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1  
2 + 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 + %Figure~\ref{fig:venndiagram} illustrates the relationship between these regions.
5  
6 < The preselection sample is based on the following criteria
6 > \subsection{Single Lepton Selection}
7 >
8 > [UPDATE SELECTION]
9 >
10 > The single lepton preselection sample is based on the following criteria
11   \begin{itemize}
12   \item satisfy the trigger requirement (see
13 <  Table.~\ref{tab:DatasetsData})
13 >  Table.~\ref{tab:DatasetsData}). Dilepton triggers are used only for the dilepton control region.
14   \item select events with one high \pt\ electron or muon, requiring
15    \begin{itemize}
16 <  \item $\pt>30~\GeVc$ and $|\eta|<2.5(2.1)$ for \E(\M)
16 >  \item $\pt>30~\GeVc$ and $|\eta|<2.1$
17    \item satisfy the identification and isolation requirements detailed
18      in the same-sign SUSY analysis (SUS-11-010) for electrons and the opposite-sign
19      SUSY analysis (SUS-11-011) for muons
20    \end{itemize}
21    \item require at least 4 PF jets in the event with $\pt>30~\GeV$
22 <    within $|\eta|<2.5$, out of which at least 1 is b-tagged based on
23 <    the SSV medium working point.
22 >    within $|\eta|<2.5$ out of which at least 1 satisfies the CSV
23 >    medium working point b-tagging requirement
24    \item require moderate $\met>50~\GeV$
25   \end{itemize}
26  
27 < Currently, we focus on the muon channel because it is cleaner (the QCD contribution is negligible)
21 < and the triggers are simpler (we use single muon triggers, as opposed to electron + 3-jet triggers).
22 < We will add the electron channel, time permitting. However, since this is a systematics-dominated
23 < analysis, increasing the statistics by adding the electrons is not expected to significantly improve
24 < the sensitivity, especialy because the electron selection efficiency is smaller and the systematic
25 < uncertainty associated with the QCD background is larger.
27 > Table~\ref{tab:preselectionyield} shows the yields in data and MC without any corrections for this preselection region.
28  
29 < A benchmark signal region is selected by tightening the \met\ and
30 < adding an \mt\ requirement
31 < \begin{itemize}
32 < \item $\met>100~\GeV$
33 < \item $\mt>150~\GeV$
34 < \end{itemize}
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 > \subsection{Signal Region Selection}
40 >
41 > [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 > 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 > \begin{table}[!h]
52 > \begin{center}
53 > \begin{tabular}{l|c|c}
54 > \hline
55 > Signal Region & Minimum \mt\ [GeV] & Minimum \met\ [GeV] \\
56 > \hline
57 > \hline
58 > SRA & 150 & 100 \\
59 > SRB & 120 & 150 \\
60 > SRC & 120 & 200 \\
61 > SRD & 120 & 250 \\
62 > SRE & 120 & 300 \\
63 > \hline
64 > \end{tabular}
65 > \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 > \end{center}
70 > \end{table}
71 >
72 > 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 > \begin{table}[!h]
80 > \begin{center}
81 > \begin{tabular}{l||c|c|c|c}
82 > \hline
83 > Sample              & SRA & SRB & SRC & SRD \\
84 > \hline
85 > \hline
86 > \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 > \hline
91 > Total            & $932 \pm 39$& $576 \pm 38$& $195 \pm 27$& $80 \pm 26$ \\
92 > \hline
93 > \end{tabular}
94 > \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 > \end{center}
99 > \end{table}
100 >
101 > \subsection{Control Region Selection}
102 >
103 > [1 PARAGRAPH BLURB RELATING BACKGROUNDS (IN TABLE FROM PREVIOUS SECTION)
104 > TO INTRODUCE CONTROL REGIONS]
105 >
106 > 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 >
114 > \begin{table}
115 > \begin{center}
116 > {\small
117 > \begin{tabular}{l|c|c|c}
118 > \hline
119 > 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 > \hline
153 > \end{tabular}
154 > }
155 > \caption{Summary of signal and control regions.
