| 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 |
| 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. |
| 17 |
> |
and LM1 SUSY benchmark points are 15.1 and |
| 18 |
> |
6.0 events respectively. {\color{red} I took these |
| 19 |
> |
numbers from the twiki, rescaling from 11.06 to 30/pb. |
| 20 |
> |
They seem too large...are they really right?} |
| 21 |
|
|
| 22 |
|
|
| 23 |
|
\subsection{ABCD method} |
| 29 |
|
Thus, we can use an ABCD method in the \met$/\sqrt{\rm SumJetPt}$ vs |
| 30 |
|
sumJetPt plane to estimate the background in a data driven way. |
| 31 |
|
|
| 32 |
< |
\begin{figure}[htb] |
| 32 |
> |
\begin{figure}[tb] |
| 33 |
|
\begin{center} |
| 34 |
|
\includegraphics[width=0.75\linewidth]{uncorrelated.pdf} |
| 35 |
|
\caption{\label{fig:uncor}\protect Distributions of SumJetPt |
| 38 |
|
\end{center} |
| 39 |
|
\end{figure} |
| 40 |
|
|
| 41 |
< |
\begin{figure}[htb] |
| 41 |
> |
\begin{figure}[bt] |
| 42 |
|
\begin{center} |
| 43 |
< |
\includegraphics[width=0.75\linewidth]{abcdMC.jpg} |
| 43 |
> |
\includegraphics[width=0.5\linewidth, angle=90]{abcdMC.pdf} |
| 44 |
|
\caption{\label{fig:abcdMC}\protect Distributions of SumJetPt |
| 45 |
|
vs. MET$/\sqrt{\rm SumJetPt}$ for SM Monte Carlo. Here we also |
| 46 |
< |
show our choice of ABCD regions. {\color{red} We need a better |
| 47 |
< |
picture with the letters A-B-C-D and with the numerical values |
| 46 |
< |
of the boundaries clearly indicated.}} |
| 46 |
> |
show our choice of ABCD regions. {\color{red} Derek, I |
| 47 |
> |
do not know if this is SM or $t\bar{t}$ only.}} |
| 48 |
|
\end{center} |
| 49 |
|
\end{figure} |
| 50 |
|
|
| 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 |
< |
prediction AC/B is given in Table~\ref{tab:abcdMC} for an integrated |
| 55 |
> |
prediction AC/B are given in Table~\ref{tab:abcdMC} for an integrated |
| 56 |
|
luminosity of 30 pb$^{-1}$. The ABCD method is accurate |
| 57 |
|
to about 10\%. |
| 58 |
|
|
| 63 |
|
\begin{tabular}{|l|c|c|c|c||c|} |
| 64 |
|
\hline |
| 65 |
|
Sample & A & B & C & D & AC/D \\ \hline |
| 66 |
< |
ttdil & 6.4 & 28.4 & 4.2 & 1.0 & 0.9 \\ |
| 67 |
< |
Zjets & 0.0 & 1.3 & 0.2 & 0.0 & 0.0 \\ |
| 68 |
< |
Other SM & 0.6 & 2.1 & 0.2 & 0.1 & 0.0 \\ \hline |
| 69 |
< |
total MC & 7.0 & 31.8 & 4.5 & 1.1 & 1.0 \\ \hline |
| 66 |
> |
ttdil & 6.9 & 28.6 & 4.2 & 1.0 & 1.0 \\ |
| 67 |
> |
Zjets & 0.0 & 1.3 & 0.1 & 0.1 & 0.0 \\ |
| 68 |
> |
Other SM & 0.5 & 2.0 & 0.1 & 0.1 & 0.0 \\ \hline |
| 69 |
> |
total MC & 7.4 & 31.9 & 4.4 & 1.2 & 1.0 \\ \hline |
| 70 |
|
\end{tabular} |
| 71 |
|
\end{center} |
| 72 |
|
\end{table} |
| 73 |
|
|
| 74 |
+ |
\subsection{Dilepton $P_T$ method} |
| 75 |
+ |
\label{sec:victory} |
| 76 |
+ |
This method is based on a suggestion by V. Pavlunin\cite{ref:victory}, |
| 77 |
+ |
and was investigated by our group in 2009\cite{ref:ourvictory}. |
| 78 |
+ |
The idea is that in dilepton $t\bar{t}$ events the lepton and neutrinos |
| 79 |
+ |
from $W$ decays have the same $P_T$ spectrum (modulo $W$ polarization |
| 80 |
+ |
effects). One can then use the observed |
| 81 |
