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\appendix |
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\section{Additional Cross Check on Background Estimation Studies} |
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\subsection{Further cross-checks} |
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The test described in the previous Section illustrates the robustness of the |
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matrix method to estimate the background correctly for a different |
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jet flavor composition in the $\Z+jet$ sample. |
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|
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In the following we further scrutinize the details of the background estimation. |
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We test the performance of the matrix method on a sample selected with the |
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full selection criteria but the requirement on the \W candidate transverse mass. |
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We also test a possibility of extracting the background without categorization |
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of the instrumental background contributions into genuine/fake \Z bosons. |
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|
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\subsubsection{Background estimation without the \W boson transverse mass requirement} |
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One of the ways to validate the matrix method is a comparison of its background |
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prediction with the MC truth information at different stage of application of the |
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\WZ signal selection criteria. We show that the matrix method works well with a very |
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loose selection criteria (see the Section above). In the following we perform |
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the comparison after applying the full selection criteria but the requirement on the |
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\W candidate transverse mass. |
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|
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We repeat the procedure described in Section~\ref{sec:moreDetailsBackground} for |
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every signature channels and provide the results of background estimation from processes |
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without real \Z boson in Table~\ref{tab:FitNoMWt} and final results in |
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Tables~\ref{tab:FinalNoMWtCutLoose} and \ref{tab:FinalNoMWtCut} for ``Loose'' |
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and ``Tight'' requirements on the \W lepton. The results agree with each other |
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within one sigma of uncertainty. |
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|
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In figures~\ref{fig:AllFits}, the fit approximation of the invariant |
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mass of \Z boson candidate is shown for each channel and for loose and |
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tight criteria. The fit is performed using an addition of a |
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convolution of a Gaussian and Breit-Wigner function and a line in |
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order to fit the background. |
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|
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|
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\begin{figure}[hbt] |
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\begin{center} |
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\scalebox{0.3}{\includegraphics{figs/Fit3eLoose.eps}\includegraphics{figs/Fit3eTight.eps}}\\ |
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\scalebox{0.3}{\includegraphics{figs/Fit2e1muLoose.eps}\includegraphics{figs/Fit2e1muTight.eps}}\\ |
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\scalebox{0.3}{\includegraphics{figs/Fit2mu1eLoose.eps}\includegraphics{figs/Fit2mu1eTight.eps}}\\ |
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\scalebox{0.3}{\includegraphics{figs/Fit3muLoose.eps}\includegraphics{figs/Fit3muTight.eps}}\\ |
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\caption{Invariante mass of \Z boson candidate for the different samples studied on the left when the lepton pass the loose criteria, on the right when the lepton pass the tight criteria.} |
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\label{fig:AllFits} |
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\end{center} |
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\end{figure} |
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|
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|
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The linear fit will take into account the background with non-genuine |
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\Z candidate but it will also account for some part of \Z+jets and |
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$Zb\bar{b}$ background as the gamma$^*$ will populate the side band. |
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The comparison can be seen in table~\ref{tab:CompFit}. |
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\begin{table}[h] |
