| 1 |
claudioc |
1.1 |
\section{Data Driven Background Estimation Methods}
|
| 2 |
|
|
\label{sec:datadriven}
|
| 3 |
|
|
We have developed two data-driven methods to
|
| 4 |
|
|
estimate the background in the signal region.
|
| 5 |
benhoob |
1.10 |
The first one exploits the fact that
|
| 6 |
claudioc |
1.1 |
\met and \met$/\sqrt{\rm SumJetPt}$ are nearly
|
| 7 |
|
|
uncorrelated for the $t\bar{t}$ background
|
| 8 |
|
|
(Section~\ref{sec:abcd}); the second one
|
| 9 |
|
|
is based on the fact that in $t\bar{t}$ the
|
| 10 |
|
|
$P_T$ of the dilepton pair is on average
|
| 11 |
|
|
nearly the same as the $P_T$ of the pair of neutrinos
|
| 12 |
|
|
from $W$-decays, which is reconstructed as \met in the
|
| 13 |
|
|
detector.
|
| 14 |
|
|
|
| 15 |
benhoob |
1.12 |
In 35 pb$^{-1}$ we expect 1.4 SM event in
|
| 16 |
claudioc |
1.1 |
the signal region. The expectations from the LMO
|
| 17 |
benhoob |
1.12 |
and LM1 SUSY benchmark points are 6.5 and
|
| 18 |
|
|
2.6 events respectively.
|
| 19 |
claudioc |
1.6 |
%{\color{red} I took these
|
| 20 |
|
|
%numbers from the twiki, rescaling from 11.06 to 30/pb.
|
| 21 |
|
|
%They seem too large...are they really right?}
|
| 22 |
claudioc |
1.1 |
|
| 23 |
|
|
|
| 24 |
|
|
\subsection{ABCD method}
|
| 25 |
|
|
\label{sec:abcd}
|
| 26 |
|
|
|
| 27 |
|
|
We find that in $t\bar{t}$ events \met and
|
| 28 |
|
|
\met$/\sqrt{\rm SumJetPt}$ are nearly uncorrelated.
|
| 29 |
|
|
This is demonstrated in Figure~\ref{fig:uncor}.
|
| 30 |
|
|
Thus, we can use an ABCD method in the \met$/\sqrt{\rm SumJetPt}$ vs
|
| 31 |
|
|
sumJetPt plane to estimate the background in a data driven way.
|
| 32 |
|
|
|
| 33 |
claudioc |
1.2 |
\begin{figure}[tb]
|
| 34 |
claudioc |
1.1 |
\begin{center}
|
| 35 |
|
|
\includegraphics[width=0.75\linewidth]{uncorrelated.pdf}
|
| 36 |
|
|
\caption{\label{fig:uncor}\protect Distributions of SumJetPt
|
| 37 |
|
|
in MC $t\bar{t}$ events for different intervals of
|
| 38 |
|
|
MET$/\sqrt{\rm SumJetPt}$.}
|
| 39 |
|
|
\end{center}
|
| 40 |
|
|
\end{figure}
|
| 41 |
|
|
|
| 42 |
claudioc |
1.2 |
\begin{figure}[bt]
|
| 43 |
claudioc |
1.1 |
\begin{center}
|
| 44 |
claudioc |
1.3 |
\includegraphics[width=0.5\linewidth, angle=90]{abcdMC.pdf}
|
| 45 |
claudioc |
1.1 |
\caption{\label{fig:abcdMC}\protect Distributions of SumJetPt
|
| 46 |
|
|
vs. MET$/\sqrt{\rm SumJetPt}$ for SM Monte Carlo. Here we also
|
| 47 |
dbarge |
1.5 |
show our choice of ABCD regions.}
|
| 48 |
claudioc |
1.1 |
\end{center}
|
| 49 |
|
|
\end{figure}
|
| 50 |
|
|
|
| 51 |
|
|
|
| 52 |
|
|
Our choice of ABCD regions is shown in Figure~\ref{fig:abcdMC}.
