| 3 |
|
We have developed two data-driven methods to |
| 4 |
|
estimate the background in the signal region. |
| 5 |
|
The first one exploits the fact that |
| 6 |
< |
\met and \met$/\sqrt{\rm SumJetPt}$ are nearly |
| 6 |
> |
SumJetPt 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 |
| 21 |
|
\subsection{ABCD method} |
| 22 |
|
\label{sec:abcd} |
| 23 |
|
|
| 24 |
< |
We find that in $t\bar{t}$ events \met and |
| 24 |
> |
We find that in $t\bar{t}$ events SumJetPt and |
| 25 |
|
\met$/\sqrt{\rm SumJetPt}$ are nearly uncorrelated, |
| 26 |
|
as demonstrated in Figure~\ref{fig:uncor}. |
| 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}[tb] |
| 30 |
> |
%\begin{figure}[bht] |
| 31 |
> |
%\begin{center} |
| 32 |
> |
%\includegraphics[width=0.75\linewidth]{uncorrelated.pdf} |
| 33 |
> |
%\caption{\label{fig:uncor}\protect Distributions of SumJetPt |
| 34 |
> |
%in MC $t\bar{t}$ events for different intervals of |
| 35 |
> |
%MET$/\sqrt{\rm SumJetPt}$.} |
| 36 |
> |
%\end{center} |
| 37 |
> |
%\end{figure} |
| 38 |
> |
|
| 39 |
> |
\begin{figure}[bht] |
| 40 |
|
\begin{center} |
| 41 |
< |
\includegraphics[width=0.75\linewidth]{uncorrelated.pdf} |
| 41 |
> |
\includegraphics[width=0.75\linewidth]{uncor.png} |
| 42 |
|
\caption{\label{fig:uncor}\protect Distributions of SumJetPt |
| 43 |
|
in MC $t\bar{t}$ events for different intervals of |
| 44 |
< |
MET$/\sqrt{\rm SumJetPt}$.} |
| 44 |
> |
MET$/\sqrt{\rm SumJetPt}$. h1, h2, and h3 refer to the MET$/\sqrt{\rm SumJetPt}$ |
| 45 |
> |
intervals 4.5-6.5, 6.5-8.5 and $>$8.5, respectively.} |
| 46 |
|
\end{center} |
| 47 |
|
\end{figure} |
| 48 |
|
|
| 49 |
< |
\begin{figure}[bt] |
| 49 |
> |
\begin{figure}[tb] |
| 50 |
|
\begin{center} |
| 51 |
|
\includegraphics[width=0.5\linewidth, angle=90]{abcdMC.pdf} |
| 52 |
< |
\caption{\label{fig:abcdMC}\protect Distributions of SumJetPt |
| 53 |
< |
vs. MET$/\sqrt{\rm SumJetPt}$ for SM Monte Carlo. Here we also |
| 44 |
< |
show our choice of ABCD regions.} |
| 52 |
> |
\caption{\label{fig:abcdMC}\protect Distributions of MET$/\sqrt{\rm SumJetPt}$ vs. |
| 53 |
> |
SumJetPt for SM Monte Carlo. Here we also show our choice of ABCD regions.} |
| 54 |
|
\end{center} |
| 55 |
|
\end{figure} |
| 56 |
|
|
| 57 |
|
|
| 58 |
|
Our choice of ABCD regions is shown in Figure~\ref{fig:abcdMC}. |
| 59 |
|
The signal region is region D. The expected number of events |
| 60 |
< |
in the four regions for the SM Monte Carlo, as well as the BG |
| 61 |
< |
prediction AC/B are given in Table~\ref{tab:abcdMC} for an integrated |
| 62 |
< |
luminosity of 35 pb$^{-1}$. The ABCD method is accurate |
| 63 |
< |
to about 20\%. |
| 60 |
> |
in the four regions for the SM Monte Carlo, as well as the background |
| 61 |
> |
prediction A $\times$ C / B are given in Table~\ref{tab:abcdMC} for an integrated |
| 62 |
> |
