    &       0.111\\
Pythia         &       0.108\\
Powheg       &       0.108\\
\hline
\end{tabular}
\caption{Leptonic branching fractions for the various \ttbar\ samples
  used in the analysis. The primary \ttbar\ MC sample produced with
  Madgraph has a branching fraction that is almost $3\%$ higher than
  the PDG value. \label{tab:wlepbf}}
\end{center}
\end{table}


\subsubsection{Modeling of Additional Hard Jets in Top Dilepton Events}
\label{sec:jetmultiplicity}

[CHECK, UPDATE, ADD EQUATIONS COMMENTED IN THE BOTTOM OF FILE \\
REFERENCE APPENDIX INFO. (FROM 7 TEV) AND SUMMARIZE THAT INFORMATION HERE]

Dilepton \ttbar\ events have 2 jets from the top decays, so additional
jets from radiation or higher order contributions are required to
enter the signal sample. The modeling of addtional jets in \ttbar\
events is checked in a \ttll\ control sample,
selected by requiring
\begin{itemize}
\item exactly 2 selected electrons or muons with \pt $>$ 20 GeV
\item \met\ $>$ 100 GeV
\item $\geq1$ b-tagged jet
\item Z-veto 
\end{itemize}
Figure~\ref{fig:dileptonnjets} shows a comparison of the jet
multiplicity distribution in data and MC for this two-lepton control
sample. After requiring at least 1 b-tagged jet, most of the
events have 2 jets, as expected from the dominant process \ttll. There is also a
significant fraction of events with additional jets. 
The 3-jet sample is mainly comprised of \ttbar\ events with 1 additional
emission and similarly the $\ge4$-jet sample contains primarily
$\ttbar+\ge2$ jet events. 
%Even though the primary \ttbar\
%Madgraph sample used includes up to 3 additional partons at the Matrix
%Element level, which are intended to describe additional hard jets,
%Figure~\ref{fig:dileptonnjets} shows a slight mis-modeling of the
%additional jets. 


\begin{figure}[hbt]
  \begin{center}
        \includegraphics[width=0.5\linewidth]{plots/njets_all_met100_mueg.pdf}
        \includegraphics[width=0.5\linewidth]{plots/njets_all_met100_diel.pdf}%
        \includegraphics[width=0.5\linewidth]{plots/njets_all_met100_dimu.pdf}
        \caption{
          \label{fig:dileptonnjets}%\protect 
          Comparison of the jet multiplicity distribution in data and MC for dilepton events in the \E-\M\
          (top), \E-\E\ (bottom left) and \M-\M\ (bottom right) channels.}  
      \end{center}
\end{figure}

It should be noted that in the case of \ttll\ events
with a single reconstructed lepton, the other lepton may be
mis-reconstructed as a jet. For example, a hadronic tau may be
mis-identified as a jet (since no $\tau$ identification is used). 
In this case only 1 additional jet from radiation may suffice for 
a \ttll\ event to enter the signal sample. As a result, both the
samples with $\ttbar+1$ jet and $\ttbar+\ge2$ jets are relevant for
estimating the top dilepton bkg in the signal region.

%In this section we discuss a correction to $ N_{2 lep}^{MC} $ in Equation XXX
%due to differences in the modelling of the jet multiplicity in data versus MC.
%The same correction also enters $ N_{peak}^{MC}$ in Equation XXX to the extend that the 
%dilepton contributions to $ N_{peak}^{MC}$ gets corrected.

%The dilepton control sample is defined by the following requirements:
%\begin{itemize}
%\item Exactly 2 selected electrons or muons with \pt $>$ 20 GeV
%\item \met\ $>$ 50 GeV
%\item $\geq1$ b-tagged jet
%\end{itemize}
%
%This sample is dominated by \ttll. The distribution of \njets\ for data and MC passing this selection is displayed in Fig.~\ref{fig:dilepton_njets}. 
