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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
25 < \met$/\sqrt{\rm SumJetPt}$ are nearly uncorrelated.
26 < This is demonstrated in Figure~\ref{fig:uncor}.
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  
# Line 50 | Line 59 | Our choice of ABCD regions is shown in F
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\%.
62 > luminosity of 35 pb$^{-1}$.  The ABCD method with chosen boundaries is accurate
63 > to about 20\%. As shown in Table~\ref{tab:abcdsyst}, we assess systematic uncertainties
64 > by varying the boundaries by an amount consistent with the hadronic energy scale uncertainty,
65 > which we take as $\pm$5\% for SumJetPt and $\pm$2.5\% for MET/$\sqrt{\rm SumJetPt}$, since the
66 > uncertainty on this quantity partially cancels due to the fact that it is a ratio of correlated
67 > quantities. Based on these studies we assess a correction factor $k_{ABCD} = 1.2 \pm 0.2$ to the
68 > predicted yield using the ABCD method.
69 >
70 >
71   %{\color{red} Avi wants some statement about stability
72   %wrt changes in regions.  I am not sure that we have done it and
73   %I am not sure it is necessary (Claudio).}
74  
75 < \begin{table}[htb]
75 > \begin{table}[ht]
76   \begin{center}
77   \caption{\label{tab:abcdMC} Expected SM Monte Carlo yields for
78   35 pb$^{-1}$ in the ABCD regions, as well as the predicted yield in
79 < the signal region given by A$\times$C/B. Here 'SM other' is the sum
79 > the signal region given by A $\times$ C / B. Here `SM other' is the sum
80   of non-dileptonic $t\bar{t}$ decays, $W^{\pm}$+jets, $W^+W^-$,
81   $W^{\pm}Z^0$, $Z^0Z^0$ and single top.}
82 < \begin{tabular}{l||c|c|c|c||c}
82 > \begin{tabular}{lccccc}
83 > \hline
84 >              sample   &                   A   &                   B   &                   C   &                   D   &                      A $\times$ C / B  \\
85   \hline
86 <         sample                          &              A   &              B   &              C   &              D   &    A$\times$C/B \\
86 > $t\bar{t}\rightarrow \ell^{+}\ell^{-}$   &   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  \\
87 > $Z^0 \rightarrow \ell^{+}\ell^{-}$       &   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  \\
88 >            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  \\
89 > \hline
90 >         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  \\
91 > \hline
92 > \end{tabular}
93 > \end{center}
94 > \end{table}
95 >
96 >
97 >
98 > \begin{table}[ht]
99 > \begin{center}
100 > \caption{\label{tab:abcdsyst}
101 > {\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??? }
102 > Results of the systematic study of the ABCD method by varying the boundaries
103 > between the ABCD regions shown in Fig.~\ref{fig:abcdMC}. Here $x_1$ is the lower SumJetPt boundary and
104 > $x_2$ is the boundary separating regions A and B from C and D, their nominal values are 125 and 300~GeV,
105 > respectively. $y_1$ is the lower MET/$\sqrt{\rm SumJetPt}$ boundary and
106 > $y_2$ is the boundary separating regions B and C from A and D, their nominal values are 4.5 and 8.5~GeV$^{1/2}$,
107 > respectively.}
108 > \begin{tabular}{cccc|c}
109   \hline
110 < $t\bar{t}\rightarrow \ell^{+}\ell^{-}$   &           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  \\
110 > $x_1$   &   $x_2$ & $y_1$   &   $y_2$ & Observed/Predicted \\
111   \hline
112 <    total SM MC                          &           8.61   &          36.54   &           5.05   &           1.41   &           1.19  \\
112 > nominal & nominal & nominal & nominal & $1.20 \pm 0.12$    \\
113 > +5\%    & +5\%    & +2.5\%  & +2.5\%  & $1.38 \pm 0.15$    \\
114 > +5\%    & +5\%    & nominal & nominal & $1.31 \pm 0.14$    \\
115 > nominal & nominal & +2.5\%  & +2.5\%  & $1.25 \pm 0.13$    \\
116 > nominal & +5\%    & nominal & +2.5\%  & $1.32 \pm 0.14$    \\
117 > nominal & -5\%    & nominal & -2.5\%  & $1.16 \pm 0.09$    \\
118 > -5\%    & -5\%    & +2.5\%  & +2.5\%  & $1.21 \pm 0.11$    \\
119 > +5\%    & +5\%    & -2.5\%  & -2.5\%  & $1.26 \pm 0.12$    \\
120   \hline
121   \end{tabular}
122   \end{center}
# Line 93 | Line 138 | In practice one has to rescale the resul
138   to account for the fact that any dilepton selection must include a
139   moderate \met cut in order to reduce Drell Yan backgrounds.  This
140   is discussed in Section 5.3 of Reference~\cite{ref:ourvictory}; for a \met
141 < cut of 50 GeV, the rescaling factor is obtained from the data as
141 > cut of 50 GeV, the rescaling factor is obtained from the MC as
142  
143   \newcommand{\ptll} {\ensuremath{P_T(\ell\ell)}}
144   \begin{center}
# Line 118 | Line 163 | There are several effects that spoil the
163   $P_T(\ell\ell)$:
164   \begin{itemize}
165   \item $Ws$ in top events are polarized.  Neutrinos are emitted preferentially
166 < forward in the $W$ rest frame, thus the $P_T(\nu\nu)$ distribution is harder
166 > parallel to the $W$ velocity while charged leptons are emitted prefertially
167 > anti-parallel. Thus the $P_T(\nu\nu)$ distribution is harder
168   than the $P_T(\ell\ell)$ distribution for top dilepton events.