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\begin{center} |
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\begin{tabular}{|l|c|c|c|c|c|c|c|} \hline |
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& \multicolumn{2}{c|}{Background with genuine \Z} & \multicolumn{4}{c|}{Background without |
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genuine \Z boson} \\ |
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Channel & $\Z+jets$ & $\Z b\bar{b}$ & $t\bar{t}$ & $\W+jets$ & $t\bar{t}$ + $\W+jets$ & Fit result \\ \hline |
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$3e$ Loose &2.8 & 2.9 & 0.8 & 0.1 & 0.9 & 1.0$ \pm $2.7 \\\hline |
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$3e$ Tight &0.8 & 1.2 & 0.4 & 0.1 & 0.5 & 0.7$ \pm $2.5 \\\hline |
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$2e1\mu$ Loose &1.3 & 4.7 & 4.5 & 0 & 4.5 & 4.2$ \pm $3.7 \\\hline |
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$2e1\mu$ Tight &0.0 & 0.1 & 0.5 & 0 & 0.5 & 0.6$ \pm $2.5 \\\hline |
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$2\mu1e$ Loose &4.1 & 2.9 & 0.5 & 0 & 0.5 & 0.9$ \pm $2.7 \\\hline |
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$2\mu1e$ Tight &0.8 & 1.3 & 0.4 & 0 & 0.4 & 0.6$ \pm $2.4 \\\hline |
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$3\mu$ Loose &1.9 & 4.2 & 4.1 & 0 & 4.1 & 2.3$ \pm $3.3 \\\hline |
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$3\mu$ Tight &0.1 & 0.3 & 0.2 & 0 & 0.2 & 0.4$ \pm $2.4 \\\hline |
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$3e$ Loose &44.6 & 12.7 & 1.6 & 0.4 & 2.0 & 6.6$\pm$4.2 \\\hline |
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$3e$ Tight &13.9 & 5.0 & 0.8 & 0.4 & 1.2 & 3.8$\pm$3.5 \\\hline |
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$2e1mu$ Loose &41.5 & 78.9 & 12.6 & 0 & 12.6 & 16.9$\pm$5.5 \\\hline |
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$2e1mu$ Tight &1.0 & 2.0 & 0.9 & 0 & 0.9 & 1.5$\pm$3.2 \\\hline |
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$2mu1e$ Loose &56.3 & 15.4 & 1.9 & 0 & 1.9 & 6.9$\pm$4.4 \\\hline |
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$2mu1e$ Tight &17.3 & 5.6 & 0.8 & 0 & 0.8 & 4.1$\pm$2.5 \\\hline |
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$3mu$ Loose &43.7 & 84.9 & 12.0 & 0 & 12.0 & 11.0$\pm$5.0 \\\hline |
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$3mu$ Tight &0.8 & 2.3 & 0.3 & 0 & 0.3 & 0.8$\pm$2.8 \\\hline |
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\end{tabular} |
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\end{center} |
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\caption{Comparison between Monte Carlo truth information and the results of the fit for the background without genuine \Z boson. Number of events are obtained in the invariant mass range between 81 and 101 GeV. The ``Loose'' and ``Tight'' selection criteria applied for third lepton considered. |
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%I AM NOT SURE I UNDERSTAND WHAT IS WRITTEN HERE |
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% One has to consider that this study as been perform on a smaller sample than the other part of the analysis a 10\% statistics error as to be counted until the study is performed on the whole samples. |
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} |
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\label{tab:CompFit} |
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\caption{Comparison between Monte Carlo truth information and the results of the fit for the background |
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without genuine \Z boson. Number of events are obtained in the invariant mass range between 81 and 101 GeV. The |
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``Loose'' and ``Tight'' selection criteria applied on the \W lepton. No requirement is applied on the transverse |
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\W candidate mass.} |
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\label{tab:FitNoMWt} |
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\end{table} |
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|
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|
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Nevertheless in association with the matrix method the background is |
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well estimated as one can see in table~\ref{tab:FinalXC}. |
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|
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\begin{table}[h] |
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\begin{center} |
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\begin{tabular}{lcccc} \hline \hline |
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& 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline |
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%$N_{Loose}$ - ZZ -Zgamma &19.7$\pm$1.1 &22.9$\pm$0.7 &22.9$\pm$1.1 &25.6$\pm$0.8 \\ |
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%$N_{Loose} ^{non genuine Z}$ (Fit) &1.0$\pm$1.5 &11.2$\pm$5.5 &3.1$\pm$2.4 & 4.8$\pm$3.7\\ |
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$N$ - ZZ -Zgamma &12.2$\pm$1.1 &8.7$\pm$0.6 &12.8$\pm$1.0 &11.1$\pm$0.7\\ |
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$N^{non genuine Z}$ (Fit)&0.7$\pm$2.5 &0.6$\pm$2.5 &0.6$\pm$2.4 &0.4$\pm$2.4\\ |
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$N^{genuine Z}$ (matrix method)& 3.2$\pm$1.8 &0.7$\pm$0.9 &4.6$\pm$2.1 &0.9$\pm$1.1\\\hline |
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$N^{WZ}$ & 8.3$\pm$3.2 &7.4$\pm$2.8 &7.6$\pm$3.3 &9.8$\pm$2.7\\\hline |