%We use this distribution to derive scale factors which reweight the \ttll\ MC \njets\ distribution to match the data. We define the following
%quantities
%
%\begin{itemize}
%\item $N_{2}=$ data yield minus non-dilepton \ttbar\ MC yield for \njets\ $\leq$ 2
%\item $N_{3}=$ data yield minus non-dilepton \ttbar\ MC yield for \njets\ = 3
%\item $N_{4}=$ data yield minus non-dilepton \ttbar\ MC yield for \njets\ $\geq$ 4
%\item $M_{2}=$ dilepton \ttbar\ MC yield for \njets\ $\leq$ 2
%\item $M_{3}=$ dilepton \ttbar\ MC yield for \njets\ = 3
%\item $M_{4}=$ dilepton \ttbar\ MC yield for \njets\ $\geq$ 4
%\end{itemize}
%
%We use these yields to define 3 scale factors, which quantify the data/MC ratio in the 3 \njets\ bins:
%
%\begin{itemize}
%\item $SF_2 = N_2 / M_2$
%\item $SF_3 = N_3 / M_3$
%\item $SF_4 = N_4 / M_4$
%\end{itemize}
%
%And finally, we define the scale factors $K_3$ and $K_4$:
%
%\begin{itemize}
%\item $K_3 = SF_3 / SF_2$
%\item $K_4 = SF_4 / SF_2$
%\end{itemize}
%
%The scale factor $K_3$ is extracted from dilepton \ttbar\ events with \njets = 3, which have exactly 1 ISR jet.
%The scale factor $K_4$ is extracted from dilepton \ttbar\ events with \njets $\geq$ 4, which have at least 2 ISR jets.
%Both of these scale factors are needed since dilepton \ttbar\ events which fall in our signal region (including
%the \njets $\geq$ 4 requirement) may require exactly 1 ISR jet, in the case that the second lepton is reconstructed
%as a jet, or at least 2 ISR jets, in the case that the second lepton is not reconstructed as a jet. These scale
%factors are applied to the dilepton \ttbar\ MC only. For a given MC event, we determine whether to use $K_3$ or $K_4$
%by counting the number of reconstructed jets in the event ($N_{\rm{jets}}^R$) , and subtracting off any reconstructed 
%jet which is matched to the second lepton at generator level ($N_{\rm{jets}}^\ell$); $N_{\rm{jets}}^{\rm{cor}} = N_{\rm{jets}}^R - N_{\rm{jets}}^\ell$.
%For events with $N_{\rm{jets}}^{\rm{cor}}=3$ the factor $K_3$ is applied, while for events with $N_{\rm{jets}}^{\rm{cor}}\geq4$ the factor $K_4$ is applied.
%For all subsequent steps, the scale factors $K_3$ and $K_4$ have been
%applied to the \ttll\ MC.


Table~\ref{tab:njetskfactors}  shows scale factors to correct the
fraction of events with additional jets in MC to the observed fraction
in data. These are applied to the \ttll\ MC throughout the entire analysis, i.e. whenever \ttll\ MC is used to estimate or subtract
a yield or distribution. 
%
In order to do so, it is first necessary to count the number of
additional jets from radiation and exclude leptons mis-identified as
jets. A jet is considered a mis-identified lepton if it is matched to a
generator-level second lepton with sufficient energy to satisfy the jet
\pt\ requirement ($\pt>30~\GeV$). 

