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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}[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
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).}
79  
80 < \begin{table}[htb]
80 > \begin{table}[ht]
81   \begin{center}
82   \caption{\label{tab:abcdMC} Expected SM Monte Carlo yields for
83   35 pb$^{-1}$ in the ABCD regions, as well as the predicted yield in
# 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 > {\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??? }
107 > Results of the systematic study of the ABCD method by varying the boundaries
108 > between the ABCD regions shown in Fig.~\ref{fig:abcdMC}. Here $x_1$ is the lower SumJetPt boundary and
109 > $x_2$ is the boundary separating regions A and B from C and D, their nominal values are 125 and 300~GeV,
110 > respectively. $y_1$ is the lower MET/$\sqrt{\rm SumJetPt}$ boundary and
111 > $y_2$ is the boundary separating regions B and C from A and D, their nominal values are 4.5 and 8.5~GeV$^{1/2}$,
112 > respectively.}
113 > \begin{tabular}{cccc|c}
114   \hline
115 < $t\bar{t}\rightarrow \ell^{+}\ell^{-}$   &           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  \\
115 > $x_1$   &   $x_2$ & $y_1$   &   $y_2$ & Observed/Predicted \\
116   \hline
117 <    total SM MC                          &           8.61   &          36.54   &           5.05   &           1.41   &           1.19  \\
117 > nominal & nominal & nominal & nominal & $1.03 \pm 0.10$    \\
118 > +5\%    & +5\%    & +2.5\%  & +2.5\%  & $1.13 \pm 0.13$    \\
119 > +5\%    & +5\%    & nominal & nominal & $1.08 \pm 0.12$    \\
120 > nominal & nominal & +2.5\%  & +2.5\%  & $1.07 \pm 0.11$    \\
121 > nominal & +5\%    & nominal & +2.5\%  & $1.09 \pm 0.12$    \\
122 > nominal & -5\%    & nominal & -2.5\%  & $0.98 \pm 0.08$    \\
123 > -5\%    & -5\%    & +2.5\%  & +2.5\%  & $1.03 \pm 0.09$    \\
124 > +5\%    & +5\%    & -2.5\%  & -2.5\%  & $1.03 \pm 0.11$    \\
125   \hline
126   \end{tabular}
127   \end{center}
# Line 97 | Line 147 | cut of 50 GeV, the rescaling factor is o
147  
148   \newcommand{\ptll} {\ensuremath{P_T(\ell\ell)}}
149   \begin{center}
150 < $ K = \frac{\int_0^{\infty} {\cal N}(\ptll)~~d\ptll~}{\int_{50}^{\infty} {\cal N}(\ptll)~~d\ptll~}$
150 > $ K = \frac{\int_0^{\infty} {\cal N}(\ptll)~~d\ptll~}{\int_{50}^{\infty} {\cal N}(\ptll)~~d\ptll~} = 1.52$
151   \end{center}
152  
153  
104 Monte Carlo studies give values of $K$ that are typically between 1.5 and 1.6,
105 depending on selection details.  
154   %%%TO BE REPLACED
155   %Given the integrated luminosity of the
156   %present dataset, the determination of $K$ in data is severely statistics
# Line 118 | Line 166 | There are several effects that spoil the
166   $P_T(\ell\ell)$:
167   \begin{itemize}
168   \item $Ws$ in top events are polarized.  Neutrinos are emitted preferentially
169 < forward in the $W$ rest frame, thus the $P_T(\nu\nu)$ distribution is harder
169 > parallel to the $W$ velocity while charged leptons are emitted prefertially
170 > anti-parallel. Thus the $P_T(\nu\nu)$ distribution is harder
171   than the $P_T(\ell\ell)$ distribution for top dilepton events.
172   \item The lepton selections results in $P_T$ and $\eta$ cuts on the individual
173   leptons that have no simple correspondance to the neutrino requirements.