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\WZ from MC &7.9&8.0& 8.9 &10.1\\ |
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|
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$N$ - ZZ -Z$\gamma$ &75.3$\pm$7.3 &146.6$\pm$0.1 & 90.4$\pm$5.9 & 156.9$\pm$0.1\\ \hline |
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$N^{non genuine~Z}$ (Fit) &6.6$\pm$4.2 &16.9$\pm$5.5 & 6.9$\pm$ 4.4 & 11.0$\pm$5.0\\ \hline |
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$N^{genuine~Z}$ (matrix method)&52.5 $\pm$17.6 &122.2 $\pm$8.6 & 68.7 $\pm$15.1 & 136.0 $\pm$ 8.5\\ \hline |
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$N^{\WZ}$ &16.3$\pm$19.5 &7.5 $\pm$10.2 &14.8 $\pm$16.8 & 10.0 $\pm$9.8\\\hline |
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\WZ from MC &12.0&14.2& 13.6 &17.2\\ |
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\hline |
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\end{tabular} |
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|
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\caption{Expected number of selected events for an integrated luminosity of 300 |
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pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.} |
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\label{tab:FinalXC} |
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\caption{Expected number of selected events for an integrated luminosity of 300 \invpb |
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for the signal and estimated background for 81 GeV $< M_Z < $ 101 GeV and for ``Loose'' |
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\W lepton. No requirement is applied on the transverse \W candidate mass.} |
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\label{tab:FinalNoMWtCutLoose} |
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\end{center} |
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\end{table} |
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|
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|
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|
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|
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Check on Loosy Samples~\ref{tab:FitLoosy} (Linear Fit): |
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\begin{table}[h] |
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\begin{center} |
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\begin{tabular}{|l|c|c|c|c|c|c|c|} \hline |
| 71 |
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& \multicolumn{2}{c|}{Background with genuine \Z} & \multicolumn{4}{c|}{Background without |
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genuine \Z boson} \\ |
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Channel & $\Z+jets$ & $\Z b\bar{b}$ & $t\bar{t}$ & $\W+jets$ & $t\bar{t}$ + $\W+jets$ & Fit result \\ \hline |
| 74 |
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$3e$ Loose &17.4 & 14.1 & 1.2 & 0.1 & 1.3 & 4.0$ \pm $3.6 \\\hline |
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$3e$ Tight &5.3 & 5.8 & 0.7 & 0.1 & 0.8 & 2.7$ \pm $3.2 \\\hline |
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$2e1\mu$ Loose &16.5 & 83.1 & 10.0 & 0 & 10.0 & 13.1$ \pm $5.0 \\\hline |
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$2e1\mu$ Tight &0.3 & 2.0 & 1.0 & 0 & 1.0 & 1.3$ \pm $3.0 \\\hline |
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$2\mu1e$ Loose &27.5 & 20.1 & 15.0 & 0.2 & 15.3 & 23.7$ \pm $5.5 \\ \hline |
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$2\mu1e$ Tight &7.7 & 6.9 & 13.2 & 0.1 & 13.3 & 19.7$ \pm $5.2 \\ \hline |
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$3\mu$ Loose &33.4 & 138.2 & 45.8 & 0.7 & 46.4 & 48.7$ \pm $6.7 \\\hline |
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$3\mu$ Tight &8.9 & 25.2 & 19.7 & 0.2 & 19.9 & 23.5$ \pm $5.5 \\\hline |
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\begin{center} |
| 70 |
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\begin{tabular}{lcccc} \hline \hline |
| 71 |
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& 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline |
| 72 |
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$N$ - ZZ -Z$\gamma$ & 36.0 $\pm$7.1 & 15.2$\pm$0.1 & 40.2$\pm$5.7 & 18.0$\pm$0.1\\ \hline |
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$N^{non genuine~Z}$ (Fit) & 3.8 $\pm$3.5 & 1.5$\pm$3.2 & 4.1$\pm$2.5 & 0.8$\pm$2.8\\ \hline |
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$N^{genuine~Z}$ (matrix method) & 16.8 $\pm$6.1 & 7.3 $\pm$5.8 & 22.0 $\pm$7.4 & 8.2 $\pm$6.6\\ \hline |
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$N^{\WZ}$ & 15.4 $\pm$10.0 & 7.1 $\pm$6.6 & 14.1 $\pm$9.7 & 9.1 $\pm$7.1\\ \hline |
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\WZ from MC &11.6&12.3& 13.3 &14.9\\ |
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\hline |
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\end{tabular} |
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\caption{Expected number of data events for an integrated luminosity of 300 \invpb for the signal and estimated background for 81 GeV $< M_Z < $ 101 GeV and for ``Tight'' \W lepton. No requirement is applied |
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on the transverse \W candidate mass.} |
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\label{tab:FinalNoMWtCut} |
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\end{center} |
