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\section{Cross-checks using Pseudo Experiment} |
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\section{Cross-checks using pseudo-experiments} |
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The statistics of Chowder soup should correspond to 1fb$^{-1}$ of data |
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taking, so 10 pseudo experiment have been done by steps of |
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100pb$^{-1}$. In |
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table~\ref{tab:Pseudo3e}~\ref{tab:Pseudo2e1mu}~\ref{tab:Pseudo2mu1e}~\ref{tab:Pseudo3mu}, |
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the event yield for each steps of luminosity is given respectively for |
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each channel. The non-genuine \Z background is not considered as a |
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separate background and it is included in the Matrix Method. The |
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results are in agreement within one sigma. |
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The statistics of Chowder soup should correspond to 1 \invfb of integrated luminosity. |
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Thus, in this Section we perform 10 pseudo experiments with a step of 100 \invpb each. In |
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Tables~\ref{tab:Pseudo3e}, \ref{tab:Pseudo2e1mu}, \ref{tab:Pseudo2mu1e}, and \ref{tab:Pseudo3mu} |
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the measured event yield is given for every signature channel as function of the integrated |
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luminosity. The uncertainties are systematic uncertainties associated with the background |
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estimation method only. The results agree with Monte Carlo truth information within one sigma. |
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\begin{table}[h] |
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\begin{center} |
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\WZ from MC & 3 &4 &5 &9 &14 \\ |
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\hline |
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\end{tabular} |
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\\ |
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\\ |
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\begin{tabular}{lccccc} \hline \hline |
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Luminosity (pb$^{-1}$) &600 &700 & 800 & 900 & 1000 \\ \hline |
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Observed Number of Events & 25 & 28 & 32 & 36 & 38\\ |
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\WZ from MC & 2 & 3 & 7 & 11 & 14 \\ |
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\hline |
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\end{tabular} |
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\\ |
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\\ |
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\begin{tabular}{lccccc} \hline \hline |
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Luminosity (pb$^{-1}$) &600 &700 & 800 & 900 & 1000 \\ \hline |
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Observed Number of Events & 21 & 23 & 27 & 27 & 29\\\hline |
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\WZ from MC & 2 & 6 & 9 & 12 & 14 \\ |
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\hline |
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\end{tabular} |
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\\ |
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\\ |
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\begin{tabular}{lccccc} \hline \hline |
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Luminosity (pb$^{-1}$) &600 &700 & 800 & 900 & 1000 \\ \hline |
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Observed Number of Events & 32 & 35 & 40 & 46 & 55 \\ \hline |
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\WZ from MC & 1 & 1 & 4 & 6 & 8 \\ |
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\hline |
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\end{tabular} |
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\\ |
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\\ |
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\begin{tabular}{lccccc} \hline \hline |
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Luminosity (pb$^{-1}$) &600 &700 & 800 & 900 & 1000 \\ \hline |
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Observed Number of Events & 10 & 14 & 18 & 22 & 24 \\ \hline |
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$N^{genuine Z}$ (matrix method) &2.4 $\pm$2.1 & 2.7 $\pm$2.4 & 2.7 $\pm$2.7 & 3.2 $\pm$3.1 & 3.4 $\pm$3.4\\ \hline |
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$N^{WZ}$ &6.2 $\pm$2.5 & 9.7 $\pm$2.9 &13.4 $\pm$3.3 &16.7 $\pm$3.8 &18.2 $\pm$4.1\\\hline |
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\WZ from MC & 10 & 13 & 15 & 19 & 21\\ |
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\hline\\ |
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\end{tabular} |
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\caption{Expected number of selected events for an integrated luminosity from 100 |
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pb$^{-1}$ to 1000 pb$^{-1}$ for 3$\mu$-channel and estimated background with 81 GeV $< M_Z < $ 101 GeV |
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.} |
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\label{tab:Pseudo3mu} |
