[ViewVC] Diff of: cvsroot/UserCode/claudioc/OSNote2010/datadriven.tex

Comparing UserCode/claudioc/OSNote2010/datadriven.tex (file contents):
Revision 1.1 by claudioc, Thu Oct 28 05:28:08 2010 UTC vs.
Revision 1.2 by claudioc, Fri Oct 29 02:29:40 2010 UTC

+Thus, we can use an ABCD method in the \met$/\sqrt{\rm SumJetPt}$ vs
+sumJetPt plane to estimate the background in a data driven way.
-<
+\begin{figure}[htb]
->
+\begin{figure}[tb]
+\begin{center}
+\includegraphics[width=0.75\linewidth]{uncorrelated.pdf}
+\caption{\label{fig:uncor}\protect Distributions of SumJetPt
+\end{center}
+\end{figure}
-<
+\begin{figure}[htb]
->
+\begin{figure}[bt]
+\begin{center}
+\includegraphics[width=0.75\linewidth]{abcdMC.jpg}
+\caption{\label{fig:abcdMC}\protect Distributions of SumJetPt
+Our choice of ABCD regions is shown in Figure~\ref{fig:abcdMC}.
+The signal region is region D.  The expected number of events
+in the four regions for the SM Monte Carlo, as well as the BG
-<
+prediction AC/B is given in Table~\ref{tab:abcdMC} for an integrated
->
+prediction AC/B are given in Table~\ref{tab:abcdMC} for an integrated
+luminosity of 30 pb$^{-1}$.  The ABCD method is accurate
+to about 10\%.
+\end{center}
+\end{table}
-+
+\subsection{Dilepton $P_T$ method}
-+
+\label{sec:victory}
-+
+This method is based on a suggestion by V. Pavlunin\cite{ref:victory},
-+
+and was investigated by our group in 2009\cite{ref:ourvictory}.
-+
+The idea is that in dilepton $t\bar{t}$ events the lepton and neutrinos
-+
+from $W$ decays have the same $P_T$ spectrum (modulo $W$ polarization
-+
+effects).  One can then use the observed
-+
+$P_T(\ell\ell)$ distribution to model the sum of neutrino $P_T$'s which
-+
+is identified with the \met.
-+
-+
+Then, in order to predict the $t\bar{t} \to$ dilepton contribution to a
-+
+selection with \met$+$X, one applies a cut on $P_T(\ell\ell)+$X instead.
-+
+In practice one has to rescale the result of the $P_T(\ell\ell)+$X selection
-+
+to account for the fact that any dilepton selection must include a
-+
+moderate \met cut in order to reduce Drell Yan backgrounds.  This
-+
+is discussed in Section 5.3 of Reference~\cite{ref:ourvictory}; for a \met
-+
+cut of 50 GeV, the rescaling factor is obtained from the data as
-+
-+
+\newcommand{\ptll} {\ensuremath{P_T(\ell\ell)}}
-+
+\begin{center}
-+
+$ K = \frac{\int_0^{\infty} {\cal N}(\ptll)~~d\ptll~}{\int_{50}^{\infty} {\cal N}(\ptll)~~d\ptll~}$
-+
+\end{center}
-+
-+
-+
+Monte Carlo studies give values of $K$ that are typically between 1.5 and 1.6,
-+
+depending on selection details.
-+
-+
+There are several effects that spoil the correspondance between \met and
-+
+$P_T(\ell\ell)$:
-+
+\begin{itemize}
-+
+\item $Ws$ in top events are polarized.  Neutrinos are emitted preferentially
-+
+forward in the $W$ rest frame, thus the $P_T(\nu\nu)$ distribution is harder
-+
+than the $P_T(\ell\ell)$ distribution for top dilepton events.
-+
+\item The lepton selections results in $P_T$ and $\eta$ cuts on the individual
-+
+leptons that have no simple correspondance to the neutrino requirements.
-+
+\item Similarly, the \met$>$50 GeV cut introduces an asymmetry between leptons and
-+
+neutrinos which is only partially compensated by the $K$ factor above.
-+
+\item The \met resolution is much worse than the dilepton $P_T$ resolution.
-+
+When convoluted with a falling spectrum in the tails of \met, this result
-+
+in a harder spectrum for \met than the original $P_T(\nu\nu)$.