luminosity of 35 pb$^{-1}$. The ABCD method with chosen boundaries is accurate |
| 63 |
> |
to about 20\%, and we assess a corresponding systematic uncertainty. |
| 64 |
> |
|
| 65 |
> |
%As shown in Table~\ref{tab:abcdsyst}, we assess systematic uncertainties |
| 66 |
> |
%by varying the boundaries by an amount consistent with the hadronic energy scale uncertainty, |
| 67 |
> |
%which we take as $\pm$5\% for SumJetPt and $\pm$2.5\% for MET/$\sqrt{\rm SumJetPt}$, since the |
| 68 |
> |
%uncertainty on this quantity partially cancels due to the fact that it is a ratio of correlated |
| 69 |
> |
%quantities. Based on these studies we assess a correction factor $k_{ABCD} = 1.2 \pm 0.2$ to the |
| 70 |
> |
%predicted yield using the ABCD method. |
| 71 |
> |
|
| 72 |
> |
|
| 73 |
|
%{\color{red} Avi wants some statement about stability |
| 74 |
|
%wrt changes in regions. I am not sure that we have done it and |
| 75 |
|
%I am not sure it is necessary (Claudio).} |
| 76 |
|
|
| 77 |
< |
\begin{table}[htb] |
| 77 |
> |
\begin{table}[ht] |
| 78 |
|
\begin{center} |
| 79 |
|
\caption{\label{tab:abcdMC} Expected SM Monte Carlo yields for |
| 80 |
|
35 pb$^{-1}$ in the ABCD regions, as well as the predicted yield in |
| 83 |
|
$W^{\pm}Z^0$, $Z^0Z^0$ and single top.} |
| 84 |
|
\begin{tabular}{lccccc} |
| 85 |
|
\hline |
| 86 |
< |
sample & A & B & C & D & A $\times$ C / B \\ |
| 86 |
> |
sample & A & B & C & D & A $\times$ C / B \\ |
| 87 |
> |
\hline |
| 88 |
> |
$t\bar{t}\rightarrow \ell^{+}\ell^{-}$ & 8.27 $\pm$ 0.18 & 32.16 $\pm$ 0.35 & 4.69 $\pm$ 0.13 & 1.05 $\pm$ 0.06 & 1.21 $\pm$ 0.04 \\ |
| 89 |
> |
$Z^0 \rightarrow \ell^{+}\ell^{-}$ & 0.22 $\pm$ 0.11 & 1.54 $\pm$ 0.29 & 0.05 $\pm$ 0.05 & 0.16 $\pm$ 0.09 & 0.01 $\pm$ 0.01 \\ |
| 90 |
> |
SM other & 0.54 $\pm$ 0.03 & 2.28 $\pm$ 0.12 & 0.23 $\pm$ 0.03 & 0.07 $\pm$ 0.01 & 0.05 $\pm$ 0.01 \\ |
| 91 |
|
\hline |
| 92 |
+ |
total SM MC & 9.03 $\pm$ 0.21 & 35.97 $\pm$ 0.46 & 4.97 $\pm$ 0.15 & 1.29 $\pm$ 0.11 & 1.25 $\pm$ 0.05 \\ |
| 93 |
+ |
\hline |
| 94 |
+ |
\end{tabular} |
| 95 |
+ |
\end{center} |
| 96 |
+ |
\end{table} |
| 97 |
+ |
|
| 98 |
|
|
| 99 |
|
|
| 100 |
+ |
\begin{table}[ht] |
| 101 |
+ |
\begin{center} |
| 102 |
+ |
\caption{\label{tab:abcdsyst} |
| 103 |
+ |
{\bf \color{red} Do we need this study at all? Observed/predicted is consistent within stat uncertainties as the boundaries are varied- is it enough to simply state this fact in the text??? } |
| 104 |
+ |
Results of the systematic study of the ABCD method by varying the boundaries |
| 105 |
+ |
between the ABCD regions shown in Fig.~\ref{fig:abcdMC}. Here $x_1$ is the lower SumJetPt boundary and |
| 106 |
+ |
$x_2$ is the boundary separating regions A and B from C and D, their nominal values are 125 and 300~GeV, |
| 107 |
+ |
respectively. $y_1$ is the lower MET/$\sqrt{\rm SumJetPt}$ boundary and |
| 108 |
+ |