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\end{center} |
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\end{table} |
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|
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|
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Tables~\ref{tab:Pseudo3eFit}~\ref{tab:Pseudo2mu1eFit}~\ref{tab:Pseudo2e1muFit}~\ref{tab:Pseudo3muFit} |
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presents the event yield of pseudo experiment with this time but |
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separating out the background containing a non-genuine \Z. The |
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residual errors coming from the fit are dominating the measurement |
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but all measurement are in perfect agreement. |
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|
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\begin{table}[h] |
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\begin{center} |
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\begin{tabular}{lccccc} \hline \hline |
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Luminosity (pb$^{-1}$) &300 &400 & 500 \\ \hline |
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Observed Number of Events & 10 & 17 & 23 \\ \hline |
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$N$ - ZZ -Zgamma &8.6 $\pm$1.1 &15.1$\pm$1.4 &20.7 $\pm$1.8 \\ |
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$N^{non genuine Z}$ (Fit) &1.4 $\pm$3.0 & 1.5 $\pm$3.1 &2.6 $\pm$3.6 \\ |
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$N^{genuine Z}$ (matrix method) &2.8 $\pm$1.4 & 5.6 $\pm$2.4 & 7.0 $\pm$3.0 \\\hline |
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$N^{WZ}$ &4.4 $\pm$3.5 & 8.1 $\pm$4.1 &11.1 $\pm$5.0 \\ \hline |
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\WZ from MC &5 &9 &14 \\ |
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\hline |
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\end{tabular} |
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\\ |
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\begin{tabular}{lccccc} \hline \hline |
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Luminosity (pb$^{-1}$) &600 &700 & 800 & 900 & 1000 \\ \hline |
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Observed Number of Events & 25 & 28 & 32 & 36 & 38\\ |
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$N$ - ZZ -Zgamma &22.2 $\pm$2.2 &24.7 $\pm$2.5 &28.3 $\pm$2.9 &54.5 $\pm$3.5 &58.0 $\pm$3.9 \\ |
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$N^{non genuine Z}$ (Fit) & 2.8 $\pm$3.7 & 2.9 $\pm$3.6 & 3.5 $\pm$4.0 & 3.7 $\pm$4.1 & 4.4 $\pm$4.1 \\ |
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$N^{genuine Z}$ (matrix method) & 7.4 $\pm$3.2 & 9.3 $\pm$3.7 & 9.3 $\pm$4.0 & 8.3 $\pm$4.2 &11.1 $\pm$4.7 \\\hline |
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$N^{WZ}$ &12.0 $\pm$5.4 &12.6 $\pm$5.7 &15.5 $\pm$6.3 &19.8 $\pm$6.7 &17.8 $\pm$7.2 \\\hline |
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\WZ from MC &15 &18 &20 &23 &24\\ |
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\hline |
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\end{tabular} |
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\caption{Expected number of selected events for an integrated luminosity from 100 |
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pb$^{-1}$ to 1000 pb$^{-1}$ for 3e-channel and estimated background with 81 GeV $< M_Z < $ 101 GeV |
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.} |
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\label{tab:Pseudo3eFit} |
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\end{center} |
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\end{table} |
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|
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\begin{table}[h] |
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\begin{center} |
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\begin{tabular}{lccccc} \hline \hline |
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Luminosity (pb$^{-1}$) &300 &400 & 500 \\ \hline |
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Observed Number of Events & 9 &12 & 18\\ \hline |
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$N$ - ZZ -Zgamma &8.4 $\pm$0.6 &13.2 $\pm$0.8 &17.0 $\pm$1.0\\ |
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$N^{non genuine Z}$ (Fit) &0.6 $\pm$3.2 & 0.5 $\pm$0.9 &1.3$\pm$3.4\\ |
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$N^{genuine Z}$ (matrix method) &0.5 $\pm$0.7 & 0.7 $\pm$1.0 &0.7 $\pm$1.2\\ \hline |
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$N^{WZ}$ &7.3 $\pm$3.3 &12.1 $\pm$1.6 &15.0 $\pm$3.7\\ \hline |
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\WZ from MC & 7 & 11 & 14 \\ |
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\hline |
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\end{tabular} |
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\\ |
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\begin{tabular}{lccccc} \hline \hline |
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Luminosity (pb$^{-1}$) &600 &700 & 800 & 900 & 1000 \\ \hline |
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Observed Number of Events & 21 & 23 & 27 & 27 & 29\\\hline |
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$N$ - ZZ -Zgamma &19.8 $\pm$1.2 &21.6 $\pm$1.4 &25.4 $\pm$1.6 &25.2 $\pm$1.8 &27.0 $\pm$2.0\\ |
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$N^{non genuine Z}$ (Fit) & 1.2 $\pm$3.2 & 1.7 $\pm$3.4 & 2.5 $\pm$3.7 & 2.6 $\pm$3.7 & 2.8 $\pm$3.8\\ |
