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\label{sec:datadriven} |
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We have developed two data-driven methods to |
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estimate the background in the signal region. |
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The first one explouts the fact that |
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The first one exploits the fact that |
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\met and \met$/\sqrt{\rm SumJetPt}$ are nearly |
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uncorrelated for the $t\bar{t}$ background |
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(Section~\ref{sec:abcd}); the second one |
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from $W$-decays, which is reconstructed as \met in the |
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detector. |
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|
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in 30 pb$^{-1}$ we expect $\approx$ 1 SM event in |
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In 35 pb$^{-1}$ we expect 1.4 SM event in |
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the signal region. The expectations from the LMO |
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and LM1 SUSY benchmark points are {\color{red} XX} and |
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{\color{red} XX} events respectively. |
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and LM1 SUSY benchmark points are 6.5 and |
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2.6 events respectively. |
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%{\color{red} I took these |
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%numbers from the twiki, rescaling from 11.06 to 30/pb. |
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%They seem too large...are they really right?} |
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|
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|
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\subsection{ABCD method} |
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|
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\begin{figure}[bt] |
| 43 |
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\begin{center} |
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< |
\includegraphics[width=0.75\linewidth]{abcdMC.jpg} |
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> |
\includegraphics[width=0.5\linewidth, angle=90]{abcdMC.pdf} |
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\caption{\label{fig:abcdMC}\protect Distributions of SumJetPt |
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vs. MET$/\sqrt{\rm SumJetPt}$ for SM Monte Carlo. Here we also |
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show our choice of ABCD regions. {\color{red} We need a better |
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picture with the letters A-B-C-D and with the numerical values |
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< |
of the boundaries clearly indicated.}} |
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> |
show our choice of ABCD regions.} |
| 48 |
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\end{center} |
| 49 |
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\end{figure} |
| 50 |
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|
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The signal region is region D. The expected number of events |
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in the four regions for the SM Monte Carlo, as well as the BG |
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prediction AC/B are given in Table~\ref{tab:abcdMC} for an integrated |
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luminosity of 30 pb$^{-1}$. The ABCD method is accurate |
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to about 10\%. |
