| 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 |
| 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 |
|
|
| 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 |
> |
|
| 87 |
> |
|
| 88 |
|
\hline |
| 89 |
|
$t\bar{t}\rightarrow \ell^{+}\ell^{-}$ & 7.96 & 33.07 & 4.81 & 1.20 & 1.16 \\ |
| 90 |
< |
$Z^0$ + jets & 0.00 & 1.16 & 0.08 & 0.08 & 0.00 \\ |
| 90 |
> |
$Z^0 \rightarrow \ell^{+}\ell^{-}$ & 0.03 & 1.47 & 0.10 & 0.10 & 0.00 \\ |
| 91 |
|
SM other & 0.65 & 2.31 & 0.17 & 0.14 & 0.05 \\ |
| 92 |
|
\hline |
| 93 |
< |
total SM MC & 8.61 & 36.54 & 5.05 & 1.41 & 1.19 \\ |
| 93 |
> |
total SM MC & 8.63 & 36.85 & 5.07 & 1.43 & 1.19 \\ |
| 94 |
> |
\hline |
| 95 |
> |
\end{tabular} |
| 96 |
> |
\end{center} |
| 97 |
> |
\end{table} |
| 98 |
> |
|
| 99 |
> |
|
| 100 |
> |
|
| 101 |
> |
\begin{table}[ht] |
| 102 |
> |
\begin{center} |
| 103 |
> |
\caption{\label{tab:abcdsyst} Results of the systematic study of the ABCD method by varying the boundaries |
| 104 |
> |
between the ABCD regions shown in Fig.~\ref{fig:abcdMC}. Here $x_1$ is the lower SumJetPt boundary and |
| 105 |
> |
$x_2$ is the boundary separating regions A and B from C and D, their nominal values are 125 and 300~GeV, |
| 106 |
> |
respectively. $y_1$ is the lower MET/$\sqrt{\rm SumJetPt}$ boundary and |
| 107 |
> |
$y_2$ is the boundary separating regions B and C from A and D, their nominal values are 4.5 and 8.5~GeV$^{1/2}$, |
| 108 |
> |
respectively.} |
| 109 |
> |
\begin{tabular}{cccc|c} |
| 110 |
> |
\hline |
| 111 |
> |
$x_1$ & $x_2$ & $y_1$ & $y_2$ & Observed/Predicted \\ |
| 112 |
> |
\hline |
| 113 |
> |
nominal & nominal & nominal & nominal & 1.20 \\ |
| 114 |
> |
+5\% & +5\% & +2.5\% & +2.5\% & 1.38 \\ |
| 115 |
> |
+5\% & +5\% & nominal & nominal & 1.31 \\ |
| 116 |
> |
nominal & nominal & +2.5\% & +2.5\% & 1.25 \\ |
| 117 |
> |
nominal & +5\% & nominal & +2.5\% & 1.32 \\ |
| 118 |
> |
nominal & -5\% & nominal & -2.5\% & 1.16 \\ |
| 119 |
> |
-5\% & -5\% & +2.5\% & +2.5\% & 1.21 \\ |
| 120 |
> |
+5\% & +5\% & -2.5\% & -2.5\% & 1.26 \\ |
| 121 |
|
\hline |
| 122 |
|
\end{tabular} |
| 123 |
|
\end{center} |
| 139 |
|
to account for the fact that any dilepton selection must include a |
| 140 |
|
moderate \met cut in order to reduce Drell Yan backgrounds. This |
| 141 |
|
is discussed in Section 5.3 of Reference~\cite{ref:ourvictory}; for a \met |
| 142 |
< |
cut of 50 GeV, the rescaling factor is obtained from the data as |
| 142 |
> |
cut of 50 GeV, the rescaling factor is obtained from the MC as |
| 143 |
|
|
| 144 |
|
\newcommand{\ptll} {\ensuremath{P_T(\ell\ell)}} |
| 145 |
|
\begin{center} |
| 164 |
|
$P_T(\ell\ell)$: |
| 165 |
|
\begin{itemize} |
| 166 |
|
\item $Ws$ in top events are polarized. Neutrinos are emitted preferentially |
| 167 |
< |
forward in the $W$ rest frame, thus the $P_T(\nu\nu)$ distribution is harder |
| 167 |
> |
parallel to the $W$ velocity while charged leptons are emitted prefertially |
| 168 |
> |
anti-parallel. Thus the $P_T(\nu\nu)$ distribution is harder |
| 169 |
|
than the $P_T(\ell\ell)$ distribution for top dilepton events. |
| 170 |
|
\item The lepton selections results in $P_T$ and $\eta$ cuts on the individual |
| 171 |
|
leptons that have no simple correspondance to the neutrino requirements. |