|
| 53 |
|
|
The signal region is region D. The expected number of events
|
| 54 |
|
|
in the four regions for the SM Monte Carlo, as well as the BG
|
| 55 |
claudioc |
1.2 |
prediction AC/B are given in Table~\ref{tab:abcdMC} for an integrated
|
| 56 |
benhoob |
1.12 |
luminosity of 35 pb$^{-1}$. The ABCD method is accurate
|
| 57 |
|
|
to about 20\%.
|
| 58 |
claudioc |
1.9 |
%{\color{red} Avi wants some statement about stability
|
| 59 |
|
|
%wrt changes in regions. I am not sure that we have done it and
|
| 60 |
|
|
%I am not sure it is necessary (Claudio).}
|
| 61 |
claudioc |
1.1 |
|
| 62 |
|
|
\begin{table}[htb]
|
| 63 |
|
|
\begin{center}
|
| 64 |
|
|
\caption{\label{tab:abcdMC} Expected SM Monte Carlo yields for
|
| 65 |
benhoob |
1.13 |
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
|
| 71 |
|
|
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 |
claudioc |
1.1 |
\hline
|
| 79 |
|
|
\end{tabular}
|
| 80 |
|
|
\end{center}
|
| 81 |
|
|
\end{table}
|
| 82 |
|
|
|
| 83 |
claudioc |
1.2 |
\subsection{Dilepton $P_T$ method}
|
| 84 |
|
|
\label{sec:victory}
|
| 85 |
|
|
This method is based on a suggestion by V. Pavlunin\cite{ref:victory},
|
| 86 |
|
|
and was investigated by our group in 2009\cite{ref:ourvictory}.
|
| 87 |
|
|
The idea is that in dilepton $t\bar{t}$ events the lepton and neutrinos
|
| 88 |
|
|
from $W$ decays have the same $P_T$ spectrum (modulo $W$ polarization
|
| 89 |
|
|
effects). One can then use the observed
|
| 90 |
|
|
$P_T(\ell\ell)$ distribution to model the sum of neutrino $P_T$'s which
|
| 91 |
|
|
is identified with the \met.
|
| 92 |
|
|
|
| 93 |
|
|
Then, in order to predict the $t\bar{t} \to$ dilepton contribution to a
|
| 94 |
|
|
selection with \met$+$X, one applies a cut on $P_T(\ell\ell)+$X instead.
|
| 95 |
|
|
In practice one has to rescale the result of the $P_T(\ell\ell)+$X selection
|
| 96 |
|
|
to account for the fact that any dilepton selection must include a
|
| 97 |
|
|
moderate \met cut in order to reduce Drell Yan backgrounds. This
|
| 98 |
|
|
is discussed in Section 5.3 of Reference~\cite{ref:ourvictory}; for a \met
|
| 99 |
|
|
cut of 50 GeV, the rescaling factor is obtained from the data as
|
| 100 |
|
|
|
| 101 |
|
|
\newcommand{\ptll} {\ensuremath{P_T(\ell\ell)}}
|
| 102 |
|
|
\begin{center}
|
| 103 |
|
|
$ K = \frac{\int_0^{\infty} {\cal N}(\ptll)~~d\ptll~}{\int_{50}^{\infty} {\cal N}(\ptll)~~d\ptll~}$
|
| 104 |
|
|
\end{center}
|
| 105 |
|
|
|
| 106 |
|
|
|
| 107 |
|
|
Monte Carlo studies give values of $K$ that are typically between 1.5 and 1.6,
|
| 108 |
benhoob |
1.10 |
depending on selection details.