$y_2$ is the boundary separating regions B and C from A and D, their nominal values are 4.5 and 8.5~GeV$^{1/2}$, |
| 109 |
+ |
respectively.} |
| 110 |
+ |
\begin{tabular}{cccc|c} |
| 111 |
|
\hline |
| 112 |
< |
$t\bar{t}\rightarrow \ell^{+}\ell^{-}$ & 7.96 & 33.07 & 4.81 & 1.20 & 1.16 \\ |
| 74 |
< |
$Z^0 \rightarrow \ell^{+}\ell^{-}$ & 0.03 & 1.47 & 0.10 & 0.10 & 0.00 \\ |
| 75 |
< |
SM other & 0.65 & 2.31 & 0.17 & 0.14 & 0.05 \\ |
| 112 |
> |
$x_1$ & $x_2$ & $y_1$ & $y_2$ & Observed/Predicted \\ |
| 113 |
|
\hline |
| 114 |
< |
total SM MC & 8.63 & 36.85 & 5.07 & 1.43 & 1.19 \\ |
| 114 |
> |
nominal & nominal & nominal & nominal & $1.20 \pm 0.12$ \\ |
| 115 |
> |
+5\% & +5\% & +2.5\% & +2.5\% & $1.38 \pm 0.15$ \\ |
| 116 |
> |
+5\% & +5\% & nominal & nominal & $1.31 \pm 0.14$ \\ |
| 117 |
> |
nominal & nominal & +2.5\% & +2.5\% & $1.25 \pm 0.13$ \\ |
| 118 |
> |
nominal & +5\% & nominal & +2.5\% & $1.32 \pm 0.14$ \\ |
| 119 |
> |
nominal & -5\% & nominal & -2.5\% & $1.16 \pm 0.09$ \\ |
| 120 |
> |
-5\% & -5\% & +2.5\% & +2.5\% & $1.21 \pm 0.11$ \\ |
| 121 |
> |
+5\% & +5\% & -2.5\% & -2.5\% & $1.26 \pm 0.12$ \\ |
| 122 |
|
\hline |
| 123 |
|
\end{tabular} |
| 124 |
|
\end{center} |
| 165 |
|
$P_T(\ell\ell)$: |
| 166 |
|
\begin{itemize} |
| 167 |
|
\item $Ws$ in top events are polarized. Neutrinos are emitted preferentially |
| 168 |
< |
forward in the $W$ rest frame, thus the $P_T(\nu\nu)$ distribution is harder |
| 168 |
> |
parallel to the $W$ velocity while charged leptons are emitted prefertially |
| 169 |
> |
anti-parallel. Thus the $P_T(\nu\nu)$ distribution is harder |
| 170 |
|
than the $P_T(\ell\ell)$ distribution for top dilepton events. |
| 171 |
|
\item The lepton selections results in $P_T$ and $\eta$ cuts on the individual |
| 172 |
|
leptons that have no simple correspondance to the neutrino requirements. |
| 196 |
|
|
| 197 |
|
\begin{table}[htb] |
| 198 |
|
\begin{center} |
| 199 |
< |
\caption{\label{tab:victorybad} Test of the data driven method in Monte Carlo |
| 199 |
> |
\caption{\label{tab:victorybad} |
| 200 |
> |
{\bf \color{red} Need to either update this with 38X MC or remove it } |
| 201 |
> |
Test of the data driven method in Monte Carlo |
| 202 |
|
under different assumptions. See text for details.} |
| 203 |
|
\begin{tabular}{|l|c|c|c|c|c|c|c|c|} |
| 204 |
|
\hline |
| 205 |
|
& True $t\bar{t}$ dilepton & $t\to W\to\tau$& other SM & GEN or & Lepton $P_T$ & Z veto & \met $>$ 50& obs/pred \\ |
| 206 |
< |
& included & included & included & RECOSIM & and $\eta$ cuts & & & \\ \hline |
| 206 |
> |
& included & included & included & RECOSIM & and $\eta$ cuts & & & \\ \hline |
| 207 |
|
1&Y & N & N & GEN & N & N & N & 1.90 \\ |
| 208 |
|
2&Y & N & N & GEN & Y & N & N & 1.64 \\ |
| 209 |
|
3&Y & N & N & GEN & Y & Y & N & 1.59 \\ |
| 211 |
|
5&Y & N & N & RECOSIM & Y & Y & Y & 1.51 \\ |
| 212 |