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\caption{Comparison between Monte Carlo truth information and the results of the fit for the background without genuine \Z boson. Number of events are obtained in the invariant mass range between 81 and 101 GeV. The ``Loose'' and ``Tight'' selection criteria applied for third lepton considered. |
| 96 |
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%I AM NOT SURE I UNDERSTAND WHAT IS WRITTEN HERE |
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% One has to consider that this study as been perform on a smaller sample than the other part of the analysis a 10\% statistics error as to be counted until the study is performed on the whole samples. |
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} |
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\label{tab:FitLoosy} |
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\end{table} |
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|
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Check on Without MWtCut Samples~\ref{tab:FitNoMWt} (Linear Fit): |
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\subsubsection{Performance of the matrix method without background categorization} |
| 86 |
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|
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The performance of the matrix method depends on the validity of the following three assumptions: |
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\begin{itemize} |
| 89 |
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\item the contribution from processes with two or more misidentified jets is negligible, |
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\item $p_{fake}$ should describe the probability of misidentified jets passing loose criteria to also |
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pass tight lepton requirements in the background to the signal, |
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\item the misidentified lepton is associated with the \W candidate decay. |
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\end{itemize} |
| 94 |
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|
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The first assumption is true for the \WZ analysis, and the second one is true if we assume |
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that the jet composition in the control sample used to establish $p_{fake}$ is the same as that |
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in the background in the \WZ data sample. This can be achieved by using $\W+X$ |
| 98 |
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processes as a control sample, as described in Section~\ref{sec:WPFake}. The latter assumption |
| 99 |
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is generally not true for $t\bar{t}$ processes, and therefore, we subtract background |
| 100 |
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without genuine \Z bosons using the fit results of the \Z candidate invariant mass. |
| 101 |
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|
| 102 |
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However, after applying the full selection criteria, the contribution from the backgrounds |
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without real \Z boson is negligible, and the fit results in an unacceptable large uncertainty |
| 104 |
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for the 300 \invpb scenario. Thus, it is possible to neglect the combinatorial bias from $t\bar{t}$ |
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processes with small integrated luminosity sample and forgo the fit altogether. In the following |
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we provide the results of estimation of the background without subtracting the estimated |
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non-genuine \Z boson background. |
| 108 |
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|
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The comparisons between predicted and true MC backgrounds are given in Tables~\ref{tab:FinalNoFitLoose} |
| 110 |
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and \ref{tab:FinalNoFit} for ``Loose'' and ``Tight'' \W lepton, respectively. |
| 111 |
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|
| 112 |
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\begin{table}[h] |
| 113 |
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\begin{center} |
| 114 |
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\begin{tabular}{|l|c|c|c|c|c|c|c|} \hline |
| 115 |
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& \multicolumn{2}{c|}{Background with genuine \Z} & \multicolumn{4}{c|}{Background without |
| 116 |
< |
genuine \Z boson} \\ |
| 117 |
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Channel & $\Z+jets$ & $\Z b\bar{b}$ & $t\bar{t}$ & $\W+jets$ & $t\bar{t}$ + $\W+jets$ & Fit result \\ \hline |
| 118 |
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$3e$ Loose &16.4 & 12.7 & 1.1 & 0.1 & 1.2 & 2.8$ \pm $3.4 \\\hline |
| 119 |
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$3e$ Tight &4.9 & 5.0 & 0.5 & 0.1 & 0.7 & 1.7$ \pm $2.9 \\\hline |
| 120 |
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$2e1\mu$ Loose &15.8 & 78.9 & 9.0 & 0 & 9.0 & 11.6$ \pm $4.9 \\\hline |
| 112 |
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$2e1\mu$ Tight &0.3 & 2.0 & 0.7 & 0 & 0.7 & 1.0$ \pm $2.8 \\\hline |
| 113 |
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$2\mu1e$ Loose &20.4 & 15.4 & 1.3 & 0 & 1.3 & 2.9$ \pm $3.5 \\\hline |
| 114 |
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$2\mu1e$ Tight &5.8 & 5.6 & 0.5 & 0 & 0.5 & 1.7$ \pm $3.0 \\\hline |