169   \item The lepton selections results in $P_T$ and $\eta$ cuts on the individual
170   leptons that have no simple correspondance to the neutrino requirements.
171   \item Similarly, the \met$>$50 GeV cut introduces an asymmetry between leptons and
172   neutrinos which is only partially compensated by the $K$ factor above.
173   \item The \met resolution is much worse than the dilepton $P_T$ resolution.
174 < When convoluted with a falling spectrum in the tails of \met, this result
174 > When convoluted with a falling spectrum in the tails of \met, this results
175   in a harder spectrum for \met than the original $P_T(\nu\nu)$.
176   \item The \met response in CMS is not exactly 1.  This causes a distortion
177   in the \met distribution that is not present in the $P_T(\ell\ell)$ distribution.
# Line 136 | Line 182 | of $P_T(\ell\ell)$ and $P_T(\nu\nu)$ do
182   sources.  These events can affect the background prediction.  Particularly
183   dangerous are high $P_T$ Drell Yan events that barely pass the \met$>$ 50
184   GeV selection.  They will tend to push the data-driven background prediction up.
185 + Therefore we estimate the number of DY events entering the background prediction
186 + using the $R_{out/in}$ method as described in Sec.~\ref{sec:othBG}.
187   \end{itemize}
188  
189   We have studied these effects in SM Monte Carlo, using a mixture of generator and
# Line 146 | Line 194 | The results are summarized in Table~\ref
194  
195   \begin{table}[htb]
196   \begin{center}
197 < \caption{\label{tab:victorybad} Test of the data driven method in Monte Carlo
197 > \caption{\label{tab:victorybad}
198 > {\bf \color{red} Need to either update this with 38X MC  or remove it }
199 > Test of the data driven method in Monte Carlo
200   under different assumptions.  See text for details.}
201   \begin{tabular}{|l|c|c|c|c|c|c|c|c|}
202   \hline
203   & True $t\bar{t}$ dilepton & $t\to W\to\tau$& other SM & GEN or  & Lepton $P_T$    & Z veto & \met $>$ 50& obs/pred \\
204 < & included                 & included       & included & RECOSIM & and $\eta$ cuts &        &            &  \\ \hline
204 > & included                 & included       & included & RECOSIM & and $\eta$ cuts &        &            &       \\ \hline
205   1&Y                        &     N          &   N      &  GEN    &   N             &   N    & N          & 1.90  \\
206   2&Y                        &     N          &   N      &  GEN    &   Y             &   N    & N          & 1.64  \\
207   3&Y                        &     N          &   N      &  GEN    &   Y             &   Y    & N          & 1.59  \\
208   4&Y                        &     N          &   N      &  GEN    &   Y             &   Y    & Y          & 1.55  \\
209   5&Y                        &     N          &   N      & RECOSIM &   Y             &   Y    & Y          & 1.51  \\
210   6&Y                        &     Y          &   N      & RECOSIM &   Y             &   Y    & Y          & 1.58  \\
211 < 7&Y                        &     Y          &   Y      & RECOSIM &   Y             &   Y    & Y          & 1.18  \\
211 > 7&Y                        &     Y          &   Y      & RECOSIM &   Y             &   Y    & Y          & 1.38  \\
212 > \hline
213 > \end{tabular}
214 > \end{center}
215 > \end{table}
216 >
217 >
218 > \begin{table}[htb]
219 > \begin{center}
220 > \caption{\label{tab:victorysyst}
221 > {Summary of uncertainties in $K_C$ due to the MET scale and resolution uncertainty, and to backgrounds other than $t\bar{t} \to$~dilepton.
