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\subsubsection{Modeling of Additional Hard Jets in Top Dilepton Events} |
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\label{sec:jetmultiplicity} |
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|
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[THIS SUBSUBSECTION IS DONE...MODULO THE LATEST PLOTS AND THE LATEST |
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NUMBERS IN THE TABLE] |
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– |
|
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Dilepton \ttbar\ events have 2 jets from the top decays, so additional |
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jets from radiation or higher order contributions are required to |
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< |
enter the signal sample. The modeling of addtional jets in \ttbar\ |
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> |
enter the signal sample. In this Section we develop an algorithm |
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> |
to be applied to all \ttll\ MC samples to ensure that the distribution |
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> |
of extra jets is properly modelled. |
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> |
|
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> |
|
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> |
The modeling of additional jets in \ttbar\ |
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events is checked in a \ttll\ control sample, |
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selected by requiring |
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\begin{itemize} |
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\item exactly 2 selected electrons or muons with \pt $>$ 20 GeV |
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< |
\item \met\ $>$ 100 GeV |
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> |
\item \met\ $>$ 50 GeV |
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\item $\geq1$ b-tagged jet |
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\item Z-veto ($|m_{\ell\ell} - 91| > 15$ GeV) |
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\end{itemize} |
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|
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\begin{figure}[hbt] |
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\begin{center} |
| 40 |
< |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met100_mueg.pdf} |
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< |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met100_diel.pdf}% |
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< |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met100_dimu.pdf} |
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> |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_mueg.pdf} |
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> |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_diel.pdf}% |
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> |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_dimu.pdf} |
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\caption{ |
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\label{fig:dileptonnjets}%\protect |
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Comparison of the jet multiplicity distribution in data and MC for dilepton events in the \E-\M\ |
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in data. These scale factors are calculated from Fig.~\ref{fig:dileptonnjets} |
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as follows: |
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\begin{itemize} |
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< |
\item $N_{2}=$ data yield minus non-dilepton \ttbar\ MC yield for \njets\ $\leq$ 2 |
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> |
\item $N_{2}=$ data yield minus non-dilepton \ttbar\ MC yield for |
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> |
\njets\ =1 or 2. |
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|
\item $N_{3}=$ data yield minus non-dilepton \ttbar\ MC yield for \njets\ = 3 |