|
6&Y & Y & N & RECOSIM & Y & Y & Y & 1.58 \\ |
| 213 |
|
7&Y & Y & Y & RECOSIM & Y & Y & Y & 1.38 \\ |
| 167 |
– |
%%%NOTE: updated value 1.18 -> 1.46 since 2/3 DY events have been removed by updated analysis selections, |
| 168 |
– |
%%%dpt/pt cut and general lepton veto |
| 214 |
|
\hline |
| 215 |
|
\end{tabular} |
| 216 |
|
\end{center} |
| 217 |
|
\end{table} |
| 218 |
|
|
| 219 |
|
|
| 220 |
+ |
\begin{table}[htb] |
| 221 |
+ |
\begin{center} |
| 222 |
+ |
\caption{\label{tab:victorysyst} |
| 223 |
+ |
Summary of uncertainties in $K_C$ due to the MET scale and resolution uncertainty, and to backgrounds other than $t\bar{t} \to$~dilepton. |
| 224 |
+ |
In the first table, `up' and `down' refer to shifting the hadronic energy scale up and down by 5\%. In the second table, the quoted value |
| 225 |
+ |
refers to the amount of additional smearing of the MET, as discussed in the text. In the third table, the normalization of all backgrounds |
| 226 |
+ |
other than $t\bar{t} \to$~dilepton is varied. |
| 227 |
+ |
{\bf \color{red} Should I remove `observed' and `predicted' and show only the ratio? }} |
| 228 |
+ |
|
| 229 |
+ |
\begin{tabular}{ lcccc } |
| 230 |
+ |
\hline |
| 231 |
+ |
MET scale & Predicted & Observed & Obs/pred \\ |
| 232 |
+ |
\hline |
| 233 |
+ |
nominal & 0.92 $ \pm $ 0.11 & 1.29 $ \pm $ 0.11 & 1.40 $ \pm $ 0.20 \\ |
| 234 |
+ |
up & 0.92 $ \pm $ 0.11 & 1.53 $ \pm $ 0.12 & 1.66 $ \pm $ 0.23 \\ |
| 235 |
+ |
down & 0.81 $ \pm $ 0.07 & 1.08 $ \pm $ 0.11 & 1.32 $ \pm $ 0.17 \\ |
| 236 |
+ |
\hline |
| 237 |
+ |
|
| 238 |
+ |
\hline |
| 239 |
+ |
MET smearing & Predicted & Observed & Obs/pred \\ |
| 240 |
+ |
\hline |
| 241 |
+ |
nominal & 0.92 $ \pm $ 0.11 & 1.29 $ \pm $ 0.11 & 1.40 $ \pm $ 0.20 \\ |
| 242 |
+ |
10\% & 0.90 $ \pm $ 0.11 & 1.30 $ \pm $ 0.11 & 1.44 $ \pm $ 0.21 \\ |
| 243 |
+ |
20\% & 0.84 $ \pm $ 0.07 & 1.36 $ \pm $ 0.11 & 1.61 $ \pm $ 0.19 \\ |
| 244 |
+ |
30\% & 1.05 $ \pm $ 0.18 & 1.32 $ \pm $ 0.11 & 1.27 $ \pm $ 0.24 \\ |
| 245 |
+ |
40\% & 0.85 $ \pm $ 0.07 & 1.37 $ \pm $ 0.11 & 1.61 $ \pm $ 0.19 \\ |
| 246 |
+ |
50\% & 1.08 $ \pm $ 0.18 & 1.36 $ \pm $ 0.11 & 1.26 $ \pm $ 0.24 \\ |
| 247 |
+ |
\hline |
| 248 |
+ |
|
| 249 |
+ |
\hline |
| 250 |
+ |
non-$t\bar{t} \to$~dilepton scale factor & Predicted & Observed & Obs/pred \\ |
| 251 |
+ |
\hline |
| 252 |
+ |
ttdil only & 0.77 $ \pm $ 0.07 & 1.05 $ \pm $ 0.06 & 1.36 $ \pm $ 0.14 \\ |
| 253 |
+ |
nominal & 0.92 $ \pm $ 0.11 & 1.29 $ \pm $ 0.11 & 1.40 $ \pm $ 0.20 \\ |
| 254 |
+ |
double non-ttdil yield & 1.06 $ \pm $ 0.18 & 1.52 $ \pm $ 0.20 & 1.43 $ \pm $ 0.30 \\ |
| 255 |
+ |
\hline |
| 256 |
+ |
\end{tabular} |
| 257 |
+ |
\end{center} |
| 258 |
+ |
\end{table} |
| 259 |
+ |
|
| 260 |
+ |
|
| 261 |
+ |
|
| 262 |
|
The largest discrepancy between prediction and observation occurs on the first |
| 263 |
|
