| 2 |
|
\label{sec:datadriven} |
| 3 |
|
We have developed two data-driven methods to |
| 4 |
|
estimate the background in the signal region. |
| 5 |
< |
The first one explouts the fact that |
| 5 |
> |
The first one exploits the fact that |
| 6 |
|
\met and \met$/\sqrt{\rm SumJetPt}$ are nearly |
| 7 |
|
uncorrelated for the $t\bar{t}$ background |
| 8 |
|
(Section~\ref{sec:abcd}); the second one |
| 12 |
|
from $W$-decays, which is reconstructed as \met in the |
| 13 |
|
detector. |
| 14 |
|
|
| 15 |
< |
in 30 pb$^{-1}$ we expect $\approx$ 1 SM event in |
| 16 |
< |
the signal region. The expectations from the LMO |
| 17 |
< |
and LM1 SUSY benchmark points are {\color{red} XX} and |
| 18 |
< |
{\color{red} XX} events respectively. |
| 15 |
> |
|
| 16 |
> |
%{\color{red} I took these |
| 17 |
> |
%numbers from the twiki, rescaling from 11.06 to 30/pb. |
| 18 |
> |
%They seem too large...are they really right?} |
| 19 |
|
|
| 20 |
|
|
| 21 |
|
\subsection{ABCD method} |
| 27 |
|
Thus, we can use an ABCD method in the \met$/\sqrt{\rm SumJetPt}$ vs |
| 28 |
|
sumJetPt plane to estimate the background in a data driven way. |
| 29 |
|
|
| 30 |
< |
\begin{figure}[htb] |
| 30 |
> |
\begin{figure}[tb] |
| 31 |
|
\begin{center} |
| 32 |
|
\includegraphics[width=0.75\linewidth]{uncorrelated.pdf} |
| 33 |
|
\caption{\label{fig:uncor}\protect Distributions of SumJetPt |
| 36 |
|
\end{center} |
| 37 |
|
\end{figure} |
| 38 |
|
|
| 39 |
< |
\begin{figure}[htb] |
| 39 |
> |
\begin{figure}[bt] |
| 40 |
|
\begin{center} |
| 41 |
< |
\includegraphics[width=0.75\linewidth]{abcdMC.jpg} |
| 41 |
> |
\includegraphics[width=0.5\linewidth, angle=90]{abcdMC.pdf} |
| 42 |
|
\caption{\label{fig:abcdMC}\protect Distributions of SumJetPt |
| 43 |
|
vs. MET$/\sqrt{\rm SumJetPt}$ for SM Monte Carlo. Here we also |
| 44 |
< |
show our choice of ABCD regions. {\color{red} We need a better |
| 45 |
< |
picture with the letters A-B-C-D and with the numerical values |
| 46 |
< |
of the boundaries clearly indicated.}} |
| 44 |
> |
show our choice of ABCD regions.} |
| 45 |
|
\end{center} |
| 46 |
|
\end{figure} |
| 47 |
|
|
| 49 |
|
Our choice of ABCD regions is shown in Figure~\ref{fig:abcdMC}. |
| 50 |
|
The signal region is region D. The expected number of events |
| 51 |
|
in the four regions for the SM Monte Carlo, as well as the BG |
| 52 |
< |
prediction AC/B is given in Table~\ref{tab:abcdMC} for an integrated |
| 53 |
< |
luminosity of 30 pb$^{-1}$. The ABCD method is accurate |
| 54 |
< |
to about 10\%. |
| 52 |
> |
prediction AC/B are given in Table~\ref{tab:abcdMC} for an integrated |
| 53 |
> |
luminosity of 35 pb$^{-1}$. The ABCD method is accurate |
| 54 |
> |
to about 20\%. |
| 55 |
> |
%{\color{red} Avi wants some statement about stability |
| 56 |
> |
%wrt changes in regions. I am not sure that we have done it and |
| 57 |
> |
%I am not sure it is necessary (Claudio).} |
| 58 |
|
|
| 59 |
|
\begin{table}[htb] |
| 60 |
|
\begin{center} |
| 61 |
|
\caption{\label{tab:abcdMC} Expected SM Monte Carlo yields for |
| 62 |
< |
30 pb$^{-1}$ in the ABCD regions.} |
| 63 |
< |
\begin{tabular}{|l|c|c|c|c||c|} |
| 62 |
> |
35 pb$^{-1}$ in the ABCD regions, as well as the predicted yield in |
| 63 |
> |
the signal region given by A$\times$C/B. Here 'SM other' is the sum |
