| 23 |
|
The data yields in the |
| 24 |
|
four regions are summarized in Table~\ref{tab:datayield}. |
| 25 |
|
The prediction of the ABCD method is is given by $A\times C/B$ and |
| 26 |
< |
is 1.5 events. (see Table~\ref{tab:datayield}. |
| 26 |
> |
is 1.5 $\pm$ 0.9 events (statistical uncertainty only, assuming |
| 27 |
> |
Gaussian errors), as shown in Table~\ref{tab:datayield}. |
| 28 |
|
|
| 29 |
|
\begin{table}[hbt] |
| 30 |
|
\begin{center} |
| 31 |
|
\caption{\label{tab:datayield} Data yields in the four |
| 32 |
|
regions of Figure~\ref{fig:abcdData}, as well as the predicted yield in region D given |
| 33 |
< |
by A$\times$C / B. The quoted uncertainty |
| 33 |
> |
by A $\times$C / B. The quoted uncertainty |
| 34 |
|
on the prediction in data is statistical only, assuming Gaussian errors. |
| 35 |
|
We also show the SM Monte Carlo expectations, scaled to 34.85~pb$^{-1}$.} |
| 36 |
|
\begin{tabular}{l||c|c|c|c||c} |
| 37 |
|
\hline |
| 38 |
< |
sample & A & B & C & D & A$\times$C / B \\ |
| 38 |
> |
sample & A & B & C & D & A $\times$ C / B \\ |
| 39 |
|
\hline |
| 40 |
+ |
|
| 41 |
|
$t\bar{t}\rightarrow \ell^{+}\ell^{-}$ & 7.96 & 33.07 & 4.81 & 1.20 & 1.16 \\ |
| 42 |
< |
$t\bar{t}\rightarrow \mathrm{other}$ & 0.15 & 0.85 & 0.09 & 0.04 & 0.02 \\ |
| 43 |
< |
$Z^0$ + jets & 0.00 & 1.16 & 0.08 & 0.08 & 0.00 \\ |
| 44 |
< |
$W^{\pm}$ + jets & 0.00 & 0.10 & 0.00 & 0.00 & 0.00 \\ |
| 45 |
< |
$W^+W^-$ & 0.19 & 0.29 & 0.02 & 0.07 & 0.02 \\ |
| 46 |
< |
$W^{\pm}Z^0$ & 0.03 & 0.04 & 0.01 & 0.01 & 0.00 \\ |
| 47 |
< |
$Z^0Z^0$ & 0.00 & 0.03 & 0.00 & 0.00 & 0.00 \\ |
| 48 |
< |
single top & 0.28 & 1.00 & 0.04 & 0.01 & 0.01 \\ |
| 42 |
> |
$t\bar{t}\rightarrow \mathrm{other}$ & 0.15 & 0.85 & 0.09 & 0.04 & 0.02 \\ |
| 43 |
> |
$Z^0 \rightarrow \ell^{+}\ell^{-}$ & 0.03 & 1.47 & 0.10 & 0.10 & 0.00 \\ |
| 44 |
> |
$W^{\pm}$ + jets & 0.00 & 0.10 & 0.00 & 0.00 & 0.00 \\ |
| 45 |
> |
$W^+W^-$ & 0.19 & 0.29 & 0.02 & 0.07 & 0.02 \\ |
| 46 |
> |
$W^{\pm}Z^0$ & 0.03 & 0.04 & 0.01 & 0.01 & 0.00 \\ |
| 47 |
> |
$Z^0Z^0$ & 0.00 & 0.03 & 0.00 & 0.00 & 0.00 \\ |
| 48 |
> |
single top & 0.28 & 1.00 & 0.04 & 0.01 & 0.01 \\ |
| 49 |
|
\hline |
| 50 |
< |
total SM MC & 8.61 & 36.54 & 5.05 & 1.41 & 1.19 \\ |
| 50 |
> |
total SM MC & 8.63 & 36.85 & 5.07 & 1.43 & 1.19 \\ |
| 51 |
|
\hline |
| 52 |
< |
data & 11 & 36 & 5 & 1 &1.53 $\pm$ 0.86 \\ |
| 52 |
> |
data & 11 & 36 & 5 & 1 & $1.53\pm0.86$ \\ |
| 53 |
|
\hline |
| 54 |
|
\end{tabular} |
| 55 |
|
\end{center} |
| 61 |
|
%estimate of the $t\bar{t}$ contribution. The result |
| 62 |
|
%of this exercise is {\color{red} xx} events. |
| 63 |
|
|
| 64 |
+ |
\clearpage |
| 65 |
+ |
|
| 66 |
|
\subsection{Background estimate from the $P_T(\ell\ell)$ method} |
| 67 |
|
\label{sec:victoryres} |
| 68 |
|
|
| 69 |
+ |
We first use the $P_T(\ell \ell)$ method to predict the number of events |
| 70 |
+ |
in control region A, defined in Sec.~\ref{sec:abcd} as |
| 71 |
+ |
$125<{\rm SumJetPt}>300$~GeV and $\met/\sqrt{\rm SumJetPt}>$8.5. |
| 72 |
+ |
We count the number of events in region |
| 73 |
+ |