|
| 109 |
|
|
%%%TO BE REPLACED
|
| 110 |
|
|
%Given the integrated luminosity of the
|
| 111 |
|
|
%present dataset, the determination of $K$ in data is severely statistics
|
| 112 |
|
|
%limited. Thus, we take $K$ from $t\bar{t}$ Monte Carlo as
|
| 113 |
|
|
|
| 114 |
|
|
%\begin{center}
|
| 115 |
|
|
%$ K_{MC} = \frac{\int_0^{\infty} {\cal N}(\met)~~d\met~}{\int_{50}^{\infty} {\cal N}(\met)~~d\met~}$
|
| 116 |
|
|
%\end{center}
|
| 117 |
claudioc |
1.9 |
|
| 118 |
benhoob |
1.10 |
%\noindent {\color{red} For the 11 pb result we have used $K$ from data.}
|
| 119 |
claudioc |
1.2 |
|
| 120 |
|
|
There are several effects that spoil the correspondance between \met and
|
| 121 |
|
|
$P_T(\ell\ell)$:
|
| 122 |
|
|
\begin{itemize}
|
| 123 |
|
|
\item $Ws$ in top events are polarized. Neutrinos are emitted preferentially
|
| 124 |
|
|
forward in the $W$ rest frame, thus the $P_T(\nu\nu)$ distribution is harder
|
| 125 |
|
|
than the $P_T(\ell\ell)$ distribution for top dilepton events.
|
| 126 |
|
|
\item The lepton selections results in $P_T$ and $\eta$ cuts on the individual
|
| 127 |
|
|
leptons that have no simple correspondance to the neutrino requirements.
|
| 128 |
|
|
\item Similarly, the \met$>$50 GeV cut introduces an asymmetry between leptons and
|
| 129 |
|
|
neutrinos which is only partially compensated by the $K$ factor above.
|
| 130 |
|
|
\item The \met resolution is much worse than the dilepton $P_T$ resolution.
|
| 131 |
|
|
When convoluted with a falling spectrum in the tails of \met, this result
|
| 132 |
|
|
in a harder spectrum for \met than the original $P_T(\nu\nu)$.
|
| 133 |
|
|
\item The \met response in CMS is not exactly 1. This causes a distortion
|
| 134 |
|
|
in the \met distribution that is not present in the $P_T(\ell\ell)$ distribution.
|
| 135 |
|
|
\item The $t\bar{t} \to$ dilepton signal includes contributions from
|
| 136 |
|
|
$W \to \tau \to \ell$. For these events the arguments about the equivalence
|
| 137 |
|
|
of $P_T(\ell\ell)$ and $P_T(\nu\nu)$ do not apply.
|
| 138 |
|
|
\item A dilepton selection will include SM events from non $t\bar{t}$
|
| 139 |
|
|
sources. These events can affect the background prediction. Particularly
|
| 140 |
|
|
dangerous are high $P_T$ Drell Yan events that barely pass the \met$>$ 50
|
| 141 |
|
|
GeV selection. They will tend to push the data-driven background prediction up.
|
| 142 |
|
|
\end{itemize}
|
| 143 |
|
|
|
| 144 |
|
|
We have studied these effects in SM Monte Carlo, using a mixture of generator and
|
| 145 |
|
|
reconstruction level studies, putting the various effects in one at a time.
|
| 146 |
|
|
For each configuration, we apply the data-driven method and report as figure
|
| 147 |
|
|
of merit the ratio of observed and predicted events in the signal region.
|
| 148 |
|
|
The results are summarized in Table~\ref{tab:victorybad}.