\begin{table}[!ht]
\begin{center}
\begin{tabular}{l|c}
\hline
            Jet Multiplicity Sample
            &                Data/MC Scale Factor \\
\hline
\hline
N jets $= 3$ (sensitive to $\ttbar+1$ extra jet from radiation)   &       $0.97 \pm 0.03$\\
N jets $\ge4$ (sensitive to $\ttbar+\ge2$ extra jets from radiation)   &       $0.91 \pm 0.04$\\
\hline
\end{tabular}
\caption{Data/MC scale factors used to account for differences in the
  fraction of events with additional hard jets from radiation in
  \ttll\ events. \label{tab:njetskfactors}}
\end{center}
\end{table}


\subsubsection{Efficiency Corrections}

[TO BE UDPATED WITH T\&P STUDIES ON ID, TRIGGER ETC]

Revision:	1.8
Committed:	Wed Oct 3 05:48:26 2012 UTC (12 years, 7 months ago) by vimartin
Content type:	application/x-tex
Branch:	MAIN
Changes since 1.7:	+18 -134 lines
Log Message:	updated missing info
#	User	Rev	Content
1	benhoob	1.1
2	fkw	1.5	This analysis uses several different control regions in addition to the signal regions.
3			All of these different regions are defined in this section.
4	vimartin	1.7	%Figure~\ref{fig:venndiagram} illustrates the relationship between these regions.
5	benhoob	1.1
6	vimartin	1.7	\subsection{Single Lepton Selection}
7
8			[UPDATE SELECTION]
9	fkw	1.5
10			The single lepton preselection sample is based on the following criteria
11	benhoob	1.1	\begin{itemize}
12	vimartin	1.2	\item satisfy the trigger requirement (see
13	fkw	1.4	Table.~\ref{tab:DatasetsData}). Dilepton triggers are used only for the dilepton control region.
14	vimartin	1.2	\item select events with one high \pt\ electron or muon, requiring
15			\begin{itemize}
16	vimartin	1.7	\item $\pt>30~\GeVc$ and $\|\eta\|<2.1$
17	vimartin	1.2	\item satisfy the identification and isolation requirements detailed
18	benhoob	1.3	in the same-sign SUSY analysis (SUS-11-010) for electrons and the opposite-sign
19			SUSY analysis (SUS-11-011) for muons
20	vimartin	1.2	\end{itemize}
21			\item require at least 4 PF jets in the event with $\pt>30~\GeV$
22	vimartin	1.7	within $\|\eta\|<2.5$ out of which at least 1 satisfies the CSV
23			medium working point b-tagging requirement
24	vimartin	1.2	\item require moderate $\met>50~\GeV$
25	benhoob	1.1	\end{itemize}
26
27	fkw	1.6	Table~\ref{tab:preselectionyield} shows the yields in data and MC without any corrections for this preselection region.
28
29			\begin{table}[!h]
30			\begin{center}
31			\begin{tabular}{c\|c}
32			\hline
33			\hline
34			\end{tabular}
35			\caption{ Raw Data and MC predictions without any corrections are shown after preselection. \label{tab:preselectionyield}}
36			\end{center}
37			\end{table}
38
39	vimartin	1.7	\subsection{Signal Region Selection}
40
41	vimartin	1.8	[MOTIVATIONAL BLURB ON MET AND MT, \\
42			CAN ADD SIGNAL VS. TTBAR MC PLOT \\
43			ADD SIGNAL YIELDS FOR AVAILABLE POINTS, \\
44			DISCUSS CHOICE SIG REGIONS]
45
46	vimartin	1.7	The signal regions (SRs) are selected to improve the sensitivity for the
47			single lepton requirements and cover a range of scalar top
48			scenarios. The \mt\ and \met\ variables are used to define the signal
49			regions and the requirements are listed in Table~\ref{tab:srdef}.
50
51	fkw	1.6	\begin{table}[!h]
52			\begin{center}
53	vimartin	1.7	\begin{tabular}{l\|c\|c}
54	fkw	1.6	\hline
55	vimartin	1.7	Signal Region & Minimum \mt\ [GeV] & Minimum \met\ [GeV] \\
56	fkw	1.6	\hline
57			\hline
58	vimartin	1.7	SRA & 150 & 100 \\
59			SRB & 120 & 150 \\
60			SRC & 120 & 200 \\
61			SRD & 120 & 250 \\
62			SRE & 120 & 300 \\
63	fkw	1.6	\hline
64			\end{tabular}
65	vimartin	1.7	\caption{ Signal region definitions based on \mt\ and \met\
66			requirements. These requirements are applied in addition to the
67			baseline single lepton selection.