| 64 |
> |
of non-dileptonic $t\bar{t}$ decays, $W^{\pm}$+jets, $W^+W^-$, |
| 65 |
> |
$W^{\pm}Z^0$, $Z^0Z^0$ and single top.} |
| 66 |
> |
\begin{tabular}{l||c|c|c|c||c} |
| 67 |
> |
\hline |
| 68 |
> |
sample & A & B & C & D & A$\times$C/B \\ |
| 69 |
> |
\hline |
| 70 |
> |
$t\bar{t}\rightarrow \ell^{+}\ell^{-}$ & 7.96 & 33.07 & 4.81 & 1.20 & 1.16 \\ |
| 71 |
> |
$Z^0$ + jets & 0.00 & 1.16 & 0.08 & 0.08 & 0.00 \\ |
| 72 |
> |
SM other & 0.65 & 2.31 & 0.17 & 0.14 & 0.05 \\ |
| 73 |
> |
\hline |
| 74 |
> |
total SM MC & 8.61 & 36.54 & 5.05 & 1.41 & 1.19 \\ |
| 75 |
> |
\hline |
| 76 |
> |
\end{tabular} |
| 77 |
> |
\end{center} |
| 78 |
> |
\end{table} |
| 79 |
> |
|
| 80 |
> |
\subsection{Dilepton $P_T$ method} |
| 81 |
> |
\label{sec:victory} |
| 82 |
> |
This method is based on a suggestion by V. Pavlunin\cite{ref:victory}, |
| 83 |
> |
and was investigated by our group in 2009\cite{ref:ourvictory}. |
| 84 |
> |
The idea is that in dilepton $t\bar{t}$ events the lepton and neutrinos |
| 85 |
> |
from $W$ decays have the same $P_T$ spectrum (modulo $W$ polarization |
| 86 |
> |
effects). One can then use the observed |
| 87 |
> |
$P_T(\ell\ell)$ distribution to model the sum of neutrino $P_T$'s which |
| 88 |
> |
is identified with the \met. |
| 89 |
> |
|
| 90 |
> |
Then, in order to predict the $t\bar{t} \to$ dilepton contribution to a |
| 91 |
> |
selection with \met$+$X, one applies a cut on $P_T(\ell\ell)+$X instead. |
| 92 |
> |
In practice one has to rescale the result of the $P_T(\ell\ell)+$X selection |
| 93 |
> |
to account for the fact that any dilepton selection must include a |
| 94 |
> |
moderate \met cut in order to reduce Drell Yan backgrounds. This |
| 95 |
> |
is discussed in Section 5.3 of Reference~\cite{ref:ourvictory}; for a \met |
| 96 |
> |
cut of 50 GeV, the rescaling factor is obtained from the data as |
| 97 |
> |
|
| 98 |
> |
\newcommand{\ptll} {\ensuremath{P_T(\ell\ell)}} |
| 99 |
> |
\begin{center} |
| 100 |
> |
$ K = \frac{\int_0^{\infty} {\cal N}(\ptll)~~d\ptll~}{\int_{50}^{\infty} {\cal N}(\ptll)~~d\ptll~}$ |
| 101 |
> |
\end{center} |
| 102 |
> |
|
| 103 |
> |
|
| 104 |
> |
Monte Carlo studies give values of $K$ that are typically between 1.5 and 1.6, |
| 105 |
> |
depending on selection details. |
| 106 |
> |
%%%TO BE REPLACED |
| 107 |
> |
%Given the integrated luminosity of the |
| 108 |
> |
%present dataset, the determination of $K$ in data is severely statistics |
| 109 |
> |
%limited. Thus, we take $K$ from $t\bar{t}$ Monte Carlo as |
| 110 |
> |
|
| 111 |
> |
%\begin{center} |
| 112 |
> |
%$ K_{MC} = \frac{\int_0^{\infty} {\cal N}(\met)~~d\met~}{\int_{50}^{\infty} {\cal N}(\met)~~d\met~}$ |
| 113 |
> |
%\end{center} |
| 114 |
> |
|
| 115 |
> |
%\noindent {\color{red} For the 11 pb result we have used $K$ from data.} |
| 116 |
> |
|
| 117 |
> |
There are several effects that spoil the correspondance between \met and |
| 118 |
> |
$P_T(\ell\ell)$: |
| 119 |
> |
\begin{itemize} |
| 120 |
> |
\item $Ws$ in top events are polarized. Neutrinos are emitted preferentially |
| 121 |
> |
forward in the $W$ rest frame, thus the $P_T(\nu\nu)$ distribution is harder |
| 122 |
> |
than the $P_T(\ell\ell)$ distribution for top dilepton events. |
| 123 |
> |