+ |
$P_T(\ell\ell)$ distribution to model the sum of neutrino $P_T$'s which |
| 82 |
+ |
is identified with the \met. |
| 83 |
+ |
|
| 84 |
+ |
Then, in order to predict the $t\bar{t} \to$ dilepton contribution to a |
| 85 |
+ |
selection with \met$+$X, one applies a cut on $P_T(\ell\ell)+$X instead. |
| 86 |
+ |
In practice one has to rescale the result of the $P_T(\ell\ell)+$X selection |
| 87 |
+ |
to account for the fact that any dilepton selection must include a |
| 88 |
+ |
moderate \met cut in order to reduce Drell Yan backgrounds. This |
| 89 |
+ |
is discussed in Section 5.3 of Reference~\cite{ref:ourvictory}; for a \met |
| 90 |
+ |
cut of 50 GeV, the rescaling factor is obtained from the data as |
| 91 |
+ |
|
| 92 |
+ |
\newcommand{\ptll} {\ensuremath{P_T(\ell\ell)}} |
| 93 |
+ |
\begin{center} |
| 94 |
+ |
$ K = \frac{\int_0^{\infty} {\cal N}(\ptll)~~d\ptll~}{\int_{50}^{\infty} {\cal N}(\ptll)~~d\ptll~}$ |
| 95 |
+ |
\end{center} |
| 96 |
+ |
|
| 97 |
+ |
|
| 98 |
+ |
Monte Carlo studies give values of $K$ that are typically between 1.5 and 1.6, |
| 99 |
+ |
depending on selection details. |
| 100 |
+ |
|
| 101 |
+ |
There are several effects that spoil the correspondance between \met and |
| 102 |
+ |
$P_T(\ell\ell)$: |
| 103 |
+ |
\begin{itemize} |
| 104 |
+ |
\item $Ws$ in top events are polarized. Neutrinos are emitted preferentially |
| 105 |
+ |
forward in the $W$ rest frame, thus the $P_T(\nu\nu)$ distribution is harder |
| 106 |
+ |
than the $P_T(\ell\ell)$ distribution for top dilepton events. |
| 107 |
+ |
\item The lepton selections results in $P_T$ and $\eta$ cuts on the individual |
| 108 |
+ |
leptons that have no simple correspondance to the neutrino requirements. |
| 109 |
+ |
\item Similarly, the \met$>$50 GeV cut introduces an asymmetry between leptons and |
| 110 |
+ |
neutrinos which is only partially compensated by the $K$ factor above. |
| 111 |
+ |
\item The \met resolution is much worse than the dilepton $P_T$ resolution. |
| 112 |
+ |
When convoluted with a falling spectrum in the tails of \met, this result |
| 113 |
+ |
in a harder spectrum for \met than the original $P_T(\nu\nu)$. |
| 114 |
+ |
\item The \met response in CMS is not exactly 1. This causes a distortion |
| 115 |
+ |
in the \met distribution that is not present in the $P_T(\ell\ell)$ distribution. |
| 116 |
+ |
\item The $t\bar{t} \to$ dilepton signal includes contributions from |
| 117 |
+ |
$W \to \tau \to \ell$. For these events the arguments about the equivalence |
| 118 |
+ |
of $P_T(\ell\ell)$ and $P_T(\nu\nu)$ do not apply. |
| 119 |
+ |
\item A dilepton selection will include SM events from non $t\bar{t}$ |
| 120 |
+ |
sources. These events can affect the background prediction. Particularly |
| 121 |
+ |
dangerous are high $P_T$ Drell Yan events that barely pass the \met$>$ 50 |
| 122 |
+ |
GeV selection. They will tend to push the data-driven background prediction up. |
| 123 |
+ |
\end{itemize} |
| 124 |
+ |
|
| 125 |
+ |
We have studied these effects in SM Monte Carlo, using a mixture of generator and |
| 126 |
+ |