| 115 |
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$3\mu$ Loose &16.8 & 84.9 & 8.5 & 0 & 8.5 & 7.1$ \pm $4.4 \\\hline |
| 116 |
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$3\mu$ Tight &0.3 & 2.3 & 0.2 & 0 & 0.2 & 0.7$ \pm $2.8 \\\hline |
| 113 |
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\begin{center} |
| 114 |
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\begin{tabular}{lcccc} \hline \hline |
| 115 |
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& 3e &2e1$\mu$ & 2$\mu$1e &3$\mu$\\ \hline |
| 116 |
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$N$ - ZZ - Z$\gamma$ & 19.9$\pm$1.0 & 23.6$\pm$0.1 & 23.4$\pm$1.0 & 25.5$\pm$0.0\\ \hline |
| 117 |
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$N^{genuine~Z}$ (matrix method) & 10.0 $\pm$2.2 & 15.8 $\pm$0.7 & 14.5 $\pm$2.2 & 15.8 $\pm$0.7\\ \hline |
| 118 |
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$N^{WZ}$ & 9.9 $\pm$2.4 & 7.8 $\pm$0.7 & 8.9 $\pm$2.4 & 9.8 $\pm$0.7\\ \hline |
| 119 |
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\WZ from MC &8.1&9.0& 9.2 &11.3\\ |
| 120 |
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\hline |
| 121 |
|
\end{tabular} |
| 122 |
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\caption{Expected number of events for an integrated luminosity of 300 \invpb for the signal |
| 123 |
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and estimated background for 81 GeV $< M_Z < $ 101 GeV with ``Loose'' \W lepton criteria.} |
| 124 |
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\label{tab:FinalNoFitLoose} |
| 125 |
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\end{center} |
| 119 |
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\caption{Comparison between Monte Carlo truth information and the results of the fit for the background without genuine \Z boson. Number of events are obtained in the invariant mass range between 81 and 101 GeV. The ``Loose'' and ``Tight'' selection criteria applied for third lepton considered. |
| 120 |
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%I AM NOT SURE I UNDERSTAND WHAT IS WRITTEN HERE |
| 121 |
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% One has to consider that this study as been perform on a smaller sample than the other part of the analysis a 10\% statistics error as to be counted until the study is performed on the whole samples. |
| 122 |
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} |
| 123 |
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\label{tab:FitNoMWt} |
| 126 |
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\end{table} |
| 127 |
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|
| 126 |
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|
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In table~\ref{tab:FinalNoMWtCut}, the final results are presented if we remove the cut on the W transverse mass. Everthing is still in perfect agreement... |
| 128 |
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|
| 128 |
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\begin{table}[h] |
| 129 |
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\begin{center} |
| 130 |
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\begin{tabular}{lcccc} \hline \hline |
| 131 |
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& 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline |
| 132 |
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%$N_{Loose}$ - ZZ -Zgamma &19.7$\pm$1.1 &22.9$\pm$0.7 &22.9$\pm$1.1 &25.6$\pm$0.8 \\ |
| 133 |
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%$N_{Loose} ^{non genuine Z}$ (Fit) &1.0$\pm$1.5 &11.2$\pm$5.5 &3.1$\pm$2.4 & 4.8$\pm$3.7\\ |
| 134 |
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$N$ - ZZ -Zgamma &21.9$\pm$5.4 &15.2$\pm$1.0 &24.9$\pm$4.4 &17.8$\pm$1.3\\ |
| 135 |
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$N^{non genuine Z}$ (Fit)&1.7$\pm$2.9 &1.0$\pm$2.8 &1.7$\pm$3.0 &0.7$\pm$2.8\\ |
| 137 |
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$N^{genuine Z}$ (matrix method)& 8.4$\pm$3.5 &5.7$\pm$4.7 &11.2$\pm$4.3 &6.4$\pm$5.3\\\hline |
| 138 |
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$N^{WZ}$ & 11.8$\pm$7.0 &8.5$\pm$5.6 &12.0$\pm$6.8 &10.7$\pm$6.1\\\hline |
| 139 |
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\WZ from MC &11.6&12.3& 13.1 &14.9\\ |
| 140 |
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|
| 141 |
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\hline |
| 132 |
> |
$N$ - ZZ -Z$\gamma$ &12.4$\pm$1.0 &8.7$\pm$0.1 &13.1$\pm$0.9 &10.6$\pm$0.0\\ \hline |
| 133 |
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$N^{genuine~Z}$ (matrix method) &3.2 $\pm$1.7 &0.9 $\pm$1.0 &4.6 $\pm$2.1 &0.9 $\pm$1.1\\ \hline |
| 134 |
> |
$N^{\WZ}$ &9.2 $\pm$2.0 &7.7 $\pm$1.0 &8.5 $\pm$2.3 &9.6$\pm$1.1\\ \hline |
| 135 |
> |
\WZ from MC &7.9&8.1& 9.0 &10.1\\ \hline |
| 136 |
|
\end{tabular} |
| 137 |
< |
|
| 138 |
< |
\caption{Expected number of selected events for an integrated luminosity of 300 |
| 139 |
< |
pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.} |
| 146 |
< |
\label{tab:FinalNoMWtCut} |
| 137 |
> |
\caption{Expected number of events for an integrated luminosity of 300 \invpb for the signal |
| 138 |
> |
and estimated background for 81 GeV $< M_Z < $ 101 GeV and ``Tight'' \W lepton requirement.} |
| 139 |
> |
\label{tab:FinalNoFit} |
| 140 |
|
\end{center} |
| 141 |
|
\end{table} |
| 142 |
+ |
The agreement between estimated and MC true backgrounds is excellent. Smaller systematic uncertainty |
| 143 |
+ |
associated with the linear fit also results in a higher discovery potential, as described in the next Section. |
| 144 |
+ |
|