68			\label{tab:srdef}}
69	fkw	1.6	\end{center}
70			\end{table}
71
72	vimartin	1.7	Table~\ref{tab:srrawmcyields} shows the expected number of SM
73			background yields for the SRs. A few stop signal yields for four
74			values of the parameters are also shown for comparison. The signal
75			regions with looser requirements are sensitive to lower stop masses
76			M(\sctop), while those with tighter requirements are more sensitive to
77			higher M(\sctop).
78
79	fkw	1.6	\begin{table}[!h]
80			\begin{center}
81	vimartin	1.7	\begin{tabular}{l\|\|c\|c\|c\|c}
82	fkw	1.6	\hline
83	vimartin	1.7	Sample & SRA & SRB & SRC & SRD \\
84	fkw	1.6	\hline
85			\hline
86	vimartin	1.7	\ttdl\ & $700 \pm 15$& $408 \pm 12$& $134 \pm 7$& $43 \pm 4$ \\
87			\ttsl\ \& single top (1\Lep) & $111 \pm 6$& $71 \pm 5$& $15 \pm 2$& $4 \pm 1$ \\
88			\wjets\ & $58 \pm 35$& $57 \pm 35$& $29 \pm 26$& $26 \pm 26$ \\
89			Rare & $63 \pm 3$& $40 \pm 3$& $17 \pm 2$& $7 \pm 1$ \\
90	fkw	1.6	\hline
91	vimartin	1.7	Total & $932 \pm 39$& $576 \pm 38$& $195 \pm 27$& $80 \pm 26$ \\
92	fkw	1.6	\hline
93			\end{tabular}
94	vimartin	1.7	\caption{ Expected SM background contributions, including both muon
95			and electron channels. The uncertainties are statistical only. ADD
96			SIGNAL POINTS.
97			\label{tab:srrawmcyields}}
98	fkw	1.6	\end{center}
99			\end{table}
100
101	vimartin	1.8	\subsection{Control Region Selection}
102	fkw	1.5
103	vimartin	1.8	[1 PARAGRAPH BLURB RELATING BACKGROUNDS (IN TABLE FROM PREVIOUS SECTION)
104			TO INTRODUCE CONTROL REGIONS]
105	fkw	1.5
106	vimartin	1.7	Control regions (CRs) are used to validate the background estimation
107			procedure and derive systematic uncertainties for some
108			contributions. The CRs are selected to have similar
109			kinematics to the SRs, but have a different requirement in terms of
110			number of b-tags and number of leptons, thus enhancing them in
111			different SM contributions. The four CRs used in this analysis are
112			summarized in Table~\ref{tab:crdef}.
113	fkw	1.5
114	vimartin	1.7	\begin{table}
115	fkw	1.6	\begin{center}
116	vimartin	1.7	{\small
117			\begin{tabular}{l\|c\|c\|c}
118	fkw	1.6	\hline
119	vimartin	1.7	Selection & \multirow{2}{}{exactly 1 lepton} & \multirow{2}{}{exactly 2
120			leptons} & \multirow{2}{*}{1 lepton + isolated
121			track}\\
122			Criteria & & & \\
123			\hline
124			\hline
125			\multirow{4}{*}{0 b-tags}
126			& CR1) W+Jets dominated:
127			& CR2) apply \Z-mass constraint
128			& CR3) not used \\
129			&
130			& $\rightarrow$ Z+Jets dominated: Validate
131			& \\
132			& Validate W+Jets \mt\ tail
133			& \ttsl\ \mt\ tail comparing
134			& \\
135			&
136			& data vs. MC ``pseudo-\mt ''
137			& \\
138			\hline
139			\multirow{4}{*}{$\ge$ 1 b-tags}
140			&
141			& CR4) Apply \Z-mass veto
142			& CR5) \ttdl, \ttlt\ and \\
143			& SIGNAL
144			& $\rightarrow$ \ttdl\ dominated: Validate
145			& \ttlf\ dominated: Validate \\
146			& REGION
147			& ``physics'' modelling of \ttdl\
148			& \Tau\ and fake lepton modeling/\\
149			&
150			&
151			& detector effects in \ttdl\ \\
152	fkw	1.6	\hline
153			\end{tabular}
154	vimartin	1.7	}
155			\caption{Summary of signal and control regions.