-+
+\item The \met response in CMS is not exactly 1.  This causes a distortion
-+
+in the \met distribution that is not present in the $P_T(\ell\ell)$ distribution.
-+
+\item The $t\bar{t} \to$ dilepton signal includes contributions from
-+
+$W \to \tau \to \ell$.  For these events the arguments about the equivalence
-+
+of $P_T(\ell\ell)$ and $P_T(\nu\nu)$ do not apply.
-+
+\item A dilepton selection will include SM events from non $t\bar{t}$
-+
+sources.  These events can affect the background prediction.  Particularly
-+
+dangerous are high $P_T$ Drell Yan events that barely pass the \met$>$ 50
-+
+GeV selection.  They will tend to push the data-driven background prediction up.
-+
+\end{itemize}
-+
-+
+We have studied these effects in SM Monte Carlo, using a mixture of generator and
-+
+reconstruction level studies, putting the various effects in one at a time.
-+
+For each configuration, we apply the data-driven method and report as figure
-+
+of merit the ratio of observed and predicted events in the signal region.
-+
+The results are summarized in Table~\ref{tab:victorybad}.
-+
-+
+\begin{table}[htb]
-+
+\begin{center}
-+
+\caption{\label{tab:victorybad} Test of the data driven method in Monte Carlo
-+
+under different assumptions.  See text for details.}
-+
+\begin{tabular}{|l|c|c|c|c|c|c|c|}
-+
+\hline
-+
+& True $t\bar{t}$ dilepton & $t\to W\to\tau$& other SM & GEN or  & Lepton $P_T$    & \met $>$ 50& obs/pred \\
-+
+& included                 & included  & included & RECOSIM & and $\eta$ cuts &      &     \\ \hline
-+
+&Y                        &     N     &   N      &  GEN    &   N             &   N  &       \\
-+
+&Y                        &     N     &   N      &  GEN    &   Y             &   N  &   \\
-+
+&Y                        &     N     &   N      &  GEN    &   Y             &   Y  &   \\
-+
+&Y                        &     N     &   N      & RECOSIM &   Y             &   Y  &   \\
-+
+&Y                        &     Y     &   N      & RECOSIM &   Y             &   Y  &   \\
-+
+&Y                        &     Y     &   Y      & RECOSIM &   Y             &   Y  &   \\
-+
+\hline
-+
+\end{tabular}
-+
+\end{center}
-+
+\end{table}
-+
-+
-+
+The largest discrepancy between prediction and observation occurs on the first
-+
+line of Table~\ref{tab:victorybad}, {\em i.e.}, at the generator level with no
-+
+cuts.  We have verified that this effect is due to the polarization of
-+
+the $W$ (we remove the polarization by reweighting the events and we get
-+
+good agreement between prediction and observation).  The kinematical
-+
+requirements (lines 2 and 3) do not have a significant additional effect.
-+
+Going from GEN to RECOSIM there is a significant change in observed/predicted.
-+
+We have tracked this down to the fact that tcMET underestimates the true \met
-+
+by $\approx 4\%$\footnote{We find that observed/predicted changes by roughly 0.1
-+
+for each 1.5\% change in \met response.}.  Finally, contamination from non $t\bar{t}$
-+
+events can have a significant impact on the BG prediction.  The changes between
-+
+lines 5 and 6 of Table~\ref{tab:victorybad} is driven by only {\color{red} 3}
-+
+Drell Yan events that pass the \met selection.
-+
-+
+An additional source of concern is that the CMS Madgraph $t\bar{t}$ MC does
-+
+not include effects of spin correlations between the two top quarks.
-+
+We have studied this effect at the generator level using Alpgen.  We find