reconstruction level studies, putting the various effects in one at a time. |
| 127 |
+ |
For each configuration, we apply the data-driven method and report as figure |
| 128 |
+ |
of merit the ratio of observed and predicted events in the signal region. |
| 129 |
+ |
The results are summarized in Table~\ref{tab:victorybad}. |
| 130 |
+ |
|
| 131 |
+ |
\begin{table}[htb] |
| 132 |
+ |
\begin{center} |
| 133 |
+ |
\caption{\label{tab:victorybad} Test of the data driven method in Monte Carlo |
| 134 |
+ |
under different assumptions. See text for details.} |
| 135 |
+ |
\begin{tabular}{|l|c|c|c|c|c|c|c|} |
| 136 |
+ |
\hline |
| 137 |
+ |
& True $t\bar{t}$ dilepton & $t\to W\to\tau$& other SM & GEN or & Lepton $P_T$ & \met $>$ 50& obs/pred \\ |
| 138 |
+ |
& included & included & included & RECOSIM & and $\eta$ cuts & & \\ \hline |
| 139 |
+ |
1&Y & N & N & GEN & N & N & \\ |
| 140 |
+ |
2&Y & N & N & GEN & Y & N & \\ |
| 141 |
+ |
3&Y & N & N & GEN & Y & Y & \\ |
| 142 |
+ |
4&Y & N & N & RECOSIM & Y & Y & \\ |
| 143 |
+ |
5&Y & Y & N & RECOSIM & Y & Y & \\ |
| 144 |
+ |
6&Y & Y & Y & RECOSIM & Y & Y & \\ |
| 145 |
+ |
\hline |
| 146 |
+ |
\end{tabular} |
| 147 |
+ |
\end{center} |
| 148 |
+ |
\end{table} |
| 149 |
+ |
|
| 150 |
+ |
|
| 151 |
+ |
The largest discrepancy between prediction and observation occurs on the first |
| 152 |
+ |
line of Table~\ref{tab:victorybad}, {\em i.e.}, at the generator level with no |
| 153 |
+ |
cuts. We have verified that this effect is due to the polarization of |
| 154 |
+ |
the $W$ (we remove the polarization by reweighting the events and we get |
| 155 |
+ |
good agreement between prediction and observation). The kinematical |
| 156 |
+ |
requirements (lines 2 and 3) do not have a significant additional effect. |
| 157 |
+ |
Going from GEN to RECOSIM there is a significant change in observed/predicted. |
| 158 |
+ |
We have tracked this down to the fact that tcMET underestimates the true \met |
| 159 |
+ |
by $\approx 4\%$\footnote{We find that observed/predicted changes by roughly 0.1 |
| 160 |
+ |
for each 1.5\% change in \met response.}. Finally, contamination from non $t\bar{t}$ |
| 161 |
+ |
events can have a significant impact on the BG prediction. The changes between |
| 162 |
+ |
lines 5 and 6 of Table~\ref{tab:victorybad} is driven by only {\color{red} 3} |
| 163 |
+ |
Drell Yan events that pass the \met selection. |
| 164 |
+ |
|
| 165 |
+ |
An additional source of concern is that the CMS Madgraph $t\bar{t}$ MC does |
| 166 |
+ |
not include effects of spin correlations between the two top quarks. |
| 167 |
+ |
We have studied this effect at the generator level using Alpgen. We find |
| 168 |
+ |
that the bias is a the few percent level. |
| 169 |
+ |
|
| 170 |
+ |
Based on the results of Table~\ref{tab:victorybad}, we conclude that the |
| 171 |
+ |
naive data driven background estimate based on $P_T{\ell\ell)}$ needs to |
| 172 |
+ |
be corrected by a factor of {\color{red} $1.4 \pm 0.3$ (We need to |
| 173 |
+ |
decide what this number should be)}. The quoted |
| 174 |
+ |