# Line 148 | Line 197 | The results are summarized in Table~\ref
197  
198   \begin{table}[htb]
199   \begin{center}
200 < \caption{\label{tab:victorybad} Test of the data driven method in Monte Carlo
200 > \caption{\label{tab:victorybad}
201 > {\bf \color{red} Should we either update this with 38X MC  or remove it?? }
202 > Test of the data driven method in Monte Carlo
203   under different assumptions.  See text for details.}
204   \begin{tabular}{|l|c|c|c|c|c|c|c|c|}
205   \hline
206   & True $t\bar{t}$ dilepton & $t\to W\to\tau$& other SM & GEN or  & Lepton $P_T$    & Z veto & \met $>$ 50& obs/pred \\
207 < & included                 & included       & included & RECOSIM & and $\eta$ cuts &        &            &  \\ \hline
207 > & included                 & included       & included & RECOSIM & and $\eta$ cuts &        &            &       \\ \hline
208   1&Y                        &     N          &   N      &  GEN    &   N             &   N    & N          & 1.90  \\
209   2&Y                        &     N          &   N      &  GEN    &   Y             &   N    & N          & 1.64  \\
210   3&Y                        &     N          &   N      &  GEN    &   Y             &   Y    & N          & 1.59  \\
211   4&Y                        &     N          &   N      &  GEN    &   Y             &   Y    & Y          & 1.55  \\
212   5&Y                        &     N          &   N      & RECOSIM &   Y             &   Y    & Y          & 1.51  \\
213   6&Y                        &     Y          &   N      & RECOSIM &   Y             &   Y    & Y          & 1.58  \\
214 < 7&Y                        &     Y          &   Y      & RECOSIM &   Y             &   Y    & Y          & 1.46  \\
215 < %%%NOTE: updated value 1.18 -> 1.46 since 2/3 DY events have been removed by updated analysis selections,
216 < %%%dpt/pt cut and general lepton veto
214 > 7&Y                        &     Y          &   Y      & RECOSIM &   Y             &   Y    & Y          & 1.38  \\
215 > \hline
216 > \end{tabular}
217 > \end{center}
218 > \end{table}
219 >
220 >
221 > \begin{table}[htb]
222 > \begin{center}
223 > \caption{\label{tab:victorysyst}
224 > Summary of uncertainties in $K_C$ due to the MET scale and resolution uncertainty, and to backgrounds other than $t\bar{t} \to$~dilepton.
225 > 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
226 > refers to the amount of additional smearing of the MET, as discussed in the text. In the third table, the normalization of all backgrounds
227 > other than $t\bar{t} \to$~dilepton is varied.
228 > {\bf \color{red} Should I remove `observed' and `predicted' and show only the ratio? }}
229 >
230 > \begin{tabular}{ lcccc }
231 > \hline
232 >       MET scale  &      Predicted       &       Observed       &       Obs/pred       \\
233 > \hline
234 >        nominal   &  0.92 $ \pm $ 0.11   &  1.29 $ \pm $ 0.11   &  1.40 $ \pm $ 0.20   \\
235 >            up    &  0.92 $ \pm $ 0.11   &  1.53 $ \pm $ 0.12   &  1.66 $ \pm $ 0.23   \\
236 >          down    &  0.81 $ \pm $ 0.07   &  1.08 $ \pm $ 0.11   &  1.32 $ \pm $ 0.17   \\
237 > \hline
238 >   MET smearing   &      Predicted       &       Observed        &       Obs/pred      \\
239 > \hline
240 >        nominal   &  0.92 $ \pm $ 0.11   &  1.29 $ \pm $ 0.11   &  1.40 $ \pm $ 0.20   \\
241 >           10\%   &  0.90 $ \pm $ 0.11   &  1.30 $ \pm $ 0.11   &  1.44 $ \pm $ 0.21   \\
242 >           20\%   &  0.84 $ \pm $ 0.07   &  1.36 $ \pm $ 0.11   &  1.61 $ \pm $ 0.19   \\
243 >           30\%   &  1.05 $ \pm $ 0.18   &  1.32 $ \pm $ 0.11   &  1.27 $ \pm $ 0.24   \\
244 >           40\%   &  0.85 $ \pm $ 0.07   &  1.37 $ \pm $ 0.11   &  1.61 $ \pm $ 0.19   \\
245 >           50\%   &  1.08 $ \pm $ 0.18   &  1.36 $ \pm $ 0.11   &  1.26 $ \pm $ 0.24   \\
246 > \hline
247 >  non-$t\bar{t} \to$~dilepton scale factor   &          Predicted   &           Observed   &           Obs/pred   \\
248 > \hline
249 >   ttdil only                                &  0.77 $ \pm $ 0.07   &  1.05 $ \pm $ 0.06   &  1.36 $ \pm $ 0.14   \\
250 >   nominal                                   &  0.92 $ \pm $ 0.11   &  1.29 $ \pm $ 0.11   &  1.40 $ \pm $ 0.20   \\
251 >   double non-ttdil yield                    &  1.06 $ \pm $ 0.18   &  1.52 $ \pm $ 0.20   &  1.43 $ \pm $ 0.30   \\
252   \hline
253   \end{tabular}
254   \end{center}
255   \end{table}
256  
257  
258 +
259   The largest discrepancy between prediction and observation occurs on the first
260   line of Table~\ref{tab:victorybad}, {\em i.e.}, at the generator level with no
261   cuts.  We have verified that this effect is due to the polarization of
# Line 191 | Line 278 | not include effects of spin correlations
278   We have studied this effect at the generator level using Alpgen.  We find
279   that the bias is at the few percent level.
280  
281 < %%%TO BE REPLACED
282 < %Based on the results of Table~\ref{tab:victorybad}, we conclude that the
283 < %naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to
284 < %be corrected by a factor of {\color{red} $ K_{\rm{fudge}} =1.2 \pm 0.3$
285 < %(We still need to settle on thie exact value of this.
286 < %For the 11 pb analysis it is taken as =1.)} . The quoted
287 < %uncertainty is based on the stability of the Monte Carlo tests under
288 < %variations of event selections, choices of \met algorithm, etc.
