ViewVC Help
View File | Revision Log | Show Annotations | Root Listing
root/cvsroot/UserCode/claudioc/OSNote2010/datadriven.tex
(Generate patch)

Comparing UserCode/claudioc/OSNote2010/datadriven.tex (file contents):
Revision 1.16 by benhoob, Thu Nov 11 16:43:32 2010 UTC vs.
Revision 1.38 by benhoob, Wed Dec 8 12:18:30 2010 UTC

# 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 34.0 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
83 > 34.0~pb$^{-1}$ in the ABCD regions, as well as the predicted yield in
84   the signal region given by A $\times$ C / B. Here `SM other' is the sum
85   of non-dileptonic $t\bar{t}$ decays, $W^{\pm}$+jets, $W^+W^-$,
86   $W^{\pm}Z^0$, $Z^0Z^0$ and single top.}
87   \begin{tabular}{lccccc}
88 + %%%official json v3, 38X MC (D6T ttbar and DY)
89   \hline
90 <         sample                          &              A   &              B   &              C   &              D   &    A $\times$ C / B \\
90 >              sample                     &                   A   &                   B   &                   C   &                   D   &                PRED  \\
91   \hline
92 < $t\bar{t}\rightarrow \ell^{+}\ell^{-}$   &           7.96   &          33.07   &           4.81   &           1.20   &           1.16  \\
93 <   $Z^0$ + jets                          &           0.00   &           1.16   &           0.08   &           0.08   &           0.00  \\
94 <       SM other                          &           0.65   &           2.31   &           0.17   &           0.14   &           0.05  \\
92 > $t\bar{t}\rightarrow \ell^{+}\ell^{-}$   &   8.44  $\pm$  0.18   &  32.83  $\pm$  0.35   &   4.78  $\pm$  0.14   &   1.07  $\pm$  0.06   &   1.23  $\pm$  0.05  \\
93 > $Z^0 \rightarrow \ell^{+}\ell^{-}$       &   0.17  $\pm$  0.08   &   1.18  $\pm$  0.22   &   0.04  $\pm$  0.04   &   0.12  $\pm$  0.07   &   0.01  $\pm$  0.01  \\
94 >            SM other                     &   0.53  $\pm$  0.03   &   2.26  $\pm$  0.11   &   0.23  $\pm$  0.03   &   0.07  $\pm$  0.01   &   0.05  $\pm$  0.01  \\
95   \hline
96 <    total SM MC                          &           8.61   &          36.54   &           5.05   &           1.41   &           1.19  \\
96 >         total SM MC                     &   9.14  $\pm$  0.20   &  36.26  $\pm$  0.43   &   5.05  $\pm$  0.14   &   1.27  $\pm$  0.10   &   1.27  $\pm$  0.05  \\
97 > \hline
98 > \end{tabular}
99 > \end{center}
100 > \end{table}
101 >
102 >
103 >
104 > \begin{table}[ht]
105 > \begin{center}
106 > \caption{\label{tab:abcdsyst}
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 > $x_1$   &   $x_2$ & $y_1$   &   $y_2$ & Observed/Predicted \\
116 > \hline
117 >
118 > nominal & nominal & nominal & nominal & $1.00 \pm 0.08$    \\
119 >
120 > +5\%    & +5\%    & +2.5\%  & +2.5\%  & $1.08 \pm 0.11$    \\
121 >
122 > +5\%    & +5\%    & nominal & nominal & $1.04 \pm 0.10$    \\
123 >
124 > nominal & nominal & +2.5\%  & +2.5\%  & $1.03 \pm 0.09$    \\
125 >
126 > nominal & +5\%    & nominal & +2.5\%  & $1.05 \pm 0.10$    \\
127 >
128 > nominal & -5\%    & nominal & -2.5\%  & $0.95 \pm 0.07$    \\
129 >
130 > -5\%    & -5\%    & +2.5\%  & +2.5\%  & $1.00 \pm 0.08$    \\
131 >
132 > +5\%    & +5\%    & -2.5\%  & -2.5\%  & $0.98 \pm 0.09$    \\
133   \hline
134   \end{tabular}
135   \end{center}
# Line 97 | Line 155 | cut of 50 GeV, the rescaling factor is o
155  
156   \newcommand{\ptll} {\ensuremath{P_T(\ell\ell)}}
157   \begin{center}
158 < $ K = \frac{\int_0^{\infty} {\cal N}(\ptll)~~d\ptll~}{\int_{50}^{\infty} {\cal N}(\ptll)~~d\ptll~}$
158 > $ K = \frac{\int_0^{\infty} {\cal N}(\ptll)~~d\ptll~}{\int_{50}^{\infty} {\cal N}(\ptll)~~d\ptll~} = 1.5$
159   \end{center}
160  
161  
104 Monte Carlo studies give values of $K$ that are typically between 1.5 and 1.6,
105 depending on selection details.  