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$N^{genuine Z}$ (matrix method) &0.6 $\pm$1.3 & 0.7 $\pm$1.4 & 1.0 $\pm$1.7 & 1.1 $\pm$1.8 & 1.6 $\pm$2.2\\\hline |
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$N^{WZ}$ &18.0 $\pm$3.6 &19.2 $\pm$3.9 &21.9 $\pm$4.4 &21.4 $\pm$4.5 &22.7 $\pm$4.9 \\ \hline |
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\WZ from MC & 16 & 18 & 22 & 22 & 24\\ |
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\hline\\ |
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\end{tabular} |
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\caption{Expected number of selected events for an integrated luminosity from 100 |
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pb$^{-1}$ to 1000 pb$^{-1}$ for 2e1$\mu$-channel and estimated background with 81 GeV $< M_Z < $ 101 GeV |
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.} |
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\label{tab:Pseudo2e1muFit} |
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\end{center} |
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\end{table} |
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|
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\begin{table}[h] |
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\begin{center} |
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\begin{tabular}{lccccc} \hline \hline |
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Luminosity (pb$^{-1}$) &300 &400 & 500 \\ \hline |
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Observed Number of Events &17 & 21 & 25 \\ \hline |
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$N$ - ZZ -Zgamma &16.3$\pm$0.7 &20.1 $\pm$0.9 &23.8 $\pm$1.2\\ |
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$N^{non genuine Z}$ (Fit) & 0.7 $\pm$2.9 & 1.2 $\pm$1.0 & 1.6 $\pm$4.2\\ |
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$N^{genuine Z}$ (matrix method) & 6.0 $\pm$2.5 & 7.9 $\pm$3.1 & 7.4 $\pm$3.5\\\hline |
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$N^{WZ}$ &9.6 $\pm$3.9 &10.9 $\pm$3.4 &14.8 $\pm$5.5 \\\hline |
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\WZ from MC & 9 & 12 & 14 \\ |
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\hline |
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\end{tabular} |
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\\ |
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\begin{tabular}{lccccc} \hline \hline |
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Luminosity (pb$^{-1}$) &600 &700 & 800 & 900 & 1000 \\ \hline |
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Observed Number of Events & 32 & 35 & 40 & 46 & 55 \\ \hline |
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$N$ - ZZ -Zgamma &30.6 $\pm$1.4 &33.4 $\pm$1.6 &38.1 $\pm$1.9 &43.9 $\pm$2.1 &52.7 $\pm$2.3 \\ |
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$N^{non genuine Z}$ (Fit) & 2.3 $\pm$1.2 & 2.4 $\pm$1.2 & 3.6 $\pm$3.9 & 3.8 $\pm$3.8 & 4.0 $\pm$3.9\\ |
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$N^{genuine Z}$ (matrix method) &10.2 $\pm$4.4 &10.6 $\pm$4.8 &12.5 $\pm$5.4 &12.9 $\pm$6.0 &14.3 $\pm$7.0 \\\hline |
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$N^{WZ}$ &18.2 $\pm$4.7 &20.6 $\pm$5.1 &22.0 $\pm$6.9 &27.2 $\pm$7.4 &34.4 $\pm$8.3 \\\hline |
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\WZ from MC & 19 & 22 & 26 & 29 & 32\\ |
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\hline\\ |
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\end{tabular} |
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\caption{Expected number of selected events for an integrated luminosity from 100 |
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pb$^{-1}$ to 1000 pb$^{-1}$ for 2$\mu$1e-channel and estimated background with 81 GeV $< M_Z < $ 101 GeV |
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.} |
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\label{tab:Pseudo2mu1eFit} |
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\end{center} |
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\end{table} |
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|
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\begin{table}[h] |
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\begin{center} |
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\begin{tabular}{lccc} \hline \hline |
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Luminosity (pb$^{-1}$) &300 &400 & 500 \\ \hline |
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Observed Number of Events & 4 & 6 & 8 \\ \hline |
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$N$ - ZZ -Zgamma &3.3 $\pm$0.7 &5.1 $\pm$0.9 &6.8 $\pm$1.2\\ |
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$N^{non genuine Z}$ (Fit) &0.4 $\pm$0.2 &0.3 $\pm$0.8 &1.2 $\pm$3.6\\ |
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$N^{genuine Z}$ (matrix method) &0.7 $\pm$0.6 &1.1 $\pm$1.0 &1.7 $\pm$1.4\\ \hline |
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$N^{WZ}$ &2.2 $\pm$0.9 &3.6 $\pm$1.6 &4.0 $\pm$4.1\\ \hline |
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\WZ from MC & 4 & 6 & 8 \\ |
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\hline |
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\end{tabular} |
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\\ |
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\begin{tabular}{lccccc} \hline \hline |
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Luminosity (pb$^{-1}$) &600 &700 & 800 & 900 & 1000 \\ \hline |
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Observed Number of Events & 10 & 14 & 18 & 22 & 24 \\ \hline |
