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 |
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 $(10.80 \pm 0.09)\%$. |
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 |
+ |
|