162   %%%TO BE REPLACED
163   %Given the integrated luminosity of the
164   %present dataset, the determination of $K$ in data is severely statistics
# Line 118 | Line 174 | There are several effects that spoil the
174   $P_T(\ell\ell)$:
175   \begin{itemize}
176   \item $Ws$ in top events are polarized.  Neutrinos are emitted preferentially
177 < forward in the $W$ rest frame, thus the $P_T(\nu\nu)$ distribution is harder
177 > parallel to the $W$ velocity while charged leptons are emitted prefertially
178 > anti-parallel. Thus the $P_T(\nu\nu)$ distribution is harder
179   than the $P_T(\ell\ell)$ distribution for top dilepton events.
180   \item The lepton selections results in $P_T$ and $\eta$ cuts on the individual
181   leptons that have no simple correspondance to the neutrino requirements.
# Line 148 | Line 205 | The results are summarized in Table~\ref
205  
206   \begin{table}[htb]
207   \begin{center}
208 < \caption{\label{tab:victorybad} Test of the data driven method in Monte Carlo
209 < under different assumptions.  See text for details.}
208 > \caption{\label{tab:victorybad}
209 > Test of the data driven method in Monte Carlo
210 > under different assumptions, evaluated using Spring10 MC.  See text for details.}
211   \begin{tabular}{|l|c|c|c|c|c|c|c|c|}
212   \hline
213   & True $t\bar{t}$ dilepton & $t\to W\to\tau$& other SM & GEN or  & Lepton $P_T$    & Z veto & \met $>$ 50& obs/pred \\
214 < & included                 & included       & included & RECOSIM & and $\eta$ cuts &        &            &  \\ \hline
214 > & included                 & included       & included & RECOSIM & and $\eta$ cuts &        &            &       \\ \hline
215   1&Y                        &     N          &   N      &  GEN    &   N             &   N    & N          & 1.90  \\
216   2&Y                        &     N          &   N      &  GEN    &   Y             &   N    & N          & 1.64  \\
217   3&Y                        &     N          &   N      &  GEN    &   Y             &   Y    & N          & 1.59  \\
218   4&Y                        &     N          &   N      &  GEN    &   Y             &   Y    & Y          & 1.55  \\
219   5&Y                        &     N          &   N      & RECOSIM &   Y             &   Y    & Y          & 1.51  \\
220   6&Y                        &     Y          &   N      & RECOSIM &   Y             &   Y    & Y          & 1.58  \\
221 < 7&Y                        &     Y          &   Y      & RECOSIM &   Y             &   Y    & Y          & 1.46  \\
164 < %%%NOTE: updated value 1.18 -> 1.46 since 2/3 DY events have been removed by updated analysis selections,
165 < %%%dpt/pt cut and general lepton veto
221 > 7&Y                        &     Y          &   Y      & RECOSIM &   Y             &   Y    & Y          & 1.38  \\
222   \hline
223   \end{tabular}
224   \end{center}
225   \end{table}
226  
227  
228 + \begin{table}[htb]
229 + \begin{center}
230 + \caption{\label{tab:victorysyst}
231 + Summary of variations in $K_C$ due to the MET scale and resolution uncertainty, and to backgrounds other than $t\bar{t} \to$~dilepton.
232 + 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
233 + refers to the amount of additional smearing of the MET, as discussed in the text. In the third table, the normalization of all backgrounds
234 + other than $t\bar{t} \to$~dilepton is varied. }
235 + \begin{tabular}{ lcccc }
236 + \hline
237 +       MET scale  &      Predicted       &       Observed       &       Obs/pred       \\
238 + \hline
239 +        nominal   &  0.92 $ \pm $ 0.09   &  1.27 $ \pm $ 0.10   &   1.39 $ \pm $ 0.18  \\
240 +            up    &  0.90 $ \pm $ 0.09   &  1.58 $ \pm $ 0.10   &   1.75 $ \pm $ 0.21  \\
241 +          down    &  0.70 $ \pm $ 0.06   &  0.96 $ \pm $ 0.09   &   1.37 $ \pm $ 0.18  \\
242 + \hline
243 +   MET smearing   &      Predicted       &       Observed       &       Obs/pred       \\
244 + \hline
245 +        nominal   &  0.92 $ \pm $ 0.09   &  1.27 $ \pm $ 0.10   &   1.39 $ \pm $ 0.18  \\
246 +           10\%   &  0.88 $ \pm $ 0.09   &  1.28 $ \pm $ 0.10   &   1.47 $ \pm $ 0.19  \\
247 +           20\%   &  0.87 $ \pm $ 0.09   &  1.26 $ \pm $ 0.10   &   1.44 $ \pm $ 0.19  \\
248 +           30\%   &  1.03 $ \pm $ 0.17   &  1.33 $ \pm $ 0.10   &   1.29 $ \pm $ 0.23  \\
249 +           40\%   &  0.88 $ \pm $ 0.09   &  1.36 $ \pm $ 0.10   &   1.55 $ \pm $ 0.20  \\
250 +           50\%   &  0.80 $ \pm $ 0.07   &  1.39 $ \pm $ 0.10   &   1.73 $ \pm $ 0.19  \\
251 + \hline
252 +  non-$t\bar{t} \to$~dilepton bkg   &       Predicted   &           Observed   &           Obs/pred   \\
253 + \hline
254 +   ttdil only                       &   0.79 $ \pm $ 0.07   &   1.07 $ \pm $ 0.06   &   1.36 $ \pm $ 0.14   \\
255 +   nominal                          &   0.92 $ \pm $ 0.09   &   1.27 $ \pm $ 0.10   &   1.39 $ \pm $ 0.18   \\
256 +   double non-ttdil yield           &   1.04 $ \pm $ 0.15   &   1.47 $ \pm $ 0.16   &   1.40 $ \pm $ 0.25   \\
257 + \hline
258 + \end{tabular}
259 + \end{center}
260 + \end{table}
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
# Line 191 | Line 281 | not include effects of spin correlations
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  
284 < %%%TO BE REPLACED
285 < %Based on the results of Table~\ref{tab:victorybad}, we conclude that the
286 < %naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to
287 < %be corrected by a factor of {\color{red} $ K_{\rm{fudge}} =1.2 \pm 0.3$
288 < %(We still need to settle on thie exact value of this.