156			\label{tab:crdef}%\protect
157			}
158	fkw	1.6	\end{center}
159			\end{table}
160	fkw	1.5
161	vimartin	1.7
162			\subsection{MC Corrections}
163
164			[UPDATE SECTION]
165
166			\subsubsection{Corrections to Jets and \met}
167	benhoob	1.1
168	vimartin	1.8	[UPDATE, ADD FEW MORE DETAILS ON WHAT IS DONE HERE]
169
170	vimartin	1.2	The official recommendations from the Jet/MET group are used for
171			the data and MC samples. In particular, the jet
172			energy corrections (JEC) are updated using the official recipe.
173			L1FastL2L3Residual (L1FastL2L3) corrections are applied for data (MC),
174			based on the global tags GR\_R\_42\_V23 (DESIGN42\_V17) for
175			data (MC). In addition, these jet energy corrections are propagated to
176			the \met\ calculation, following the official prescription for
177	vimartin	1.7	deriving the Type I corrections.
178
179			Events with anomalous ``rho'' pile-up corrections are excluded from the sample since these
180	vimartin	1.2	correspond to events with unphysically large \met\ and \mt\ tail
181	vimartin	1.7	signal region. In addition, the recommended MET filters are applied.
182	vimartin	1.2
183	benhoob	1.3
184	vimartin	1.7	\subsubsection{Branching Fraction Correction}
185	vimartin	1.2
186			The leptonic branching fraction used in some of the \ttbar\ MC samples
187	benhoob	1.3	differs from the value listed in the PDG $(10.80 \pm 0.09)\%$.
188	vimartin	1.2	Table.~\ref{tab:wlepbf} summarizes the branching fractions used in
189			the generation of the various \ttbar\ MC samples.
190			For \ttbar\ samples with the incorrect leptonic branching fraction, event
191			weights are applied based on the number of true leptons and the ratio
192			of the corrected and incorrect branching fractions.
193
194			\begin{table}[!h]
195			\begin{center}
196			\begin{tabular}{c\|c}
197			\hline
198			\ttbar\ Sample - Event Generator & Leptonic Branching Fraction\\
199			\hline
200			\hline
201			Madgraph & 0.111\\
202			MC@NLO & 0.111\\
203			Pythia & 0.108\\
204			Powheg & 0.108\\
205			\hline
206			\end{tabular}
207			\caption{Leptonic branching fractions for the various \ttbar\ samples
208			used in the analysis. The primary \ttbar\ MC sample produced with
209			Madgraph has a branching fraction that is almost $3\%$ higher than
210			the PDG value. \label{tab:wlepbf}}
211			\end{center}
212			\end{table}
213
214	vimartin	1.7
215			\subsubsection{Modeling of Additional Hard Jets in Top Dilepton Events}
216			\label{sec:jetmultiplicity}
217
218	vimartin	1.8	[CHECK, UPDATE, ADD EQUATIONS COMMENTED IN THE BOTTOM OF FILE \\
219			REFERENCE APPENDIX INFO. (FROM 7 TEV) AND SUMMARIZE THAT INFORMATION HERE]
220	vimartin	1.7
221			Dilepton \ttbar\ events have 2 jets from the top decays, so additional
222			jets from radiation or higher order contributions are required to
223			enter the signal sample. The modeling of addtional jets in \ttbar\
224			events is checked in a \ttll\ control sample,
225			selected by requiring
226			\begin{itemize}
227			\item exactly 2 selected electrons or muons with \pt $>$ 20 GeV
228			\item \met\ $>$ 100 GeV
229			\item $\geq1$ b-tagged jet
230			\item Z-veto
231			\end{itemize}
232			Figure~\ref{fig:dileptonnjets} shows a comparison of the jet
233			multiplicity distribution in data and MC for this two-lepton control
234			sample. After requiring at least 1 b-tagged jet, most of the
235			events have 2 jets, as expected from the dominant process \ttll. There is also a
236			significant fraction of events with additional jets.