uncertainty is based on the stability of the Monte Carlo tests under |
| 175 |
+ |
variations of event selections, choices of \met algorithm, etc. |
| 176 |
+ |
|
| 177 |
+ |
|
| 178 |
+ |
\subsection{Signal Contamination} |
| 179 |
+ |
\label{sec:sigcont} |
| 180 |
+ |
|
| 181 |
+ |
All data-driven methods are principle subject to signal contaminations |
| 182 |
+ |
in the control regions, and the methods described in |
| 183 |
+ |
Sections~\ref{sec:abcd} and~\ref{sec:victory} are not exceptions. |
| 184 |
+ |
Signal contamination tends to dilute the significance of a signal |
| 185 |
+ |
present in the data by inflating the background prediction. |
| 186 |
+ |
|
| 187 |
+ |
It is hard to quantify how important these effects are because we |
| 188 |
+ |
do not know what signal may be hiding in the data. Having two |
| 189 |
+ |
independent methods (in addition to Monte Carlo ``dead-reckoning'') |
| 190 |
+ |
adds redundancy because signal contamination can have different effects |
| 191 |
+ |
in the different control regions for the two methods. |
| 192 |
+ |
For example, in the extreme case of a |
| 193 |
+ |
new physics signal |
| 194 |
+ |
with $P_T(\ell \ell) = \met$, an excess of ev ents would be seen |
| 195 |
+ |
in the ABCD method but not in the $P_T(\ell \ell)$ method. |
| 196 |
+ |
|
| 197 |
+ |
The LM points are benchmarks for SUSY analyses at CMS. The effects |
| 198 |
+ |
of signal contaminations for a couple such points are summarized |
| 199 |
+ |
in Table~\ref{tab:sigcontABCD} and~\ref{tab:sigcontPT}. |
| 200 |
+ |
Signal contamination is definitely an important |
| 201 |
+ |
effect for these two LM points, but it does not totally hide the |
| 202 |
+ |
presence of the signal. |
| 203 |
|
|
| 204 |
|
|
| 205 |
+ |
\begin{table}[htb] |
| 206 |
+ |
\begin{center} |
| 207 |
+ |
\caption{\label{tab:sigcontABCD} Effects of signal contamination |
| 208 |
+ |
for the background predictions of the ABCD method including LM0 or |
| 209 |
+ |
LM1. Results |
| 210 |
+ |
are normalized to 30 pb$^{-1}$.} |
| 211 |
+ |
\begin{tabular}{|c||c|c||c|c|} |
| 212 |
+ |
\hline |
| 213 |
+ |
SM & LM0 & BG Prediction & LM1 & BG Prediction \\ |
| 214 |
+ |
Background & Contribution& Including LM0 & Contribution & Including LM1 \\ \hline |
| 215 |
+ |
x & x & x & x & x \\ |
| 216 |
+ |
\hline |
| 217 |
+ |
\end{tabular} |
| 218 |
+ |
\end{center} |
| 219 |
+ |
\end{table} |
| 220 |
+ |
|
| 221 |
+ |
\begin{table}[htb] |
| 222 |
+ |
\begin{center} |
| 223 |
+ |
\caption{\label{tab:sigcontPT} Effects of signal contamination |
| 224 |
+ |
for the background predictions of the $P_T(\ell\ell)$ method including LM0 or |
| 225 |
+ |
LM1. Results |
| 226 |
+ |
are normalized to 30 pb$^{-1}$.} |
| 227 |
+ |
\begin{tabular}{|c||c|c||c|c|} |
| 228 |
+ |
\hline |
| 229 |
+ |
SM & LM0 & BG Prediction & LM1 & BG Prediction \\ |
| 230 |
+ |
Background & Contribution& Including LM0 & Contribution & Including LM1 \\ \hline |
| 231 |
+ |
x & x & x & x & x \\ |
| 232 |
+ |
\hline |
| 233 |
+ |
\end{tabular} |
| 234 |
+ |
\end{center} |
| 235 |
+ |
\end{table} |
| 236 |
|
|