289 < %For example, we find that observed/predicted changes by roughly 0.1
290 < %for each 1.5\% change in the average \met response.  
291 <
292 < Based on the results of Table~\ref{tab:victorybad}, we conclude that the
293 < naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to
294 < be corrected by a factor of $ K_C = X \pm Y$.
295 < The value of this correction factor as well as the systematic uncertainty
296 < will be assessed using 38X ttbar madgraph MC. In the following we use
297 < $K_C = 1$ for simplicity. Based on previous MC studies we foresee a correction
211 < factor of $K_C \approx 1.2 - 1.5$, and we will assess an uncertainty
212 < based on the stability of the Monte Carlo tests under
213 < variations of event selections, choices of \met algorithm, etc.
214 < For example, we find that observed/predicted changes by roughly 0.1
215 < for each 1.5\% change in the average \met response.
216 <
281 > Based on the results of Table~\ref{tab:victorysyst}, we conclude that the
282 > naive data-driven background estimate based on $P_T{(\ell\ell)}$ needs to
283 > be corrected by a factor of $ K_C = 1.4 \pm 0.2({\rm stat})$.
284 >
285 > The dominant sources of systematic uncertainty in $K_C$ are due to non-$t\bar{t} \to$~dilepton backgrounds,
286 > and the MET scale and resolution uncertainties, as summarized in Table~\ref{tab:victorysyst}.
287 > The impact of non-$t\bar{t}$-dilepton background is assessed
288 > by varying the yield of all backgrounds except for $t\bar{t} \to$~dilepton.
289 > The uncertainty is assessed as the larger of the differences between the nominal $K_C$ value and the values
290 > obtained using only $t\bar{t} \to$~dilepton MC and obtained by doubling the non $t\bar{t} \to$~dilepton component,
291 > giving an uncertainty of $0.04$.
292 >
293 > The uncertainty in $K_C$ due to the MET scale uncertainty is assessed by varying the hadronic energy scale using
294 > the same method as in~\cite{ref:top}, giving an uncertainty of 0.3. We also assess the impact of the MET resolution
295 > uncertainty on $K_C$ by applying a random smearing to the MET. For each event, we determine the expected MET resolution
296 > based on the sumJetPt, and smear the MET to simulate an increase in the resolution of 10\%, 20\%, 30\%, 40\% and 50\%.
297 > The results show that $K_C$ does not depend strongly on the MET resolution and we therefore do not assess any uncertainty.
298  
299 + Incorporating all the statistical and systematic uncertainties we find $K_C = 1.4 \pm 0.4$.
300  
301   \subsection{Signal Contamination}
302   \label{sec:sigcont}
# Line 253 | Line 335 | using the ABCD and $P_T(\ell \ell)$ meth
335   \hline
336              &      Yield      &      ABCD    & $P_T(\ell \ell)$  \\
337   \hline
338 < SM only     &      1.41       &      1.19    &             0.96  \\
339 < SM + LM0    &      7.88       &      4.24    &             2.28  \\
340 < SM + LM1    &      3.98       &      1.53    &             1.44  \\
338 > SM only     &       1.29      &      1.25    &           0.92    \\
339 > SM + LM0    &       7.57      &      4.44    &           1.96    \\
340 > SM + LM1    &       3.85      &      1.60    &           1.43    \\
341   \hline
342   \end{tabular}
343   \end{center}
344   \end{table}
345  
264
265
266 %\begin{table}[htb]
267 %\begin{center}
268 %\caption{\label{tab:sigcontABCD} Effects of signal contamination
269 %for the background predictions of the ABCD method including LM0 or
270 %LM1.  Results
271 %are normalized to 30 pb$^{-1}$.}
272 %\begin{tabular}{|c|c||c|c||c|c|}
273 %\hline
274 %SM         & BG Prediction  & SM$+$LM0     & BG Prediction & SM$+$LM1     & BG Prediction \\
275 %Background & SM Only        & Contribution & Including LM0 & Contribution & Including LM1  \\ \hline
276 %1.2        & 1.0            & 6.8          & 3.7           & 3.4          & 1.3 \\
277 %\hline
278 %\end{tabular}
279 %\end{center}
280 %\end{table}
281
282 %\begin{table}[htb]
283 %\begin{center}
284 %\caption{\label{tab:sigcontPT} Effects of signal contamination
285 %for the background predictions of the $P_T(\ell\ell)$ method including LM0 or
286 %LM1.  Results
287 %are normalized to 30 pb$^{-1}$.}
288 %\begin{tabular}{|c|c||c|c||c|c|}
289 %\hline
290 %SM         & BG Prediction  & SM$+$LM0     & BG Prediction & SM$+$LM1     & BG Prediction \\
291 %Background & SM Only        & Contribution & Including LM0 & Contribution & Including LM1  \\ \hline
292 %1.2        & 1.0            & 6.8          & 2.2           & 3.4          & 1.5 \\
293 %\hline
294 %\end{tabular}
295 %\end{center}
296 %\end{table}
297

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