-+
+that the bias is a the few percent level.
-+
-+
+Based on the results of Table~\ref{tab:victorybad}, we conclude that the
-+
+naive data driven background estimate based on $P_T{\ell\ell)}$ needs to
-+
+be corrected by a factor of {\color{red} $1.4 \pm 0.3$  (We need to
-+
+decide what this number should be)}.  The quoted
-+
+uncertainty is based on the stability of the Monte Carlo tests under
-+
+variations of event selections, choices of \met algorithm, etc.
-+
-+
-+
+\subsection{Signal Contamination}
-+
+\label{sec:sigcont}
-+
-+
+All data-driven methods are principle subject to signal contaminations
-+
+in the control regions, and the methods described in
-+
+Sections~\ref{sec:abcd} and~\ref{sec:victory} are not exceptions.
-+
+Signal contamination tends to dilute the significance of a signal
-+
+present in the data by inflating the background prediction.
-+
-+
+It is hard to quantify how important these effects are because we
-+
+do not know what signal may be hiding in the data.  Having two
-+
+independent methods (in addition to Monte Carlo ``dead-reckoning'')
-+
+adds redundancy because signal contamination can have different effects
-+
+in the different control regions for the two methods.
-+
+For example, in the extreme case of a
-+
+new physics signal
-+
+with $P_T(\ell \ell) = \met$, an excess of ev ents would be seen
-+
+in the ABCD method but not in the $P_T(\ell \ell)$ method.
-+
-+
+The LM points are benchmarks for SUSY analyses at CMS.  The effects
-+
+of signal contaminations for a couple such points are summarized
-+
+in Table~\ref{tab:sigcontABCD} and~\ref{tab:sigcontPT}.
-+
+Signal contamination is definitely an important
-+
+effect for these two LM points, but it does not totally hide the
-+
+presence of the signal.
-+
+\begin{table}[htb]
-+
+\begin{center}
-+
+\caption{\label{tab:sigcontABCD} Effects of signal contamination
-+
+for the background predictions of the ABCD method including LM0 or
-+
+LM1.  Results
-+
+are normalized to 30 pb$^{-1}$.}
-+
+\begin{tabular}{|c||c|c||c|c|}
-+
+\hline
-+
+SM         & LM0         & BG Prediction & LM1          & BG Prediction \\
-+
+Background & Contribution& Including LM0 & Contribution & Including LM1  \\ \hline
-+
+x          & x           & x             & x            & x \\
-+
+\hline
-+
+\end{tabular}
-+
+\end{center}
-+
+\end{table}
-+
-+
+\begin{table}[htb]
-+
+\begin{center}
-+
+\caption{\label{tab:sigcontPT} Effects of signal contamination
-+
+for the background predictions of the $P_T(\ell\ell)$ method including LM0 or
-+
+LM1.  Results
-+
+are normalized to 30 pb$^{-1}$.}
-+
+\begin{tabular}{|c||c|c||c|c|}
-+
+\hline
-+
+SM         & LM0         & BG Prediction & LM1          & BG Prediction \\
-+
+Background & Contribution& Including LM0 & Contribution & Including LM1  \\ \hline
-+
+x          & x           & x             & x            & x \\
-+
+\hline
-+
+\end{tabular}
-+
+\end{center}
-+
+\end{table}

Diff Legend

-–
+Removed lines
-+
+Added lines
-<
+Changed lines
->
+Changed lines

Comparing UserCode/claudioc/OSNote2010/datadriven.tex (file contents): Revision 1.1 by claudioc, Thu Oct 28 05:28:08 2010 UTC vs. Revision 1.2 by claudioc, Fri Oct 29 02:29:40 2010 UTC

Diff Legend

Comparing UserCode/claudioc/OSNote2010/datadriven.tex (file contents):
Revision 1.1 by claudioc, Thu Oct 28 05:28:08 2010 UTC vs.
Revision 1.2 by claudioc, Fri Oct 29 02:29:40 2010 UTC