\item The lepton selections results in $P_T$ and $\eta$ cuts on the individual |
| 124 |
> |
leptons that have no simple correspondance to the neutrino requirements. |
| 125 |
> |
\item Similarly, the \met$>$50 GeV cut introduces an asymmetry between leptons and |
| 126 |
> |
neutrinos which is only partially compensated by the $K$ factor above. |
| 127 |
> |
\item The \met resolution is much worse than the dilepton $P_T$ resolution. |
| 128 |
> |
When convoluted with a falling spectrum in the tails of \met, this result |
| 129 |
> |
in a harder spectrum for \met than the original $P_T(\nu\nu)$. |
| 130 |
> |
\item The \met response in CMS is not exactly 1. This causes a distortion |
| 131 |
> |
in the \met distribution that is not present in the $P_T(\ell\ell)$ distribution. |
| 132 |
> |
\item The $t\bar{t} \to$ dilepton signal includes contributions from |
| 133 |
> |
$W \to \tau \to \ell$. For these events the arguments about the equivalence |
| 134 |
> |
of $P_T(\ell\ell)$ and $P_T(\nu\nu)$ do not apply. |
| 135 |
> |
\item A dilepton selection will include SM events from non $t\bar{t}$ |
| 136 |
> |
sources. These events can affect the background prediction. Particularly |
| 137 |
> |
dangerous are high $P_T$ Drell Yan events that barely pass the \met$>$ 50 |
| 138 |
> |
GeV selection. They will tend to push the data-driven background prediction up. |
| 139 |
> |
\end{itemize} |
| 140 |
> |
|
| 141 |
> |
We have studied these effects in SM Monte Carlo, using a mixture of generator and |
| 142 |
> |
reconstruction level studies, putting the various effects in one at a time. |
| 143 |
> |
For each configuration, we apply the data-driven method and report as figure |
| 144 |
> |
of merit the ratio of observed and predicted events in the signal region. |
| 145 |
> |
The results are summarized in Table~\ref{tab:victorybad}. |
| 146 |
> |
|
| 147 |
> |
\begin{table}[htb] |
| 148 |
> |
\begin{center} |
| 149 |
> |
\caption{\label{tab:victorybad} Test of the data driven method in Monte Carlo |
| 150 |
> |
under different assumptions. See text for details.} |
| 151 |
> |
\begin{tabular}{|l|c|c|c|c|c|c|c|c|} |
| 152 |
> |
\hline |
| 153 |
> |
& True $t\bar{t}$ dilepton & $t\to W\to\tau$& other SM & GEN or & Lepton $P_T$ & Z veto & \met $>$ 50& obs/pred \\ |
| 154 |
> |
& included & included & included & RECOSIM & and $\eta$ cuts & & & \\ \hline |
| 155 |
> |
1&Y & N & N & GEN & N & N & N & 1.90 \\ |
| 156 |
> |
2&Y & N & N & GEN & Y & N & N & 1.64 \\ |
| 157 |
> |
3&Y & N & N & GEN & Y & Y & N & 1.59 \\ |
| 158 |
> |
4&Y & N & N & GEN & Y & Y & Y & 1.55 \\ |
| 159 |
> |
5&Y & N & N & RECOSIM & Y & Y & Y & 1.51 \\ |
| 160 |
> |
6&Y & Y & N & RECOSIM & Y & Y & Y & 1.58 \\ |
| 161 |
> |
7&Y & Y & Y & RECOSIM & Y & Y & Y & 1.18 \\ |
| 162 |
> |
\hline |
| 163 |
> |
\end{tabular} |
| 164 |
> |
\end{center} |
| 165 |
> |
\end{table} |
| 166 |
> |
|
| 167 |
> |
|
| 168 |
> |
The largest discrepancy between prediction and observation occurs on the first |
| 169 |
> |
line of Table~\ref{tab:victorybad}, {\em i.e.}, at the generator level with no |
| 170 |
> |
cuts. We have verified that this effect is due to the polarization of |
| 171 |
> |
the $W$ (we remove the polarization by reweighting the events and we get |
| 172 |
> |