|
| 149 |
|
|
|
| 150 |
|
|
\begin{table}[htb]
|
| 151 |
|
|
\begin{center}
|
| 152 |
|
|
\caption{\label{tab:victorybad} Test of the data driven method in Monte Carlo
|
| 153 |
|
|
under different assumptions. See text for details.}
|
| 154 |
claudioc |
1.6 |
\begin{tabular}{|l|c|c|c|c|c|c|c|c|}
|
| 155 |
claudioc |
1.2 |
\hline
|
| 156 |
claudioc |
1.6 |
& 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 |
claudioc |
1.2 |
\hline
|
| 166 |
|
|
\end{tabular}
|
| 167 |
|
|
\end{center}
|
| 168 |
|
|
\end{table}
|
| 169 |
|
|
|
| 170 |
|
|
|
| 171 |
|
|
The largest discrepancy between prediction and observation occurs on the first
|
| 172 |
|
|
line of Table~\ref{tab:victorybad}, {\em i.e.}, at the generator level with no
|
| 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 |
claudioc |
1.6 |
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 |
claudioc |
1.2 |
events can have a significant impact on the BG prediction. The changes between
|
| 183 |
claudioc |
1.6 |
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 |
claudioc |
1.2 |
|
| 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 |
claudioc |
1.7 |
that the bias is at the few percent level.
|
| 191 |
claudioc |
1.2 |
|
| 192 |
benhoob |
1.10 |
%%%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 |
claudioc |
1.2 |
Based on the results of Table~\ref{tab:victorybad}, we conclude that the
|
| 204 |
claudioc |
1.6 |
naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to
|
| 205 |
benhoob |
1.11 |
be corrected by a factor of $ K_C = X \pm Y$.
|
| 206 |
benhoob |
1.10 |
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 |
benhoob |
1.11 |
$K_C = 1$ for simplicity. Based on previous MC studies we foresee a correction
|
| 209 |
benhoob |
1.14 |
factor of $K_C \approx 1.2 - 1.5$, and we will assess an uncertainty
|
| 210 |
benhoob |
1.10 |
based on the stability of the Monte Carlo tests under
|
| 211 |
claudioc |
1.2 |
variations of event selections, choices of \met algorithm, etc.
|
| 212 |
claudioc |
1.8 |
For example, we find that observed/predicted changes by roughly 0.1
|
| 213 |
benhoob |
1.10 |
for each 1.5\% change in the average \met response.
|
| 214 |
claudioc |
1.2 |
|
| 215 |
|
|
|
| 216 |
claudioc |
1.6 |
|
| 217 |
claudioc |
1.2 |
\subsection{Signal Contamination}
|
| 218 |
|
|
\label{sec:sigcont}
|
| 219 |
|
|
|
| 220 |
claudioc |
1.6 |
All data-driven methods are in principle subject to signal contaminations
|
| 221 |
claudioc |
1.2 |
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
|
| 224 |
|
|
present in the data by inflating the background prediction.
|
| 225 |
|
|
|
| 226 |
|
|
It is hard to quantify how important these effects are because we
|
| 227 |
|
|
do not know what signal may be hiding in the data. Having two
|
| 228 |
|
|
independent methods (in addition to Monte Carlo ``dead-reckoning'')
|
| 229 |
|
|
adds redundancy because signal contamination can have different effects
|
| 230 |
|
|
in the different control regions for the two methods.
|
| 231 |
|
|
For example, in the extreme case of a
|
| 232 |
|
|
new physics signal
|
| 233 |
claudioc |
1.6 |
with $P_T(\ell \ell) = \met$, an excess of events would be seen
|
| 234 |
claudioc |
1.2 |
in the ABCD method but not in the $P_T(\ell \ell)$ method.
|
| 235 |
|
|
|
| 236 |
claudioc |
1.4 |
|
| 237 |
claudioc |
1.2 |
The LM points are benchmarks for SUSY analyses at CMS. The effects
|
| 238 |
|
|
of signal contaminations for a couple such points are summarized
|
| 239 |
benhoob |
1.14 |
in Table~\ref{tab:sigcont}. Signal contamination is definitely an important
|
| 240 |
claudioc |
1.2 |
effect for these two LM points, but it does not totally hide the
|
| 241 |
|
|
presence of the signal.
