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# Line 3 | Line 3
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
# Line 21 | Line 21 | detector.
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}.
26 > as demonstrated in Fig.~\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}[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 $>$8.5, respectively.}
46   \end{center}
47   \end{figure}
48  
49   \begin{figure}[tb]
50   \begin{center}
51 < \includegraphics[width=0.5\linewidth, angle=90]{abcdMC.pdf}
52 < \caption{\label{fig:abcdMC}\protect Distributions of SumJetPt
53 < vs. MET$/\sqrt{\rm SumJetPt}$ for SM Monte Carlo.  Here we also
54 < show our choice of ABCD regions.}
51 > \includegraphics[width=0.75\linewidth]{ttdil_uncor_38X.png}
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. The correlation coefficient
54 > ${\rm corr_{XY}}$ is computed for events falling in the ABCD regions.}
55   \end{center}
56   \end{figure}
57  
58  
59   Our choice of ABCD regions is shown in Figure~\ref{fig:abcdMC}.
60   The signal region is region D.  The expected number of events
61 < in the four regions for the SM Monte Carlo, as well as the BG
62 < prediction AC/B are given in Table~\ref{tab:abcdMC} for an integrated
63 < luminosity of 35 pb$^{-1}$.  The ABCD method is accurate
64 < to about 20\%.
61 > in the four regions for the SM Monte Carlo, as well as the background
62 > prediction A $\times$ C / B are given in Table~\ref{tab:abcdMC} for an integrated
63 > luminosity of 35 pb$^{-1}$. In Table~\ref{tab:abcdsyst}, we test the stability of
64 > observed/predicted with respect to variations in the ABCD boundaries.
65 > Based on the results in Tables~\ref{tab:abcdMC} and~\ref{tab:abcdsyst}, we assess
66 > a systematic uncertainty of 20\% on the prediction of the ABCD method.
67 >
68 > %As shown in Table~\ref{tab:abcdsyst}, we assess systematic uncertainties
69 > %by varying the boundaries by an amount consistent with the hadronic energy scale uncertainty,
70 > %which we take as $\pm$5\% for SumJetPt and $\pm$2.5\% for MET/$\sqrt{\rm SumJetPt}$, since the
71 > %uncertainty on this quantity partially cancels due to the fact that it is a ratio of correlated
72 > %quantities. Based on these studies we assess a correction factor $k_{ABCD} = 1.2 \pm 0.2$ to the
73 > %predicted yield using the ABCD method.
74 >
75 >
76   %{\color{red} Avi wants some statement about stability
77   %wrt changes in regions.  I am not sure that we have done it and
78   %I am not sure it is necessary (Claudio).}
# Line 65 | Line 86 | of non-dileptonic $t\bar{t}$ decays, $W^
86   $W^{\pm}Z^0$, $Z^0Z^0$ and single top.}
87   \begin{tabular}{lccccc}
88   \hline
89 <         sample                          &              A   &              B   &              C   &              D   &    A $\times$ C / B \\
89 >              sample   &                   A   &                   B   &                   C   &                   D   &                      A $\times$ C / B  \\
90   \hline
91 + $t\bar{t}\rightarrow \ell^{+}\ell^{-}$   &   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  \\
92 + $Z^0 \rightarrow \ell^{+}\ell^{-}$       &   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  \\
93 +            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  \\
94 + \hline
95 +         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  \\
96 + \hline
97 + \end{tabular}
98 + \end{center}
99 + \end{table}
100  
101  
102 +
103 + \begin{table}[ht]
104 + \begin{center}
105 + \caption{\label{tab:abcdsyst}
106 + Results of the systematic study of the ABCD method by varying the boundaries
107 + between the ABCD regions shown in Fig.~\ref{fig:abcdMC}. Here $x_1$ is the lower SumJetPt boundary and
108 + $x_2$ is the boundary separating regions A and B from C and D, their nominal values are 125 and 300~GeV,
109 + respectively. $y_1$ is the lower MET/$\sqrt{\rm SumJetPt}$ boundary and
110 + $y_2$ is the boundary separating regions B and C from A and D, their nominal values are 4.5 and 8.5~GeV$^{1/2}$,
111 + respectively.}
112 + \begin{tabular}{cccc|c}
113   \hline
114 < $t\bar{t}\rightarrow \ell^{+}\ell^{-}$   &           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  \\
114 > $x_1$   &   $x_2$ & $y_1$   &   $y_2$ & Observed/Predicted \\
115   \hline
116 <    total SM MC                          &           8.63   &          36.85   &           5.07   &           1.43   &           1.19  \\
116 > nominal & nominal & nominal & nominal & $1.03 \pm 0.10$    \\
117 > +5\%    & +5\%    & +2.5\%  & +2.5\%  & $1.13 \pm 0.13$    \\
118 > +5\%    & +5\%    & nominal & nominal & $1.08 \pm 0.12$    \\
119 > nominal & nominal & +2.5\%  & +2.5\%  & $1.07 \pm 0.11$    \\
120 > nominal & +5\%    & nominal & +2.5\%  & $1.09 \pm 0.12$    \\
121 > nominal & -5\%    & nominal & -2.5\%  & $0.98 \pm 0.08$    \\
122 > -5\%    & -5\%    & +2.5\%  & +2.5\%  & $1.03 \pm 0.09$    \\
123 > +5\%    & +5\%    & -2.5\%  & -2.5\%  & $1.03 \pm 0.11$    \\
124   \hline
125   \end{tabular}
126   \end{center}
# Line 100 | Line 146 | cut of 50 GeV, the rescaling factor is o
146  
147   \newcommand{\ptll} {\ensuremath{P_T(\ell\ell)}}
148   \begin{center}
149 < $ K = \frac{\int_0^{\infty} {\cal N}(\ptll)~~d\ptll~}{\int_{50}^{\infty} {\cal N}(\ptll)~~d\ptll~}$
149 > $ K = \frac{\int_0^{\infty} {\cal N}(\ptll)~~d\ptll~}{\int_{50}^{\infty} {\cal N}(\ptll)~~d\ptll~} = 1.52$
150   \end{center}
151  
152  
107 Monte Carlo studies give values of $K$ that are typically between 1.5 and 1.6,
108 depending on selection details.  