good agreement between prediction and observation). The kinematical |
| 173 |
> |
requirements (lines 2,3,4) compensate somewhat for the effect of W polarization. |
| 174 |
> |
Going from GEN to RECOSIM, the change in observed/predicted is small. |
| 175 |
> |
% We have tracked this down to the fact that tcMET underestimates the true \met |
| 176 |
> |
% by $\approx 4\%$\footnote{We find that observed/predicted changes by roughly 0.1 |
| 177 |
> |
%for each 1.5\% change in \met response.}. |
| 178 |
> |
Finally, contamination from non $t\bar{t}$ |
| 179 |
> |
events can have a significant impact on the BG prediction. The changes between |
| 180 |
> |
lines 6 and 7 of Table~\ref{tab:victorybad} is driven by 3 |
| 181 |
> |
Drell Yan events that pass the \met selection in Monte Carlo (thus the effect |
| 182 |
> |
is statistically not well quantified). |
| 183 |
> |
|
| 184 |
> |
An additional source of concern is that the CMS Madgraph $t\bar{t}$ MC does |
| 185 |
> |
not include effects of spin correlations between the two top quarks. |
| 186 |
> |
We have studied this effect at the generator level using Alpgen. We find |
| 187 |
> |
that the bias is at the few percent level. |
| 188 |
> |
|
| 189 |
> |
%%%TO BE REPLACED |
| 190 |
> |
%Based on the results of Table~\ref{tab:victorybad}, we conclude that the |
| 191 |
> |
%naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to |
| 192 |
> |
%be corrected by a factor of {\color{red} $ K_{\rm{fudge}} =1.2 \pm 0.3$ |
| 193 |
> |
%(We still need to settle on thie exact value of this. |
| 194 |
> |
%For the 11 pb analysis it is taken as =1.)} . The quoted |
| 195 |
> |
%uncertainty is based on the stability of the Monte Carlo tests under |
| 196 |
> |
%variations of event selections, choices of \met algorithm, etc. |
| 197 |
> |
%For example, we find that observed/predicted changes by roughly 0.1 |
| 198 |
> |
%for each 1.5\% change in the average \met response. |
| 199 |
> |
|
| 200 |
> |
Based on the results of Table~\ref{tab:victorybad}, we conclude that the |
| 201 |
> |
naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to |
| 202 |
> |
be corrected by a factor of $ K_C = X \pm Y$. |
| 203 |
> |
The value of this correction factor as well as the systematic uncertainty |
| 204 |
> |
will be assessed using 38X ttbar madgraph MC. In the following we use |
| 205 |
> |
$K_C = 1$ for simplicity. Based on previous MC studies we foresee a correction |
| 206 |
> |
factor of $K_C \approx 1.2 - 1.5$, and we will assess an uncertainty |
| 207 |
> |
based on the stability of the Monte Carlo tests under |
| 208 |
> |
variations of event selections, choices of \met algorithm, etc. |
| 209 |
> |
For example, we find that observed/predicted changes by roughly 0.1 |
| 210 |
> |
for each 1.5\% change in the average \met response. |
| 211 |
> |
|
| 212 |
> |
|
| 213 |
> |
|
| 214 |
> |
\subsection{Signal Contamination} |
| 215 |
> |
\label{sec:sigcont} |
| 216 |
> |
|
| 217 |
> |
All data-driven methods are in principle subject to signal contaminations |
| 218 |
> |
in the control regions, and the methods described in |
| 219 |
> |
Sections~\ref{sec:abcd} and~\ref{sec:victory} are not exceptions. |
| 220 |
> |
Signal contamination tends to dilute the significance of a signal |
| 221 |
> |