$A'$, defined in Sec.~\ref{sec:othBG} by replacing the above $\met/\sqrt{\rm SumJetPt}$ |
| 74 |
+ |
cut with the same cut on the quantity $P_T(\ell\ell)/\sqrt{\rm SumJetPt}$, |
| 75 |
+ |
and find $N_{A'}=6$. To predict the yield in region A we take |
| 76 |
+ |
$N_A = K \cdot K_C \cdot N_{A'} = 10.4 \pm 4.2$ |
| 77 |
+ |
(statistical uncertainty only, assuming Gaussian errors), |
| 78 |
+ |
where we have taken $K = 1.73$ and $K_C = 1$. This yield is in good |
| 79 |
+ |
agreement with the observed yield of 11 events, as shown in |
| 80 |
+ |
Table~\ref{tab:victory_control} and displayed in Fig.~\ref{fig:victory} (left). |
| 81 |
+ |
|
| 82 |
+ |
Encouraged by the good agreement between predicted and observed yields |
| 83 |
+ |
in the control region, we proceed to perform the $P_T(\ell \ell)$ method |
| 84 |
+ |
in the signal region ${\rm SumJetPt}>300$~GeV. |
| 85 |
|
The number of data events in region $D'$, which is defined in |
| 86 |
|
Section~\ref{sec:othBG} to be the same as region $D$ but with the |
| 87 |
|
$\met/\sqrt{\rm SumJetPt}$ requirement |
| 88 |
< |
replaced by a $P_T(\ell\ell)/\sqrt{\rm SumJetPt}$ requirement |
| 89 |
< |
is $N_{D'}=2$. Thus the BG prediction is |
| 90 |
< |
$N_D = K \cdot K_C \cdot N_{D'} = 1.5$ |
| 91 |
< |
where $K=1.5 \pm xx$ as derived in Sec.~\ref{sec:victory} and |
| 92 |
< |
$K_C = 1$. |
| 93 |
< |
Note that if we were to subtract off from region $D'$ |
| 94 |
< |
the {\color{red} 0.8 $\pm$ 0.8} DY events estimated from |
| 95 |
< |
Section~\ref{sec:othBG}, the background |
| 96 |
< |
prediction would change to $N_D=1.8 \pm xx$ events. |
| 97 |
< |
|
| 98 |
< |
%%%TO BE REPLACED |
| 99 |
< |
%{\color{red}As mentioned previously, for the 11/pb analysis |
| 80 |
< |
%we use the $K$ factor from data and take $K=1$. |
| 81 |
< |
%This will change for the full dataset. We will also pay |
| 82 |
< |
%more attention to the statistical errors.} |
| 83 |
< |
|
| 84 |
< |
%The number of data events in region $D'$, which is defined in |
| 85 |
< |
%Section~\ref{sec:othBG} to be the same as region $D$ but with the |
| 86 |
< |
%$\met/\sqrt{\rm SumJetPt}$ requirement |
| 87 |
< |
%replaced by a $P_T(\ell\ell)/\sqrt{\rm SumJetPt}$ requirement |
| 88 |
< |
%is $N_{D'}=1$. Thus the BG prediction is |
| 89 |
< |
%$N_D = K \cdot K_{\rm fudge} \cdot N_{D'} = 1.5$ |
| 90 |
< |
%where we used $K=1.5 \pm xx$ and $K_{\rm fudge}=1.0 \pm 0.0$. |
| 91 |
< |
%Note that if we were to subtract off from region $D'$ |
| 92 |
< |
%the {\color{red} 0.4 $\pm$ 0.4} DY events estimated from |
| 93 |
< |
%Section~\ref{sec:othBG}, the background |
| 94 |
< |
%prediction would change to $N_D=0.9 \pm xx$ events. |
| 95 |
< |
%{\color{red} When we do this with a real |
| 96 |
< |
%$K_{\rm fudge}$, the fudge factor will be different |
| 97 |
< |
%after the DY subtraction.} |
| 98 |
< |
|
| 99 |
< |
As a cross-check, we use the $P_T(\ell \ell)$ |
| 100 |
< |
method to also predict the number of events in the |
| 101 |
< |
control region $125<{\rm SumJetPt}<300$ GeV and |
| 102 |
< |
\met/$\sqrt{\rm SumJetPt} > 8.5$. We predict |
| 103 |
< |
$5.6^{+x}_{-y}$ events and we observe 4. |
| 104 |