153   %%%TO BE REPLACED
154   %Given the integrated luminosity of the
155   %present dataset, the determination of $K$ in data is severely statistics
# Line 121 | Line 165 | There are several effects that spoil the
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.
# Line 151 | Line 196 | The results are summarized in Table~\ref
196  
197   \begin{table}[htb]
198   \begin{center}
199 < \caption{\label{tab:victorybad} Test of the data driven method in Monte Carlo
200 < under different assumptions.  See text for details.}
199 > \caption{\label{tab:victorybad}
200 > Test of the data driven method in Monte Carlo
201 > under different assumptions, evaluated using 36X MC.  See text for details.}
202   \begin{tabular}{|l|c|c|c|c|c|c|c|c|}
203   \hline
204   & True $t\bar{t}$ dilepton & $t\to W\to\tau$& other SM & GEN or  & Lepton $P_T$    & Z veto & \met $>$ 50& obs/pred \\
205 < & included                 & included       & included & RECOSIM & and $\eta$ cuts &        &            &  \\ \hline
205 > & included                 & included       & included & RECOSIM & and $\eta$ cuts &        &            &       \\ \hline
206   1&Y                        &     N          &   N      &  GEN    &   N             &   N    & N          & 1.90  \\
207   2&Y                        &     N          &   N      &  GEN    &   Y             &   N    & N          & 1.64  \\
208   3&Y                        &     N          &   N      &  GEN    &   Y             &   Y    & N          & 1.59  \\
# Line 164 | Line 210 | under different assumptions.  See text f
210   5&Y                        &     N          &   N      & RECOSIM &   Y             &   Y    & Y          & 1.51  \\
211   6&Y                        &     Y          &   N      & RECOSIM &   Y             &   Y    & Y          & 1.58  \\
212   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
213   \hline
214   \end{tabular}
215   \end{center}
216   \end{table}
217  
218  
219 + \begin{table}[htb]
220 + \begin{center}
221 + \caption{\label{tab:victorysyst}
222 + Summary of variations in $K_C$ due to the MET scale and resolution uncertainty, and to backgrounds other than $t\bar{t} \to$~dilepton.
223 + 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
224 + refers to the amount of additional smearing of the MET, as discussed in the text. In the third table, the normalization of all backgrounds
225 + other than $t\bar{t} \to$~dilepton is varied.}
226 + \begin{tabular}{ lcccc }
227 + \hline
228 +       MET scale  &      Predicted       &       Observed       &       Obs/pred       \\
229 + \hline
230 +        nominal   &  0.92 $ \pm $ 0.11   &  1.29 $ \pm $ 0.11   &  1.40 $ \pm $ 0.20   \\
231 +            up    &  0.92 $ \pm $ 0.11   &  1.53 $ \pm $ 0.12   &  1.66 $ \pm $ 0.23   \\
232 +          down    &  0.81 $ \pm $ 0.07   &  1.08 $ \pm $ 0.11   &  1.32 $ \pm $ 0.17   \\
233 + \hline
234 +   MET smearing   &      Predicted       &       Observed        &       Obs/pred      \\
235 + \hline
236 +        nominal   &  0.92 $ \pm $ 0.11   &  1.29 $ \pm $ 0.11   &  1.40 $ \pm $ 0.20   \\
237 +           10\%   &  0.90 $ \pm $ 0.11   &  1.30 $ \pm $ 0.11   &  1.44 $ \pm $ 0.21   \\
238 +           20\%   &  0.84 $ \pm $ 0.07   &  1.36 $ \pm $ 0.11   &  1.61 $ \pm $ 0.19   \\
239 +           30\%   &  1.05 $ \pm $ 0.18   &  1.32 $ \pm $ 0.11   &  1.27 $ \pm $ 0.24   \\
240 +           40\%   &  0.85 $ \pm $ 0.07   &  1.37 $ \pm $ 0.11   &  1.61 $ \pm $ 0.19   \\
241 +           50\%   &  1.08 $ \pm $ 0.18   &  1.36 $ \pm $ 0.11   &  1.26 $ \pm $ 0.24   \\
242 + \hline
243 +  non-$t\bar{t} \to$~dilepton scale factor   &          Predicted   &           Observed   &           Obs/pred   \\
244 + \hline
245 +   ttdil only                                &  0.77 $ \pm $ 0.07   &  1.05 $ \pm $ 0.06   &  1.36 $ \pm $ 0.14   \\
246 +   nominal                                   &  0.92 $ \pm $ 0.11   &  1.29 $ \pm $ 0.11   &  1.40 $ \pm $ 0.20   \\
247 +   double non-ttdil yield                    &  1.06 $ \pm $ 0.18   &  1.52 $ \pm $ 0.20   &  1.43 $ \pm $ 0.30   \\
248 + \hline
249 + \end{tabular}
250 + \end{center}
251 + \end{table}
252 +
253 +
254 +
255   The largest discrepancy between prediction and observation occurs on the first
256   line of Table~\ref{tab:victorybad}, {\em i.e.}, at the generator level with no
257   cuts.  We have verified that this effect is due to the polarization of
# Line 194 | Line 274 | not include effects of spin correlations
274   We have studied this effect at the generator level using Alpgen.  We find
275   that the bias is at the few percent level.