present in the data by inflating the background prediction. |
| 222 |
> |
|
| 223 |
> |
It is hard to quantify how important these effects are because we |
| 224 |
> |
do not know what signal may be hiding in the data. Having two |
| 225 |
> |
independent methods (in addition to Monte Carlo ``dead-reckoning'') |
| 226 |
> |
adds redundancy because signal contamination can have different effects |
| 227 |
> |
in the different control regions for the two methods. |
| 228 |
> |
For example, in the extreme case of a |
| 229 |
> |
new physics signal |
| 230 |
> |
with $P_T(\ell \ell) = \met$, an excess of events would be seen |
| 231 |
> |
in the ABCD method but not in the $P_T(\ell \ell)$ method. |
| 232 |
> |
|
| 233 |
> |
|
| 234 |
> |
The LM points are benchmarks for SUSY analyses at CMS. The effects |
| 235 |
> |
of signal contaminations for a couple such points are summarized |
| 236 |
> |
in Table~\ref{tab:sigcont}. Signal contamination is definitely an important |
| 237 |
> |
effect for these two LM points, but it does not totally hide the |
| 238 |
> |
presence of the signal. |
| 239 |
> |
|
| 240 |
> |
|
| 241 |
> |
\begin{table}[htb] |
| 242 |
> |
\begin{center} |
| 243 |
> |
\caption{\label{tab:sigcont} Effects of signal contamination |
| 244 |
> |
for the two data-driven background estimates. The three columns give |
| 245 |
> |
the expected yield in the signal region and the background estimates |
| 246 |
> |
using the ABCD and $P_T(\ell \ell)$ methods. Results are normalized to 35~pb$^{-1}$.} |
| 247 |
> |
\begin{tabular}{lccc} |
| 248 |
> |
\hline |
| 249 |
> |
& Yield & ABCD & $P_T(\ell \ell)$ \\ |
| 250 |
> |
\hline |
| 251 |
> |
SM only & 1.41 & 1.19 & 0.96 \\ |
| 252 |
> |
SM + LM0 & 7.88 & 4.24 & 2.28 \\ |
| 253 |
> |
SM + LM1 & 3.98 & 1.53 & 1.44 \\ |
| 254 |
|
\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 |
| 255 |
|
\end{tabular} |
| 256 |
|
\end{center} |
| 257 |
|
\end{table} |
| 258 |
|
|
| 259 |
|
|
| 260 |
|
|
| 261 |
+ |
%\begin{table}[htb] |
| 262 |
+ |
%\begin{center} |
| 263 |
+ |
%\caption{\label{tab:sigcontABCD} Effects of signal contamination |
| 264 |
+ |
%for the background predictions of the ABCD method including LM0 or |
| 265 |
+ |
%LM1. Results |
| 266 |
+ |
%are normalized to 30 pb$^{-1}$.} |
| 267 |
+ |
%\begin{tabular}{|c|c||c|c||c|c|} |
| 268 |
+ |
%\hline |
| 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 & 3.7 & 3.4 & 1.3 \\ |
| 272 |
+ |
%\hline |
| 273 |
+ |
%\end{tabular} |
| 274 |
+ |
%\end{center} |
| 275 |
+ |
%\end{table} |
| 276 |
+ |
|
| 277 |
+ |
%\begin{table}[htb] |
| 278 |
+ |
%\begin{center} |
| 279 |
+ |
%\caption{\label{tab:sigcontPT} Effects of signal contamination |
| 280 |
+ |
%for the background predictions of the $P_T(\ell\ell)$ method including LM0 or |
| 281 |
+ |
%LM1. Results |
| 282 |
+ |
%are normalized to 30 pb$^{-1}$.} |
| 283 |
+ |
%\begin{tabular}{|c|c||c|c||c|c|} |
| 284 |
+ |
%\hline |
| 285 |
+ |
%SM & BG Prediction & SM$+$LM0 & BG Prediction & SM$+$LM1 & BG Prediction \\ |
| 286 |
+ |
%Background & SM Only & Contribution & Including LM0 & Contribution & Including LM1 \\ \hline |
| 287 |
+ |
%1.2 & 1.0 & 6.8 & 2.2 & 3.4 & 1.5 \\ |
| 288 |
+ |
%\hline |
| 289 |
+ |
%\end{tabular} |
| 290 |
+ |
%\end{center} |
| 291 |
+ |
%\end{table} |
| 292 |
|
|