222 > 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
223 > refers to the amount of additional smearing of the MET, as discussed in the text. In the third table, the normalization of all backgrounds
224 > other than $t\bar{t} \to$~dilepton is varied.
225 > {\bf \color{ref} Should I remove `observed' and `predicted' and show only the ratio? }}
226 >
227 > \begin{tabular}{ lcccc }
228 > \hline
229 >       MET scale  &      Predicted       &       Observed       &       Obs/pred       \\
230 > \hline
231 >        nominal   &  0.92 $ \pm $ 0.11   &  1.29 $ \pm $ 0.11   &  1.40 $ \pm $ 0.20   \\
232 >            up    &  0.92 $ \pm $ 0.11   &  1.53 $ \pm $ 0.12   &  1.66 $ \pm $ 0.23   \\
233 >          down    &  0.81 $ \pm $ 0.07   &  1.08 $ \pm $ 0.11   &  1.32 $ \pm $ 0.17   \\
234 > \hline
235 >
236 > \hline
237 >   MET smearing   &      Predicted       &       Observed        &       Obs/pred      \\
238 > \hline
239 >        nominal   &  0.92 $ \pm $ 0.11   &  1.29 $ \pm $ 0.11   &  1.40 $ \pm $ 0.20   \\
240 >           10\%   &  0.90 $ \pm $ 0.11   &  1.30 $ \pm $ 0.11   &  1.44 $ \pm $ 0.21   \\
241 >           20\%   &  0.84 $ \pm $ 0.07   &  1.36 $ \pm $ 0.11   &  1.61 $ \pm $ 0.19   \\
242 >           30\%   &  1.05 $ \pm $ 0.18   &  1.32 $ \pm $ 0.11   &  1.27 $ \pm $ 0.24   \\
243 >           40\%   &  0.85 $ \pm $ 0.07   &  1.37 $ \pm $ 0.11   &  1.61 $ \pm $ 0.19   \\
244 >           50\%   &  1.08 $ \pm $ 0.18   &  1.36 $ \pm $ 0.11   &  1.26 $ \pm $ 0.24   \\
245 > \hline
246 >
247 > \hline
248 >  non-$t\bar{t} \to$~dilepton scale factor   &          Predicted   &           Observed   &           Obs/pred   \\
249 > \hline
250 >   ttdil only                                &  0.77 $ \pm $ 0.07   &  1.05 $ \pm $ 0.06   &  1.36 $ \pm $ 0.14   \\
251 >   nominal                                   &  0.92 $ \pm $ 0.11   &  1.29 $ \pm $ 0.11   &  1.40 $ \pm $ 0.20   \\
252 >   double non-ttdil yield                    &  1.06 $ \pm $ 0.18   &  1.52 $ \pm $ 0.20   &  1.43 $ \pm $ 0.30   \\
253   \hline
254   \end{tabular}
255   \end{center}
256   \end{table}
257  
258  
259 +
260   The largest discrepancy between prediction and observation occurs on the first
261   line of Table~\ref{tab:victorybad}, {\em i.e.}, at the generator level with no
262   cuts.  We have verified that this effect is due to the polarization of
# Line 176 | Line 268 | Going from GEN to RECOSIM, the change in
268   % by $\approx 4\%$\footnote{We find that observed/predicted changes by roughly 0.1
269   %for each 1.5\% change in \met response.}.  
270   Finally, contamination from non $t\bar{t}$
271 < events can have a significant impact on the BG prediction.  The changes between
272 < lines 6 and 7 of Table~\ref{tab:victorybad} is driven by 3
273 < Drell Yan events that pass the \met selection in Monte Carlo (thus the effect
274 < is statistically not well quantified).
271 > events can have a significant impact on the BG prediction.  
272 > %The changes between
273 > %lines 6 and 7 of Table~\ref{tab:victorybad} is driven by 3
274 > %Drell Yan events that pass the \met selection in Monte Carlo (thus the effect
275 > %is statistically not well quantified).
276  
277   An additional source of concern is that the CMS Madgraph $t\bar{t}$ MC does
278   not include effects of spin correlations between the two top quarks.  
279   We have studied this effect at the generator level using Alpgen.  We find
280   that the bias is at the few percent level.
281  
189 %%%TO BE REPLACED
190 %Based on the results of Table~\ref{tab:victorybad}, we conclude that the
191 %naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to
192 %be corrected by a factor of {\color{red} $ K_{\rm{fudge}} =1.2 \pm 0.3$
193 %(We still need to settle on thie exact value of this.