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> |
luminosity of 35 pb$^{-1}$. The ABCD method is accurate |
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> |
to about 20\%. |
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%{\color{red} Avi wants some statement about stability |
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%wrt changes in regions. I am not sure that we have done it and |
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%I am not sure it is necessary (Claudio).} |
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|
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\begin{table}[htb] |
| 63 |
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\begin{center} |
| 64 |
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\caption{\label{tab:abcdMC} Expected SM Monte Carlo yields for |
| 65 |
< |
30 pb$^{-1}$ in the ABCD regions.} |
| 66 |
< |
\begin{tabular}{|l|c|c|c|c||c|} |
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> |
35 pb$^{-1}$ in the ABCD regions, as well as the predicted yield in |
| 66 |
> |
the signal region given by A$\times$C/B. Here 'SM other' is the sum |
| 67 |
> |
of non-dileptonic $t\bar{t}$ decays, $W^{\pm}$+jets, $W^+W^-$, |
| 68 |
> |
$W^{\pm}Z^0$, $Z^0Z^0$ and single top.} |
| 69 |
> |
\begin{tabular}{l||c|c|c|c||c} |
| 70 |
> |
\hline |
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> |
sample & A & B & C & D & A$\times$C/B \\ |
| 72 |
> |
\hline |
| 73 |
> |
$t\bar{t}\rightarrow \ell^{+}\ell^{-}$ & 7.96 & 33.07 & 4.81 & 1.20 & 1.16 \\ |
| 74 |
> |
$Z^0$ + jets & 0.00 & 1.16 & 0.08 & 0.08 & 0.00 \\ |
| 75 |
> |
SM other & 0.65 & 2.31 & 0.17 & 0.14 & 0.05 \\ |
| 76 |
> |
\hline |
| 77 |
> |
total SM MC & 8.61 & 36.54 & 5.05 & 1.41 & 1.19 \\ |
| 78 |
|
\hline |
| 64 |
– |
Sample & A & B & C & D & AC/D \\ \hline |
| 65 |
– |
ttdil & 6.4 & 28.4 & 4.2 & 1.0 & 0.9 \\ |
| 66 |
– |
Zjets & 0.0 & 1.3 & 0.2 & 0.0 & 0.0 \\ |
| 67 |
– |
Other SM & 0.6 & 2.1 & 0.2 & 0.1 & 0.0 \\ \hline |
| 68 |
– |
total MC & 7.0 & 31.8 & 4.5 & 1.1 & 1.0 \\ \hline |
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|
\end{tabular} |
| 80 |
|
\end{center} |
| 81 |
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\end{table} |
| 105 |
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|
| 106 |
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|
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Monte Carlo studies give values of $K$ that are typically between 1.5 and 1.6, |
| 108 |
< |
depending on selection details. |
| 108 |
> |
depending on selection details. |
| 109 |
> |
%%%TO BE REPLACED |
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> |
%Given the integrated luminosity of the |
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> |
%present dataset, the determination of $K$ in data is severely statistics |
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> |
%limited. Thus, we take $K$ from $t\bar{t}$ Monte Carlo as |
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> |
|
| 114 |
> |
%\begin{center} |
| 115 |
> |
%$ K_{MC} = \frac{\int_0^{\infty} {\cal N}(\met)~~d\met~}{\int_{50}^{\infty} {\cal N}(\met)~~d\met~}$ |
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> |
%\end{center} |
| 117 |
> |
|
| 118 |
> |
%\noindent {\color{red} For the 11 pb result we have used $K$ from data.} |
| 119 |
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|
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|
There are several effects that spoil the correspondance between \met and |
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$P_T(\ell\ell)$: |
| 151 |
|
\begin{center} |
| 152 |
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\caption{\label{tab:victorybad} Test of the data driven method in Monte Carlo |
| 153 |
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under different assumptions. See text for details.} |
| 154 |
< |
\begin{tabular}{|l|c|c|c|c|c|c|c|} |
| 154 |
> |
\begin{tabular}{|l|c|c|c|c|c|c|c|c|} |