237			The 3-jet sample is mainly comprised of \ttbar\ events with 1 additional
238			emission and similarly the $\ge4$-jet sample contains primarily
239	vimartin	1.8	$\ttbar+\ge2$ jet events.
240			%Even though the primary \ttbar\
241			%Madgraph sample used includes up to 3 additional partons at the Matrix
242			%Element level, which are intended to describe additional hard jets,
243			%Figure~\ref{fig:dileptonnjets} shows a slight mis-modeling of the
244			%additional jets.
245	vimartin	1.7
246
247			\begin{figure}[hbt]
248			\begin{center}
249			\includegraphics[width=0.5\linewidth]{plots/njets_all_met100_mueg.pdf}
250			\includegraphics[width=0.5\linewidth]{plots/njets_all_met100_diel.pdf}%
251			\includegraphics[width=0.5\linewidth]{plots/njets_all_met100_dimu.pdf}
252			\caption{
253			\label{fig:dileptonnjets}%\protect
254			Comparison of the jet multiplicity distribution in data and MC for dilepton events in the \E-\M\
255			(top), \E-\E\ (bottom left) and \M-\M\ (bottom right) channels.}
256			\end{center}
257			\end{figure}
258
259			It should be noted that in the case of \ttll\ events
260			with a single reconstructed lepton, the other lepton may be
261			mis-reconstructed as a jet. For example, a hadronic tau may be
262			mis-identified as a jet (since no $\tau$ identification is used).
263			In this case only 1 additional jet from radiation may suffice for
264			a \ttll\ event to enter the signal sample. As a result, both the
265			samples with $\ttbar+1$ jet and $\ttbar+\ge2$ jets are relevant for
266			estimating the top dilepton bkg in the signal region.
267
268			%In this section we discuss a correction to $ N_{2 lep}^{MC} $ in Equation XXX
269			%due to differences in the modelling of the jet multiplicity in data versus MC.
270			%The same correction also enters $ N_{peak}^{MC}$ in Equation XXX to the extend that the
271			%dilepton contributions to $ N_{peak}^{MC}$ gets corrected.
272
273			%The dilepton control sample is defined by the following requirements:
274			%\begin{itemize}
275			%\item Exactly 2 selected electrons or muons with \pt $>$ 20 GeV
276			%\item \met\ $>$ 50 GeV
277			%\item $\geq1$ b-tagged jet
278			%\end{itemize}
279			%
280			%This sample is dominated by \ttll. The distribution of \njets\ for data and MC passing this selection is displayed in Fig.~\ref{fig:dilepton_njets}.