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$N$ - ZZ -Zgamma &8.6 $\pm$1.4 &12.3 $\pm$1.6 &16.1 $\pm$1.9 &19.9 $\pm$2.1 &21.7 $\pm$2.3\\ |
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$N^{non genuine Z}$ (Fit) &1.3 $\pm$3.0 & 1.2 $\pm$3.7 & 1.5 $\pm$3.1 & 1.3 $\pm$3.8 & 1.2 $\pm$3.0\\ |
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$N^{genuine Z}$ (matrix method) &2.0 $\pm$1.8 & 2.3 $\pm$2.1 & 2.4 $\pm$2.4 & 2.7 $\pm$2.8 & 2.9 $\pm$3.0\\ \hline |
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$N^{WZ}$ &5.3 $\pm$3.8 & 8.8 $\pm$4.5 &12.2 $\pm$4.3 &15.9 $\pm$5.1 &17.5 $\pm$4.8\\\hline |
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\WZ from MC & 10 & 13 & 15 & 19 & 21\\ |
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\hline\\ |
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\end{tabular} |
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\caption{Expected number of selected events for an integrated luminosity from 100 |
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pb$^{-1}$ to 1000 pb$^{-1}$ for 3$\mu$-channel and estimated background with 81 GeV $< M_Z < $ 101 GeV |
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.} |
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\label{tab:Pseudo3muFit} |
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\label{tab:Pseudo3mu} |
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\end{center} |
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\end{table} |
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Unfortunately, the statistics in all samples do not allow us to |
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perform proper pseudo experiment: |
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Unfortunately, the statistics in all samples do not allow us to perform proper pseudo-experiments: |
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\begin{itemize} |
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\item \W + 0 jets as a statistics below 100pb$^{-1}$, nevertheless we |
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do not expect to have so much events after the full selection been applied. |
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\item at 600 pb$^{-1}$, 12\% of W+3jet, 0$<$phat$<$100 GeV are missing to complete |
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the sample. Once again, this production is not so much expected to contribute directly |
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to the final state studied. |
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\item at 700 pb$^{-1}$, 6\% of W+5jet 0$<$phat$<$100 are missing to complete the sample. |
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\item at 700 pb$^{-1}$, 8\% of \Z + 0 jet are missing. This is not a major background |
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for the analysis. |
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\item at 900 pb$^{-1}$, a statistics of 6\% and 7\% \W +1jet 100$<$phat$<$300 and \W+2jets 100$<$phat$<$300 |
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respectively are missing. |
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\item at 1 fb$^{-1}$, mainly all \W +jets samples are missing statistics. |
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This samples are not fondammental as the efficiency is really low for this background. |
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But 9\% of \Z+1jet 0$<$phat$<$100, 10\% of \Z+2jets 0$<$phat$<$100 and 2\% of \Z+3jets 0$<$phat$<$100 |
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cannot be included in the event yield. This can be a problem and the results at 1fb$^{-1}$ should be |
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taken with care. |
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\item \W + 0 jets is generated for the statistics below 100 pb$^{-1}$, nevertheless we |
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do not expect to have so much events after the full selection is applied. |
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\item at 600 pb$^{-1}$, 12\% of \W + 3 jet, 0 $<\hat{p}<$ 100 GeV is missing to make a valid estimate. Once again, |
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this production is not so much expected to contribute directly to the final state studied. |
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\item at 700 pb$^{-1}$, 6\% of \W + 5 jet 0 $<\hat{p}<$ 100 GeV is missing to make a valid estimate. |
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\item at 700 pb$^{-1}$, 8\% of \Z + 0 jet is missing to make a valid estimate. This is not a major background |
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for the analysis, see note above. |
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\item at 900 pb$^{-1}$, 6\% and 7\% \W + 1 jet 100 $<\hat{p}<$ 300 and \W + 2 jets 100 $<\hat{p}<$ 300, respectively |
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are missing to make a valid estimation. |
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\item at 1 fb$^{-1}$, mainly all \W + jets have insufficient statistics to make a valid pseudo-experiment. |
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These samples are not fundamental as the contribution of this process to \WZ final state is very small. |
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However, 9\% of \Z + 1 jet 0$<\hat{p}<$100, 10\% of \Z + 2 jets 0$<\hat{p}<$100 and 2\% of \Z + 3 jets 0$<\hat{p}<$100 |
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cannot be included in the event yield. This can be a problem and the results at 1 \invfb should not be trusted. |
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\end{itemize} |
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