194 %For the 11 pb analysis it is taken as =1.)} . The quoted
195 %uncertainty is based on the stability of the Monte Carlo tests under
196 %variations of event selections, choices of \met algorithm, etc.
197 %For example, we find that observed/predicted changes by roughly 0.1
198 %for each 1.5\% change in the average \met response.  
199
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 $ K_C = X \pm Y$.
203 < The value of this correction factor as well as the systematic uncertainty
204 < will be assessed using 38X ttbar madgraph MC. In the following we use
205 < $K_C = 1$ for simplicity. Based on previous MC studies we foresee a correction
206 < factor of $K_C \approx 1.2 - 1.5$, and we will assess an uncertainty
207 < based on the stability of the Monte Carlo tests under
208 < variations of event selections, choices of \met algorithm, etc.
209 < For example, we find that observed/predicted changes by roughly 0.1
210 < for each 1.5\% change in the average \met response.
283 > naive data-driven background estimate based on $P_T{(\ell\ell)}$ needs to
284 > be corrected by a factor of $ K_C = 1.4 \pm 0.2(stat)$.
285  
286 + The 2 dominant sources of systematic uncertainty in $K_C$ are due to non-$t\bar{t} \to$~dilepton backgrounds,
287 + and the MET scale and resolution uncertainties. 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, as shown in Table~\ref{table_kc}.
289 + The systematic 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~\ref{} and checking how much $K_C$ changes, as summarized in Table~\ref{tab:victorysyst}.
295 + This gives an uncertainty of 0.3. We also assess the impact of the MET resolution uncertainty on $K_C$ by applying
296 + a random smearing to the MET. For each event, we determine the expected MET resolution based on the sumJetPt, and
297 + smear the MET to simulate an increase in the resolution of 10\%, 20\%, 30\%, 40\% and 50\%. The results show that
298 + $K_C$ does not depend strongly on the MET resolution and we therefore do not assess any uncertainty.
299  
300 + Incorporating all the statistical and systematic uncertainties we find $K_C = 1.4 \pm 0.4$.
301  
302   \subsection{Signal Contamination}
303   \label{sec:sigcont}
# Line 248 | Line 336 | using the ABCD and $P_T(\ell \ell)$ meth
336   \hline
337              &      Yield      &      ABCD    & $P_T(\ell \ell)$  \\
338   \hline
339 < SM only     &      1.41       &      1.19    &             0.96  \\
340 < SM + LM0    &      7.88       &      4.24    &             2.28  \\
341 < SM + LM1    &      3.98       &      1.53    &             1.44  \\
339 > SM only     &       1.29      &      1.25    &           0.92    \\
340 > SM + LM0    &       7.57      &      4.44    &           1.96    \\
341 > SM + LM1    &       3.85      &      1.60    &           1.43    \\
342   \hline
343   \end{tabular}
344   \end{center}
345   \end{table}
346  
259
260
261 %\begin{table}[htb]
262 %\begin{center}
263 %\caption{\label{tab:sigcontABCD} Effects of signal contamination
264 %for the background predictions of the ABCD method including LM0 or
265 %LM1.  Results
266 %are normalized to 30 pb$^{-1}$.}
267 %\begin{tabular}{|c|c||c|c||c|c|}
268 %\hline
269 %SM         & BG Prediction  & SM$+$LM0     & BG Prediction & SM$+$LM1     & BG Prediction \\
270 %Background & SM Only        & Contribution & Including LM0 & Contribution & Including LM1  \\ \hline
271 %1.2        & 1.0            & 6.8          & 3.7           & 3.4          & 1.3 \\
272 %\hline
273 %\end{tabular}
274 %\end{center}
275 %\end{table}
276
277 %\begin{table}[htb]
278 %\begin{center}
279 %\caption{\label{tab:sigcontPT} Effects of signal contamination
280 %for the background predictions of the $P_T(\ell\ell)$ method including LM0 or
281 %LM1.  Results
282 %are normalized to 30 pb$^{-1}$.}
283 %\begin{tabular}{|c|c||c|c||c|c|}
284 %\hline
285 %SM         & BG Prediction  & SM$+$LM0     & BG Prediction & SM$+$LM1     & BG Prediction \\
286 %Background & SM Only        & Contribution & Including LM0 & Contribution & Including LM1  \\ \hline
287 %1.2        & 1.0            & 6.8          & 2.2           & 3.4          & 1.5 \\
288 %\hline
289 %\end{tabular}
290 %\end{center}
291 %\end{table}
292

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