| 155 |
|
\hline |
| 156 |
< |
& True $t\bar{t}$ dilepton & $t\to W\to\tau$& other SM & GEN or & Lepton $P_T$ & \met $>$ 50& obs/pred \\ |
| 157 |
< |
& included & included & included & RECOSIM & and $\eta$ cuts & & \\ \hline |
| 158 |
< |
1&Y & N & N & GEN & N & N & \\ |
| 159 |
< |
2&Y & N & N & GEN & Y & N & \\ |
| 160 |
< |
3&Y & N & N & GEN & Y & Y & \\ |
| 161 |
< |
4&Y & N & N & RECOSIM & Y & Y & \\ |
| 162 |
< |
5&Y & Y & N & RECOSIM & Y & Y & \\ |
| 163 |
< |
6&Y & Y & Y & RECOSIM & Y & Y & \\ |
| 156 |
> |
& True $t\bar{t}$ dilepton & $t\to W\to\tau$& other SM & GEN or & Lepton $P_T$ & Z veto & \met $>$ 50& obs/pred \\ |
| 157 |
> |
& included & included & included & RECOSIM & and $\eta$ cuts & & & \\ \hline |
| 158 |
> |
1&Y & N & N & GEN & N & N & N & 1.90 \\ |
| 159 |
> |
2&Y & N & N & GEN & Y & N & N & 1.64 \\ |
| 160 |
> |
3&Y & N & N & GEN & Y & Y & N & 1.59 \\ |
| 161 |
> |
4&Y & N & N & GEN & Y & Y & Y & 1.55 \\ |
| 162 |
> |
5&Y & N & N & RECOSIM & Y & Y & Y & 1.51 \\ |
| 163 |
> |
6&Y & Y & N & RECOSIM & Y & Y & Y & 1.58 \\ |
| 164 |
> |
7&Y & Y & Y & RECOSIM & Y & Y & Y & 1.18 \\ |
| 165 |
|
\hline |
| 166 |
|
\end{tabular} |
| 167 |
|
\end{center} |
| 173 |
|
cuts. We have verified that this effect is due to the polarization of |
| 174 |
|
the $W$ (we remove the polarization by reweighting the events and we get |
| 175 |
|
good agreement between prediction and observation). The kinematical |
| 176 |
< |
requirements (lines 2 and 3) do not have a significant additional effect. |
| 177 |
< |
Going from GEN to RECOSIM there is a significant change in observed/predicted. |
| 178 |
< |
We have tracked this down to the fact that tcMET underestimates the true \met |
| 179 |
< |
by $\approx 4\%$\footnote{We find that observed/predicted changes by roughly 0.1 |
| 180 |
< |
for each 1.5\% change in \met response.}. Finally, contamination from non $t\bar{t}$ |
| 176 |
> |
requirements (lines 2,3,4) compensate somewhat for the effect of W polarization. |
| 177 |
> |
Going from GEN to RECOSIM, the change in observed/predicted is small. |
| 178 |
> |
% We have tracked this down to the fact that tcMET underestimates the true \met |
| 179 |
> |
% by $\approx 4\%$\footnote{We find that observed/predicted changes by roughly 0.1 |
| 180 |
> |
%for each 1.5\% change in \met response.}. |
| 181 |
> |
Finally, contamination from non $t\bar{t}$ |
| 182 |
|
events can have a significant impact on the BG prediction. The changes between |
| 183 |
< |
lines 5 and 6 of Table~\ref{tab:victorybad} is driven by only {\color{red} 3} |
| 184 |
< |
Drell Yan events that pass the \met selection. |
| 183 |
> |
lines 6 and 7 of Table~\ref{tab:victorybad} is driven by 3 |
| 184 |
> |
Drell Yan events that pass the \met selection in Monte Carlo (thus the effect |
| 185 |
> |
is statistically not well quantified). |
| 186 |
|
|
| 187 |
|
An additional source of concern is that the CMS Madgraph $t\bar{t}$ MC does |
| 188 |
|
not include effects of spin correlations between the two top quarks. |
| 189 |
|
We have studied this effect at the generator level using Alpgen. We find |
| 190 |
< |
that the bias is a the few percent level. |
| 190 |
> |
that the bias is at the few percent level. |
| 191 |
> |
|
| 192 |
> |
%%%TO BE REPLACED |
| 193 |
> |
%Based on the results of Table~\ref{tab:victorybad}, we conclude that the |
| 194 |
> |
%naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to |
| 195 |
> |
%be corrected by a factor of {\color{red} $ K_{\rm{fudge}} =1.2 \pm 0.3$ |
| 196 |
> |
%(We still need to settle on thie exact value of this. |
| 197 |
> |
%For the 11 pb analysis it is taken as =1.)} . The quoted |
| 198 |
> |
%uncertainty is based on the stability of the Monte Carlo tests under |
| 199 |
> |
%variations of event selections, choices of \met algorithm, etc. |
| 200 |
> |
%For example, we find that observed/predicted changes by roughly 0.1 |
| 201 |
> |
%for each 1.5\% change in the average \met response. |
| 202 |
|
|