< |
The results of the $P_T(\ell\ell)$ method are |
| 105 |
< |
summarized in Figure~\ref{fig:victory}. |
| 88 |
> |
replaced by a $P_T(\ell\ell)/\sqrt{\rm SumJetPt}$ requirement, |
| 89 |
> |
is $N_{D'}=2$. |
| 90 |
> |
We next subtract off the expected DY contribution of |
| 91 |
> |
$N_{DY}$ = $0.4 \pm 0.4$ events, as calculated |
| 92 |
> |
in Sec.~\ref{sec:othBG}. The BG prediction is |
| 93 |
> |
$N_D = K \cdot K_C \cdot (N_{D'}-N_{DY}) = 2.5 \pm 2.2$ (statistical |
| 94 |
> |
uncertainty only, assuming Gaussian errors), where $K=1.54 \pm xx$ |
| 95 |
> |
as derived in Sec.~\ref{sec:victory} and $K_C = 1$. |
| 96 |
> |
This prediction is consistent with the observed yield of |
| 97 |
> |
1 event, as summarized in Table~\ref{tab:victory_signal} and Fig.~\ref{fig:victory} |
| 98 |
> |
(right). |
| 99 |
> |
|
| 100 |
|
|
| 101 |
|
\begin{figure}[hbt] |
| 102 |
|
\begin{center} |
| 111 |
|
\end{figure} |
| 112 |
|
|
| 113 |
|
|
| 114 |
+ |
|
| 115 |
|
\begin{table}[hbt] |
| 116 |
|
\begin{center} |
| 117 |
< |
\label{tab:victory_control} |
| 123 |
< |
\caption{Results of the dilepton $p_{T}$ template method in the control region |
| 117 |
> |
\caption{\label{tab:victory_control}Results of the dilepton $p_{T}$ template method in the control region |
| 118 |
|
$125 < \mathrm{sumJetPt} < 300$~GeV. The predicted and observed yields for |
| 119 |
|
the region $\mathrm{tcmet}/\sqrt{\mathrm{sumJetPt}}>$~8.5 are shown for data |
| 120 |
|
and MC. The error on the prediction for data is statistical only, assuming |
| 121 |
|
Gaussian errors.} |
| 122 |
< |
\begin{tabular}{l|c|c|c} |
| 122 |
> |
\begin{tabular}{lccc} |
| 123 |
|
\hline |
| 124 |
|
& Predicted & Observed & Obs/Pred \\ |
| 125 |
|
\hline |
| 126 |
< |
total SM MC & 7.10 & 8.61 & 1.21 \\ |
| 126 |
> |
total SM MC & 7.18 & 8.63 & 1.20 \\ |
| 127 |
|
data & 10.38 $\pm$ 4.24 & 11 & 1.06 \\ |
| 128 |
|
\hline |
| 129 |
|
\end{tabular} |
| 132 |
|
|
| 133 |
|
\begin{table}[hbt] |
| 134 |
|
\begin{center} |
| 135 |
< |
\label{tab:victory_control} |
| 136 |
< |
\caption{Results of the dilepton $p_{T}$ template method in the signal region |
| 143 |
< |
$125 < \mathrm{sumJetPt} < 300$~GeV. The predicted and observed yields for |
| 135 |
> |
\caption{\label{tab:victory_signal}Results of the dilepton $p_{T}$ template method in the signal region |
| 136 |
> |
$\mathrm{sumJetPt} > 300$~GeV. The predicted and observed yields for |
| 137 |
|
the region $\mathrm{tcmet}/\sqrt{\mathrm{sumJetPt}}>$~8.5 are shown for data |
| 138 |
|
and MC. The error on the prediction for data is statistical only, assuming |
| 139 |
|
Gaussian errors.} |
| 140 |
< |
\begin{tabular}{l|c|c|c} |
| 140 |
> |
\begin{tabular}{lccc} |
| 141 |
|
\hline |
| 142 |
< |
& Predicted & Observed & Obs/Pred \\ |
| 142 |
> |
& Predicted & Observed & Obs/Pred \\ |
| 143 |
|
\hline |
| 144 |
< |
total SM MC & 0.96 & 1.41 & 1.46 \\ |
| 145 |
< |
data & 3.07 $\pm$ 2.17 & 1 & 0.33 \\ |
| 144 |
> |
total SM MC & 1.03 & 1.43 & 1.38 \\ |
| 145 |
> |
data & $2.53 \pm 2.25$ & 1 & 0.40 \\ |
| 146 |
|
\hline |
| 147 |
|
\end{tabular} |
| 148 |
|
\end{center} |