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\item $N_{4}=$ data yield minus non-dilepton \ttbar\ MC yield for \njets\ $\geq$ 4 |
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< |
\item $M_{2}=$ dilepton \ttbar\ MC yield for \njets\ $\leq$ 2 |
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> |
\item $M_{2}=$ dilepton \ttbar\ MC yield for \njets\ = 1 or 2 |
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|
\item $M_{3}=$ dilepton \ttbar\ MC yield for \njets\ = 3 |
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\item $M_{4}=$ dilepton \ttbar\ MC yield for \njets\ $\geq$ 4 |
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\end{itemize} |
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\noindent This insures that $K_3 M_3/(M_2 + K_3 M_3 + K_4 M_4) = N_3 / |
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(N_2+N_3+N_4)$ and similarly for the $\geq 4$ jet bin. |
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|
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+ |
Table~\ref{tab:njetskfactors} also shows the values of $K_3$ and $K_4$ when the \met\ cut in the control sample definition is changed from 50 GeV to 100 GeV and 150 GeV. |
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+ |
% These values of $K_3$ and $K_4$ are not used in the analysis, but |
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+ |
This demonstrates that there is no statistically significant dependence of $K_3$ and $K_4$ on the \met\ cut. |
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|
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< |
The factors $K_3$ and $K_4$ are applied to the \ttll\ MC throughout the |
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> |
|
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> |
The factors $K_3$ and $K_4$ (derived with the 100 GeV \met\ cut) are applied to the \ttll\ MC throughout the |
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|
entire analysis, i.e. |
| 144 |
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whenever \ttll\ MC is used to estimate or subtract |
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< |
a yield or distribution. |
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> |
a yield or distribution. To be explicit, whenever Powheg is used, |
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> |
the Powheg $K_3$ and $K_4$ are used; whenever default MadGraph is |
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> |
used, the MadGraph $K_3$ and $K_4$ are used, etc. |
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% |
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In order to do so, it is first necessary to count the number of |
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additional jets from radiation and exclude leptons mis-identified as |
| 156 |
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|
| 157 |
|
\begin{table}[!ht] |
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\begin{center} |
| 159 |
< |
\begin{tabular}{l|c} |
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> |
{\footnotesize |
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> |
\begin{tabular}{l|c|c|c} |
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> |
\cline{2-4} |
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> |
& \multicolumn{3}{c}{ \met\ cut for data/MC scale factors} \\ |
| 163 |
|
\hline |
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< |
Jet Multiplicity Sample |
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< |
& Data/MC Scale Factor \\ |
| 164 |
> |
Jet Multiplicity Sample & 50 GeV & 100 GeV & 150 GeV \\ |
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|
\hline |
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|
\hline |
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< |
N jets $= 3$ (sensitive to $\ttbar+1$ extra jet from radiation) & |
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< |
$K_3 = 1.01 \pm 0.03$\\ |
| 167 |
> |
N jets $= 3$ (sensitive to $\ttbar+1$ extra jet from radiation) |
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> |
& $K_3 = 0.98 \pm 0.02$ & $K_3 = 1.01 \pm 0.03$ & $K_3 = 1.00 \pm 0.08$ \\ |
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|
N jets $\ge4$ (sensitive to $\ttbar+\ge2$ extra jets from radiation) |