289 < %For the 11 pb analysis it is taken as =1.)} . The quoted
290 < %uncertainty is based on the stability of the Monte Carlo tests under
291 < %variations of event selections, choices of \met algorithm, etc.
292 < %For example, we find that observed/predicted changes by roughly 0.1
293 < %for each 1.5\% change in the average \met response.  
294 <
295 < Based on the results of Table~\ref{tab:victorybad}, we conclude that the
296 < naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to
297 < be corrected by a factor of $ K_C = X \pm Y$.
298 < The value of this correction factor as well as the systematic uncertainty
299 < will be assessed using 38X ttbar madgraph MC. In the following we use
300 < $K_C = 1$ for simplicity. Based on previous MC studies we foresee a correction
301 < 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 <
284 > Based on the results of Table~\ref{tab:victorysyst}, 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 = 1.4 \pm 0.2({\rm stat})$.
287 >
288 > The 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, as summarized in Table~\ref{tab:victorysyst}.
290 > The impact of non-$t\bar{t}$-dilepton background is assessed
291 > by varying the yield of all backgrounds except for $t\bar{t} \to$~dilepton.
292 > The uncertainty is assessed as the larger of the differences between the nominal $K_C$ value and the values
293 > obtained using only $t\bar{t} \to$~dilepton MC and obtained by doubling the non $t\bar{t} \to$~dilepton component,
294 > giving an uncertainty of $0.03$.
295 >
296 > The uncertainty in $K_C$ due to the MET scale uncertainty is assessed by varying the hadronic energy scale using
297 > the same method as in~\cite{ref:top}, giving an uncertainty of 0.36.
298 > We also assess the impact of the MET resolution
299 > uncertainty on $K_C$ by applying a random smearing to the MET. For each event, we determine the expected MET resolution
300 > based on the sumJetPt, and smear the MET to simulate an increase in the resolution of 10\%, 20\%, 30\%, 40\% and 50\%.
301 > The results show that $K_C$ does not depend strongly on the MET resolution and we therefore do not assess any uncertainty.
302  
303 + Incorporating all the statistical and systematic uncertainties we find $K_C = 1.4 \pm 0.4$.
304  
305   \subsection{Signal Contamination}
306   \label{sec:sigcont}
# Line 248 | Line 334 | presence of the signal.
334   \caption{\label{tab:sigcont} Effects of signal contamination
335   for the two data-driven background estimates. The three columns give
336   the expected yield in the signal region and the background estimates
337 < using the ABCD and $P_T(\ell \ell)$ methods. Results are normalized to 35~pb$^{-1}$.}
337 > using the ABCD and $P_T(\ell \ell)$ methods. Results are normalized to 34.0~pb$^{-1}$.}
338   \begin{tabular}{lccc}
339   \hline
340              &      Yield      &      ABCD    & $P_T(\ell \ell)$  \\
341   \hline
342 < SM only     &      1.41       &      1.19    &             0.96  \\
343 < SM + LM0    &      7.88       &      4.24    &             2.28  \\
344 < SM + LM1    &      3.98       &      1.53    &             1.44  \\
342 > SM only     &       1.3      &      1.3    &       0.9        \\
343 > SM + LM0    &       7.4      &      4.4    &       1.9        \\
344 > SM + LM1    &       3.8      &      1.6    &       1.4        \\
345 > %SM only     &       1.27      &      1.27    &       0.92        \\
346 > %SM + LM0    &       7.39      &      4.38    &       1.93        \\
347 > %SM + LM1    &       3.77      &      1.62    &       1.41        \\
348   \hline
349   \end{tabular}
350   \end{center}
351   \end{table}
352  
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

Diff Legend

Removed lines
+ Added lines
< Changed lines
> Changed lines