276  
277 < %%%TO BE REPLACED
278 < %Based on the results of Table~\ref{tab:victorybad}, we conclude that the
279 < %naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to
280 < %be corrected by a factor of {\color{red} $ K_{\rm{fudge}} =1.2 \pm 0.3$
281 < %(We still need to settle on thie exact value of this.
282 < %For the 11 pb analysis it is taken as =1.)} . The quoted
283 < %uncertainty is based on the stability of the Monte Carlo tests under
284 < %variations of event selections, choices of \met algorithm, etc.
285 < %For example, we find that observed/predicted changes by roughly 0.1
286 < %for each 1.5\% change in the average \met response.  
287 <
288 < Based on the results of Table~\ref{tab:victorybad}, we conclude that the
289 < naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to
290 < be corrected by a factor of $ K_C = X \pm Y$.
291 < The value of this correction factor as well as the systematic uncertainty
292 < will be assessed using 38X ttbar madgraph MC. In the following we use
293 < $K_C = 1$ 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.
219 <
277 > Based on the results of Table~\ref{tab:victorysyst}, we conclude that the
278 > naive data-driven background estimate based on $P_T{(\ell\ell)}$ needs to
279 > be corrected by a factor of $ K_C = 1.4 \pm 0.2({\rm stat})$.
280 >
281 > The dominant sources of systematic uncertainty in $K_C$ are due to non-$t\bar{t} \to$~dilepton backgrounds,
282 > and the MET scale and resolution uncertainties, as summarized in Table~\ref{tab:victorysyst}.
283 > The impact of non-$t\bar{t}$-dilepton background is assessed
284 > by varying the yield of all backgrounds except for $t\bar{t} \to$~dilepton.
285 > The uncertainty is assessed as the larger of the differences between the nominal $K_C$ value and the values
286 > obtained using only $t\bar{t} \to$~dilepton MC and obtained by doubling the non $t\bar{t} \to$~dilepton component,
287 > giving an uncertainty of $0.04$.
288 >
289 > The uncertainty in $K_C$ due to the MET scale uncertainty is assessed by varying the hadronic energy scale using
290 > the same method as in~\cite{ref:top}, giving an uncertainty of 0.3. We also assess the impact of the MET resolution
291 > uncertainty on $K_C$ by applying a random smearing to the MET. For each event, we determine the expected MET resolution
292 > based on the sumJetPt, and smear the MET to simulate an increase in the resolution of 10\%, 20\%, 30\%, 40\% and 50\%.
293 > The results show that $K_C$ does not depend strongly on the MET resolution and we therefore do not assess any uncertainty.
294  
295 + Incorporating all the statistical and systematic uncertainties we find $K_C = 1.4 \pm 0.4$.
296  
297   \subsection{Signal Contamination}
298   \label{sec:sigcont}
# Line 256 | Line 331 | using the ABCD and $P_T(\ell \ell)$ meth
331   \hline
332              &      Yield      &      ABCD    & $P_T(\ell \ell)$  \\
333   \hline
334 < SM only     &      1.43       &      1.19    &             1.03  \\
335 < SM + LM0    &      7.90       &      4.23    &             2.35  \\
336 < SM + LM1    &      4.00       &      1.53    &             1.51  \\
334 > SM only     &       1.29      &      1.25    &           0.92    \\
335 > SM + LM0    &       7.57      &      4.44    &           1.96    \\
336 > SM + LM1    &       3.85      &      1.60    &           1.43    \\
337   \hline
338   \end{tabular}
339   \end{center}
340   \end{table}
341  
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

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