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& $K_4 = 0.93 \pm 0.04$\\ |
| 170 |
> |
& $K_4 = 0.94 \pm 0.02$ & $K_4 = 0.93 \pm 0.04$ & $K_4 = 1.00 \pm 0.08$ \\ |
| 171 |
|
\hline |
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< |
\end{tabular} |
| 172 |
> |
\end{tabular}} |
| 173 |
|
\caption{Data/MC scale factors used to account for differences in the |
| 174 |
|
fraction of events with additional hard jets from radiation in |
| 175 |
< |
\ttll\ events. \label{tab:njetskfactors}} |
| 175 |
> |
\ttll\ events. The values derived with the 100 GeV \met\ cut are applied |
| 176 |
> |
to the \ttll\ MC throughout the analysis. \label{tab:njetskfactors}} |
| 177 |
|
\end{center} |
| 178 |
|
\end{table} |
| 179 |
|
|
| 185 |
|
MC in CR4} |
| 186 |
|
\label{sec:CR4-valid} |
| 187 |
|
|
| 176 |
– |
[THE TEXT IN THIS SUBSECTION IS ESSENTIALLY COMPLETE] |
| 177 |
– |
|
| 188 |
|
As mentioned above, $t\bar{t} \to $ dileptons where one of the leptons |
| 189 |
|
is somehow lost constitutes the main background. |
| 190 |
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The object of this test is to validate the $M_T$ distribution of this |
| 196 |
|
|
| 197 |
|
The $t\bar{t}$ MC is corrected using the $K_3$ and $K_4$ factors |
| 198 |
|
from Section~\ref{sec:jetmultiplicity}. It is also normalized to the |
| 199 |
< |
total data yield separately for the \met\ requirements of signal |
| 200 |
< |
regions A, B, C, and D. These normalization factors are listed |
| 199 |
> |
total data yield separately for the \met\ requirements of the various signal |
| 200 |
> |
regions. These normalization factors are listed |
| 201 |
|
in Table~\ref{tab:cr4mtsf} and are close to unity. |
| 202 |
|
|
| 203 |
|
The underlying \met\ and $M_T$ distributions are shown in |
| 204 |
|
Figures~\ref{fig:cr4met} and~\ref{fig:cr4mtrest}. The data-MC agreement |
| 205 |
|
is quite good. Quantitatively, this is also shown in Table~\ref{tab:cr4yields}. |
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< |
|
| 206 |
> |
This is a {\bf very} important Table. It shows that for well |
| 207 |
> |
identified \ttdl\ , the MC can predict the $M_T$ tail. Since the |
| 208 |
> |
main background is also \ttdl\ except with one ``missed'' lepton, |
| 209 |
> |
this is a key test. |
| 210 |
|
|
| 211 |
|
\begin{table}[!h] |
| 212 |
|
\begin{center} |
| 240 |
|
CR4D & CR4E & CR4F\\ |
| 241 |
|
\hline |
| 242 |
|
\hline |
| 243 |
< |
$\mu$ MC & $256 \pm 5$ & $152 \pm 4$ & $91 \pm 3$ & $26 \pm 2$ & $6 \pm 1$ & $4 \pm 1$ & $2 \pm 1$ \\ |
| 243 |
> |
$\mu$ MC & $256 \pm 14$ & $152 \pm 11$ & $91 \pm 9$ & $26 \pm 5$ & $6 \pm 2$ & $4 \pm 2$ & $2 \pm 1$ \\ |
| 244 |
|
$\mu$ Data & $251$ & $156$ & $98$ & $27$ & $8$ & $6$ & $4$ \\ |
| 245 |
|
\hline |
| 246 |
< |
$\mu$ Data/MC SF & $0.98 \pm 0.07$ & $1.02 \pm 0.09$ & $1.08 \pm 0.12$ & $1.04 \pm 0.21$ & $1.29 \pm 0.48$ & $1.35 \pm 0.59$ & $2.10 \pm 1.28$ \\ |
| 246 |
> |
$\mu$ Data/MC SF & $0.98 \pm 0.08$ & $1.02 \pm 0.11$ & $1.08 \pm 0.16$ & $1.04 \pm 0.28$ & $1.29 \pm 0.65$ & $1.35 \pm 0.80$ & $2.10 \pm 1.72$ \\ |
| 247 |
|
\hline |
| 248 |
|
\hline |
| 249 |
< |
e MC & $227 \pm 5$ & $139 \pm 4$ & $73 \pm 3$ & $21 \pm 1$ & $5 \pm 1$ & $2 \pm 0$ & $1 \pm 0$ \\ |
| 249 |
> |
e MC & $227 \pm 13$ & $139 \pm 11$ & $73 \pm 8$ & $21 \pm 4$ & $5 \pm 2$ & $2 \pm 1$ & $1 \pm 1$ \\ |
| 250 |
|
e Data & $219$ & $136$ & $72$ & $19$ & $2$ & $1$ & $1$ \\ |
| 251 |
|
\hline |
| 252 |
< |
e Data/MC SF & $0.96 \pm 0.07$ & $0.98 \pm 0.09$ & $0.99 \pm 0.12$ & $0.92 \pm 0.22$ & $0.41 \pm 0.29$ & $0.53 \pm 0.54$ & $0.76 \pm 0.78$ \\ |
| 252 |
> |
e Data/MC SF & $0.96 \pm 0.09$ & $0.98 \pm 0.11$ & $0.99 \pm 0.16$ & $0.92 \pm 0.29$ & $0.41 \pm 0.33$ & $0.53 \pm 0.62$ & $0.76 \pm 0.96$ \\ |
| 253 |
> |
\hline |
| 254 |
> |
\hline |
| 255 |
> |
$\mu$+e MC & $483 \pm 19$ & $291 \pm 16$ & $164 \pm 13$ & $47 \pm 7$ & $11 \pm 3$ & $6 \pm 2$ & $3 \pm 2$ \\ |
| 256 |
> |
$\mu$+e Data & $470$ & $292$ & $170$ & $46$ & $10$ & $7$ & $5$ \\ |
| 257 |
> |
\hline |
| 258 |
> |
$\mu$+e Data/MC SF & $0.97 \pm 0.06$ & $1.00 \pm 0.08$ & $1.04 \pm 0.11$ & $0.99 \pm 0.20$ & $0.90 \pm 0.37$ & $1.11 \pm 0.57$ & $1.55 \pm 1.04$ \\ |
| 259 |
|
\hline |
| 260 |
|
\end{tabular}} |
| 261 |
|
\caption{ Yields in \mt\ tail comparing the MC prediction (after |