281			%We use this distribution to derive scale factors which reweight the \ttll\ MC \njets\ distribution to match the data. We define the following
282			%quantities
283			%
284			%\begin{itemize}
285			%\item $N_{2}=$ data yield minus non-dilepton \ttbar\ MC yield for \njets\ $\leq$ 2
286			%\item $N_{3}=$ data yield minus non-dilepton \ttbar\ MC yield for \njets\ = 3
287			%\item $N_{4}=$ data yield minus non-dilepton \ttbar\ MC yield for \njets\ $\geq$ 4
288			%\item $M_{2}=$ dilepton \ttbar\ MC yield for \njets\ $\leq$ 2
289			%\item $M_{3}=$ dilepton \ttbar\ MC yield for \njets\ = 3
290			%\item $M_{4}=$ dilepton \ttbar\ MC yield for \njets\ $\geq$ 4
291			%\end{itemize}
292			%
293			%We use these yields to define 3 scale factors, which quantify the data/MC ratio in the 3 \njets\ bins:
294			%
295			%\begin{itemize}
296			%\item $SF_2 = N_2 / M_2$
297			%\item $SF_3 = N_3 / M_3$
298			%\item $SF_4 = N_4 / M_4$
299			%\end{itemize}
300			%
301			%And finally, we define the scale factors $K_3$ and $K_4$:
302			%
303			%\begin{itemize}
304			%\item $K_3 = SF_3 / SF_2$
305			%\item $K_4 = SF_4 / SF_2$
306			%\end{itemize}
307			%
308			%The scale factor $K_3$ is extracted from dilepton \ttbar\ events with \njets = 3, which have exactly 1 ISR jet.
309			%The scale factor $K_4$ is extracted from dilepton \ttbar\ events with \njets $\geq$ 4, which have at least 2 ISR jets.
310			%Both of these scale factors are needed since dilepton \ttbar\ events which fall in our signal region (including
311			%the \njets $\geq$ 4 requirement) may require exactly 1 ISR jet, in the case that the second lepton is reconstructed
312			%as a jet, or at least 2 ISR jets, in the case that the second lepton is not reconstructed as a jet. These scale
313			%factors are applied to the dilepton \ttbar\ MC only. For a given MC event, we determine whether to use $K_3$ or $K_4$
314			%by counting the number of reconstructed jets in the event ($N_{\rm{jets}}^R$) , and subtracting off any reconstructed
315			%jet which is matched to the second lepton at generator level ($N_{\rm{jets}}^\ell$); $N_{\rm{jets}}^{\rm{cor}} = N_{\rm{jets}}^R - N_{\rm{jets}}^\ell$.
316			%For events with $N_{\rm{jets}}^{\rm{cor}}=3$ the factor $K_3$ is applied, while for events with $N_{\rm{jets}}^{\rm{cor}}\geq4$ the factor $K_4$ is applied.
317			%For all subsequent steps, the scale factors $K_3$ and $K_4$ have been
318			%applied to the \ttll\ MC.
319
320
321			Table~\ref{tab:njetskfactors} shows scale factors to correct the
322			fraction of events with additional jets in MC to the observed fraction
323			in data. These are applied to the \ttll\ MC throughout the entire analysis, i.e. whenever \ttll\ MC is used to estimate or subtract
324			a yield or distribution.
325			%
326			In order to do so, it is first necessary to count the number of
327			additional jets from radiation and exclude leptons mis-identified as
328			jets. A jet is considered a mis-identified lepton if it is matched to a
329			generator-level second lepton with sufficient energy to satisfy the jet
330			\pt\ requirement ($\pt>30~\GeV$).
331
332			\begin{table}[!ht]
333			\begin{center}
334			\begin{tabular}{l\|c}
335			\hline
336			Jet Multiplicity Sample
337			& Data/MC Scale Factor \\
338			\hline
339			\hline
340			N jets $= 3$ (sensitive to $\ttbar+1$ extra jet from radiation) & $0.97 \pm 0.03$\\
341			N jets $\ge4$ (sensitive to $\ttbar+\ge2$ extra jets from radiation) & $0.91 \pm 0.04$\\
342			\hline
343			\end{tabular}
344			\caption{Data/MC scale factors used to account for differences in the
345			fraction of events with additional hard jets from radiation in
346			\ttll\ events. \label{tab:njetskfactors}}
347			\end{center}
348			\end{table}
349
350
351
352			\subsubsection{Efficiency Corrections}
353
354			[TO BE UDPATED WITH T\&P STUDIES ON ID, TRIGGER ETC]
355