line of Table~\ref{tab:victorybad}, {\em i.e.}, at the generator level with no |
| 264 |
|
cuts. We have verified that this effect is due to the polarization of |
| 281 |
|
We have studied this effect at the generator level using Alpgen. We find |
| 282 |
|
that the bias is at the few percent level. |
| 283 |
|
|
| 197 |
– |
%%%TO BE REPLACED |
| 198 |
– |
%Based on the results of Table~\ref{tab:victorybad}, we conclude that the |
| 199 |
– |
%naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to |
| 200 |
– |
%be corrected by a factor of {\color{red} $ K_{\rm{fudge}} =1.2 \pm 0.3$ |
| 201 |
– |
%(We still need to settle on thie exact value of this. |
| 202 |
– |
%For the 11 pb analysis it is taken as =1.)} . The quoted |
| 203 |
– |
%uncertainty is based on the stability of the Monte Carlo tests under |
| 204 |
– |
%variations of event selections, choices of \met algorithm, etc. |
| 205 |
– |
%For example, we find that observed/predicted changes by roughly 0.1 |
| 206 |
– |
%for each 1.5\% change in the average \met response. |
| 207 |
– |
|
| 284 |
|
Based on the results of Table~\ref{tab:victorybad}, we conclude that the |
| 285 |
< |
naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to |
| 286 |
< |
be corrected by a factor of $ K_C = X \pm Y$. |
| 211 |
< |
The value of this correction factor as well as the systematic uncertainty |
| 212 |
< |
will be assessed using 38X ttbar madgraph MC. In the following we use |
| 213 |
< |
$K_C = 1$ for simplicity. Based on previous MC studies we foresee a correction |
| 214 |
< |
factor of $K_C \approx 1.2 - 1.5$, and we will assess an uncertainty |
| 215 |
< |
based on the stability of the Monte Carlo tests under |
| 216 |
< |
variations of event selections, choices of \met algorithm, etc. |
| 217 |
< |
For example, we find that observed/predicted changes by roughly 0.1 |
| 218 |
< |
for each 1.5\% change in the average \met response. |
| 285 |
> |
naive data-driven background estimate based on $P_T{(\ell\ell)}$ needs to |
| 286 |
> |
be corrected by a factor of $ K_C = 1.4 \pm 0.2(stat)$. |
| 287 |
|
|
| 288 |
+ |
The 2 dominant sources of systematic uncertainty in $K_C$ are due to non-$t\bar{t} \to$~dilepton backgrounds, |
| 289 |
+ |
and the MET scale and resolution uncertainties. The impact of non-$t\bar{t}$-dilepton background is assessed |
| 290 |
+ |
by varying the yield of all backgrounds except for $t\bar{t} \to$~dilepton, as shown in Table~\ref{table_kc}. |
| 291 |
+ |
The systematic is assessed as the larger of the differences between the nominal $K_C$ value and the values |
| 292 |
+ |
obtained using only $t\bar{t} \to$~dilepton MC and obtained by doubling the non $t\bar{t} \to$~dilepton component, |
| 293 |
+ |
giving an uncertainty of $0.04$. |
| 294 |
+ |
|
| 295 |
+ |
The uncertainty in $K_C$ due to the MET scale uncertainty is assessed by varying the hadronic energy scale using |