|
| 242 |
claudioc |
1.1 |
|
| 243 |
|
|
|
| 244 |
claudioc |
1.2 |
\begin{table}[htb]
|
| 245 |
|
|
\begin{center}
|
| 246 |
benhoob |
1.14 |
\caption{\label{tab:sigcont} Effects of signal contamination
|
| 247 |
|
|
for the two data-driven background estimates. The three columns give
|
| 248 |
|
|
the expected yield in the signal region and the background estimates
|
| 249 |
|
|
using the ABCD and $P_T(\ell \ell)$ methods. Results are normalized to 35~pb$^{-1}$.}
|
| 250 |
|
|
\begin{tabular}{lccc}
|
| 251 |
claudioc |
1.2 |
\hline
|
| 252 |
benhoob |
1.14 |
& Yield & ABCD & $P_T(\ell \ell)$ \\
|
| 253 |
|
|
\hline
|
| 254 |
|
|
SM only & 1.41 & 1.19 & 0.96 \\
|
| 255 |
|
|
SM + LM0 & 7.88 & 4.24 & 2.28 \\
|
| 256 |
|
|
SM + LM1 & 3.98 & 1.53 & 1.44 \\
|
| 257 |
claudioc |
1.2 |
\hline
|
| 258 |
|
|
\end{tabular}
|
| 259 |
|
|
\end{center}
|
| 260 |
|
|
\end{table}
|
| 261 |
|
|
|
| 262 |
benhoob |
1.14 |
|
| 263 |
|
|
|
| 264 |
|
|
%\begin{table}[htb]
|
| 265 |
|
|
%\begin{center}
|
| 266 |
|
|
%\caption{\label{tab:sigcontABCD} Effects of signal contamination
|
| 267 |
|
|
%for the background predictions of the ABCD method including LM0 or
|
| 268 |
|
|
%LM1. Results
|
| 269 |
|
|
%are normalized to 30 pb$^{-1}$.}
|
| 270 |
|
|
%\begin{tabular}{|c|c||c|c||c|c|}
|
| 271 |
|
|
%\hline
|
| 272 |
|
|
%SM & BG Prediction & SM$+$LM0 & BG Prediction & SM$+$LM1 & BG Prediction \\
|
| 273 |
|
|
%Background & SM Only & Contribution & Including LM0 & Contribution & Including LM1 \\ \hline
|
| 274 |
|
|
%1.2 & 1.0 & 6.8 & 3.7 & 3.4 & 1.3 \\
|
| 275 |
|
|
%\hline
|
| 276 |
|
|
%\end{tabular}
|
| 277 |
|
|
%\end{center}
|
| 278 |
|
|
%\end{table}
|
| 279 |
|
|
|
| 280 |
|
|
%\begin{table}[htb]
|
| 281 |
|
|
%\begin{center}
|
| 282 |
|
|
%\caption{\label{tab:sigcontPT} Effects of signal contamination
|
| 283 |
|
|
%for the background predictions of the $P_T(\ell\ell)$ method including LM0 or
|
| 284 |
|
|
%LM1. Results
|
| 285 |
|
|
%are normalized to 30 pb$^{-1}$.}
|
| 286 |
|
|
%\begin{tabular}{|c|c||c|c||c|c|}
|
| 287 |
|
|
%\hline
|
| 288 |
|
|
%SM & BG Prediction & SM$+$LM0 & BG Prediction & SM$+$LM1 & BG Prediction \\
|
| 289 |
|
|
%Background & SM Only & Contribution & Including LM0 & Contribution & Including LM1 \\ \hline
|
| 290 |
|
|
%1.2 & 1.0 & 6.8 & 2.2 & 3.4 & 1.5 \\
|
| 291 |
|
|
%\hline
|
| 292 |
|
|
%\end{tabular}
|
| 293 |
|
|
%\end{center}
|
| 294 |
|
|
%\end{table}
|
| 295 |
claudioc |
1.1 |
|