156 >  \label{tab:crdef}%\protect
157 > }
158 > \end{center}
159 > \end{table}
160 >
161 >
162 > \subsection{MC Corrections}
163  
164 < {\bf We have not looked at the data in the signal region after the first 1 fb$^{-1}$ of data.}
164 > [UPDATE SECTION]
165  
166 < \subsection{Corrections to Jets and \met}
166 > \subsubsection{Corrections to Jets and \met}
167 >
168 > [UPDATE, ADD FEW MORE DETAILS ON WHAT IS DONE HERE]
169  
170   The official recommendations from the Jet/MET group are used for
171   the data and MC samples. In particular, the jet
# Line 42 | Line 174 | L1FastL2L3Residual (L1FastL2L3) correcti
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 < deriving the Type I corrections. It may be noted that events with
46 < anomalous ``rho'' pile-up corrections are excluded from the sample since these
47 < correspond to events with unphysically large \met\ and \mt\ tail
48 < signal region (see Figure~\ref{fig:mtrhocomp}). An additional correction to remove
49 < the $\phi$-modulation observed in the \met\ is included, improving
50 < the agreement between the data and the MC, as shown in
51 < Figure~\ref{fig:metphicomp}. This correction has an effect on this analysis,
52 < since the azimuthal angle enters the \mt\ distribution.
177 > deriving the Type I corrections.
178  
179 < \clearpage
180 <
181 < \begin{figure}[!ht]
57 <  \begin{center}
58 <        \includegraphics[width=0.5\linewidth]{plots/mt_rho_comp.png}
59 <        \caption{ \label{fig:mtrhocomp}%\protect
60 <          Comparison of the \mt\ distribution for events with
61 <          unphysical energy corrections ($\rho <0$ or $ \rho > 40$, where $\rho$ is a
62 <          measure of the average pileup energy density) and the
63 <          nominal sample. Events with large pileup corrections
64 <          correspond to noisy events. Since this correction is applied
65 <          to the jets and propagated to the \met, these events have
66 <          anomalously large \met\ and populate the \mt\ tail. These
67 <          pathological events are excluded from the analysis sample.}
68 <  \end{center}
69 < \end{figure}
70 <
71 < \begin{figure}[!hb]
72 <  \begin{center}
73 <        \includegraphics[width=0.5\linewidth]{plots/metphi.pdf}%
74 <        \includegraphics[width=0.5\linewidth]{plots/metphi_phicorr.pdf}
75 <        \caption{ \label{fig:metphicomp}%\protect
76 <          The PF \met\ $\phi$ distribution (left) exhibits a
77 <          modulation. After applying a dedicated correction, the
78 <          azimuthal dependence is reduced (right).}
79 <  \end{center}
80 < \end{figure}
179 > Events with anomalous ``rho'' pile-up corrections are excluded from the sample since these
180 > correspond to events with unphysically large \met\ and \mt\ tail
181 > signal region. In addition, the recommended MET filters are applied.
182  
82 \clearpage
183  
184 < \subsection{Branching Fraction Correction}
184 > \subsubsection{Branching Fraction Correction}
185  
186   The leptonic branching fraction used in some of the \ttbar\ MC samples
187   differs from the value listed in the PDG $(10.80 \pm 0.09)\%$.
# Line 111 | Line 211 | Powheg       &       0.108\\
211   \end{center}
212   \end{table}
213  
214 +
215 + \subsubsection{Modeling of Additional Hard Jets in Top Dilepton Events}
216 + \label{sec:jetmultiplicity}
217 +
218 + [CHECK, UPDATE, ADD EQUATIONS COMMENTED IN THE BOTTOM OF FILE \\
219 + REFERENCE APPENDIX INFO. (FROM 7 TEV) AND SUMMARIZE THAT INFORMATION HERE]
220 +
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 + $\ttbar+\ge2$ 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 +
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 +

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