| 296 |
+ |
the same method as in~\ref{} and checking how much $K_C$ changes, as summarized in Table~\ref{tab:victorysyst}. |
| 297 |
+ |
This gives an uncertainty of 0.3. We also assess the impact of the MET resolution uncertainty on $K_C$ by applying |
| 298 |
+ |
a random smearing to the MET. For each event, we determine the expected MET resolution based on the sumJetPt, and |
| 299 |
+ |
smear the MET to simulate an increase in the resolution of 10\%, 20\%, 30\%, 40\% and 50\%. The results show that |
| 300 |
+ |
$K_C$ does not depend strongly on the MET resolution and we therefore do not assess any uncertainty. |
| 301 |
|
|
| 302 |
+ |
Incorporating all the statistical and systematic uncertainties we find $K_C = 1.4 \pm 0.4$. |
| 303 |
|
|
| 304 |
|
\subsection{Signal Contamination} |
| 305 |
|
\label{sec:sigcont} |
| 338 |
|
\hline |
| 339 |
|
& Yield & ABCD & $P_T(\ell \ell)$ \\ |
| 340 |
|
\hline |
| 341 |
< |
SM only & 1.43 & 1.19 & 1.03 \\ |
| 342 |
< |
SM + LM0 & 7.90 & 4.23 & 2.35 \\ |
| 343 |
< |
SM + LM1 & 4.00 & 1.53 & 1.51 \\ |
| 341 |
> |
SM only & 1.29 & 1.25 & 0.92 \\ |
| 342 |
> |
SM + LM0 & 7.57 & 4.44 & 1.96 \\ |
| 343 |
> |
SM + LM1 & 3.85 & 1.60 & 1.43 \\ |
| 344 |
|
\hline |
| 345 |
|
\end{tabular} |
| 346 |
|
\end{center} |
| 347 |
|
\end{table} |
| 348 |
|
|
| 267 |
– |
|
| 268 |
– |
|
| 269 |
– |
%\begin{table}[htb] |
| 270 |
– |
%\begin{center} |
| 271 |
– |
%\caption{\label{tab:sigcontABCD} Effects of signal contamination |
| 272 |
– |
%for the background predictions of the ABCD method including LM0 or |
| 273 |
– |
%LM1. Results |
| 274 |
– |
%are normalized to 30 pb$^{-1}$.} |
| 275 |
– |
%\begin{tabular}{|c|c||c|c||c|c|} |
| 276 |
– |
%\hline |
| 277 |
– |
%SM & BG Prediction & SM$+$LM0 & BG Prediction & SM$+$LM1 & BG Prediction \\ |
| 278 |
– |
%Background & SM Only & Contribution & Including LM0 & Contribution & Including LM1 \\ \hline |
| 279 |
– |
%1.2 & 1.0 & 6.8 & 3.7 & 3.4 & 1.3 \\ |
| 280 |
– |
%\hline |
| 281 |
– |
%\end{tabular} |
| 282 |
– |
%\end{center} |
| 283 |
– |
%\end{table} |
| 284 |
– |
|
| 285 |
– |
%\begin{table}[htb] |
| 286 |
– |
%\begin{center} |
| 287 |
– |
%\caption{\label{tab:sigcontPT} Effects of signal contamination |
| 288 |
– |
%for the background predictions of the $P_T(\ell\ell)$ method including LM0 or |
| 289 |
– |
%LM1. Results |
| 290 |
– |
%are normalized to 30 pb$^{-1}$.} |
| 291 |
– |
%\begin{tabular}{|c|c||c|c||c|c|} |
| 292 |
– |
%\hline |
| 293 |
– |
%SM & BG Prediction & SM$+$LM0 & BG Prediction & SM$+$LM1 & BG Prediction \\ |
| 294 |
– |
%Background & SM Only & Contribution & Including LM0 & Contribution & Including LM1 \\ \hline |
| 295 |
– |
%1.2 & 1.0 & 6.8 & 2.2 & 3.4 & 1.5 \\ |
| 296 |
– |
%\hline |
| 297 |
– |
%\end{tabular} |
| 298 |
– |
%\end{center} |
| 299 |
– |
%\end{table} |
| 300 |
– |
|