| 203 |
|
Based on the results of Table~\ref{tab:victorybad}, we conclude that the |
| 204 |
< |
naive data driven background estimate based on $P_T{\ell\ell)}$ needs to |
| 205 |
< |
be corrected by a factor of {\color{red} $1.4 \pm 0.3$ (We need to |
| 206 |
< |
decide what this number should be)}. The quoted |
| 207 |
< |
uncertainty is based on the stability of the Monte Carlo tests under |
| 204 |
> |
naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to |
| 205 |
> |
be corrected by a factor of $ K_C = X \pm Y$. |
| 206 |
> |
The value of this correction factor as well as the systematic uncertainty |
| 207 |
> |
will be assessed using 38X ttbar madgraph MC. In the following we use |
| 208 |
> |
$K_C = 1$ for simplicity. Based on previous MC studies we foresee a correction |
| 209 |
> |
factor of $K_C \approx 1.2 - 1.4$, and we will assess an uncertainty |
| 210 |
> |
based on the stability of the Monte Carlo tests under |
| 211 |
|
variations of event selections, choices of \met algorithm, etc. |
| 212 |
+ |
For example, we find that observed/predicted changes by roughly 0.1 |
| 213 |
+ |
for each 1.5\% change in the average \met response. |
| 214 |
+ |
|
| 215 |
|
|
| 216 |
|
|
| 217 |
|
\subsection{Signal Contamination} |
| 218 |
|
\label{sec:sigcont} |
| 219 |
|
|
| 220 |
< |
All data-driven methods are principle subject to signal contaminations |
| 220 |
> |
All data-driven methods are in principle subject to signal contaminations |
| 221 |
|
in the control regions, and the methods described in |
| 222 |
|
Sections~\ref{sec:abcd} and~\ref{sec:victory} are not exceptions. |
| 223 |
|
Signal contamination tends to dilute the significance of a signal |
| 230 |
|
in the different control regions for the two methods. |
| 231 |
|
For example, in the extreme case of a |
| 232 |
|
new physics signal |
| 233 |
< |
with $P_T(\ell \ell) = \met$, an excess of ev ents would be seen |
| 233 |
> |
with $P_T(\ell \ell) = \met$, an excess of events would be seen |
| 234 |
|
in the ABCD method but not in the $P_T(\ell \ell)$ method. |
| 235 |
|
|
| 236 |
+ |
|
| 237 |
|
The LM points are benchmarks for SUSY analyses at CMS. The effects |
| 238 |
|
of signal contaminations for a couple such points are summarized |
| 239 |
|
in Table~\ref{tab:sigcontABCD} and~\ref{tab:sigcontPT}. |
| 248 |
|
for the background predictions of the ABCD method including LM0 or |
| 249 |
|
LM1. Results |
| 250 |
|
are normalized to 30 pb$^{-1}$.} |
| 251 |
< |
\begin{tabular}{|c||c|c||c|c|} |
| 251 |
> |
\begin{tabular}{|c|c||c|c||c|c|} |
| 252 |
|
\hline |
| 253 |
< |
SM & LM0 & BG Prediction & LM1 & BG Prediction \\ |
| 254 |
< |
Background & Contribution& Including LM0 & Contribution & Including LM1 \\ \hline |
| 255 |
< |
x & x & x & x & x \\ |
| 253 |
> |
SM & BG Prediction & SM$+$LM0 & BG Prediction & SM$+$LM1 & BG Prediction \\ |
| 254 |
> |
Background & SM Only & Contribution & Including LM0 & Contribution & Including LM1 \\ \hline |
| 255 |
> |
1.2 & 1.0 & 6.8 & 3.7 & 3.4 & 1.3 \\ |
| 256 |
|
\hline |
| 257 |
|
\end{tabular} |
| 258 |
|
\end{center} |
| 263 |
|
\caption{\label{tab:sigcontPT} Effects of signal contamination |
| 264 |
|
for the background predictions of the $P_T(\ell\ell)$ method including LM0 or |
| 265 |
|
LM1. Results |
| 266 |
< |
are normalized to 30 pb$^{-1}$.} |
| 267 |
< |
\begin{tabular}{|c||c|c||c|c|} |
| 266 |
> |
are normalized to 30 pb$^{-1}$.} |
| 267 |
> |
\begin{tabular}{|c|c||c|c||c|c|} |
| 268 |
|
\hline |
| 269 |
< |
SM & LM0 & BG Prediction & LM1 & BG Prediction \\ |
| 270 |
< |
Background & Contribution& Including LM0 & Contribution & Including LM1 \\ \hline |
| 271 |
< |
x & x & x & x & x \\ |
| 269 |
> |
SM & BG Prediction & SM$+$LM0 & BG Prediction & SM$+$LM1 & BG Prediction \\ |
| 270 |
> |
Background & SM Only & Contribution & Including LM0 & Contribution & Including LM1 \\ \hline |
| 271 |
> |
1.2 & 1.0 & 6.8 & 2.2 & 3.4 & 1.5 \\ |
| 272 |
|
\hline |
| 273 |
|
\end{tabular} |
| 274 |
|
\end{center} |