| 172 |
|
\item Similarly, the \met$>$50 GeV cut introduces an asymmetry between leptons and |
| 173 |
|
neutrinos which is only partially compensated by the $K$ factor above. |
| 174 |
|
\item The \met resolution is much worse than the dilepton $P_T$ resolution. |
| 175 |
< |
When convoluted with a falling spectrum in the tails of \met, this result |
| 175 |
> |
When convoluted with a falling spectrum in the tails of \met, this results |
| 176 |
|
in a harder spectrum for \met than the original $P_T(\nu\nu)$. |
| 177 |
|
\item The \met response in CMS is not exactly 1. This causes a distortion |
| 178 |
|
in the \met distribution that is not present in the $P_T(\ell\ell)$ distribution. |
| 183 |
|
sources. These events can affect the background prediction. Particularly |
| 184 |
|
dangerous are high $P_T$ Drell Yan events that barely pass the \met$>$ 50 |
| 185 |
|
GeV selection. They will tend to push the data-driven background prediction up. |
| 186 |
+ |
Therefore we estimate the number of DY events entering the background prediction |
| 187 |
+ |
using the $R_{out/in}$ method as described in Sec.~\ref{sec:othBG}. |
| 188 |
|
\end{itemize} |
| 189 |
|
|
| 190 |
|
We have studied these effects in SM Monte Carlo, using a mixture of generator and |
| 207 |
|
4&Y & N & N & GEN & Y & Y & Y & 1.55 \\ |
| 208 |
|
5&Y & N & N & RECOSIM & Y & Y & Y & 1.51 \\ |
| 209 |
|
6&Y & Y & N & RECOSIM & Y & Y & Y & 1.58 \\ |
| 210 |
< |
7&Y & Y & Y & RECOSIM & Y & Y & Y & 1.18 \\ |
| 210 |
> |
7&Y & Y & Y & RECOSIM & Y & Y & Y & 1.38 \\ |
| 211 |
> |
%%%NOTE: updated value 1.18 -> 1.46 since 2/3 DY events have been removed by updated analysis selections, |
| 212 |
> |
%%%dpt/pt cut and general lepton veto |
| 213 |
|
\hline |
| 214 |
|
\end{tabular} |
| 215 |
|
\end{center} |
| 227 |
|
% by $\approx 4\%$\footnote{We find that observed/predicted changes by roughly 0.1 |
| 228 |
|
%for each 1.5\% change in \met response.}. |
| 229 |
|
Finally, contamination from non $t\bar{t}$ |
| 230 |
< |
events can have a significant impact on the BG prediction. The changes between |
| 231 |
< |
lines 6 and 7 of Table~\ref{tab:victorybad} is driven by 3 |
| 232 |
< |
Drell Yan events that pass the \met selection in Monte Carlo (thus the effect |
| 233 |
< |
is statistically not well quantified). |
| 230 |
> |
events can have a significant impact on the BG prediction. |
| 231 |
> |
%The changes between |
| 232 |
> |
%lines 6 and 7 of Table~\ref{tab:victorybad} is driven by 3 |
| 233 |
> |
%Drell Yan events that pass the \met selection in Monte Carlo (thus the effect |
| 234 |
> |
%is statistically not well quantified). |
| 235 |
|
|
| 236 |
|
An additional source of concern is that the CMS Madgraph $t\bar{t}$ MC does |
| 237 |
|
not include effects of spin correlations between the two top quarks. |
| 300 |
|
\hline |
| 301 |
|
& Yield & ABCD & $P_T(\ell \ell)$ \\ |
| 302 |
|
\hline |
| 303 |
< |
SM only & 1.41 & 1.19 & 0.96 \\ |
| 304 |
< |
SM + LM0 & 7.88 & 4.24 & 2.28 \\ |
| 305 |
< |
SM + LM1 & 3.98 & 1.53 & 1.44 \\ |
| 303 |
> |
SM only & 1.43 & 1.19 & 1.03 \\ |
| 304 |
> |
SM + LM0 & 7.90 & 4.23 & 2.35 \\ |
| 305 |
> |
SM + LM1 & 4.00 & 1.53 & 1.51 \\ |
| 306 |
|
\hline |
| 307 |
|
\end{tabular} |
| 308 |
|
\end{center} |
