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\clearpage |
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\newpage |
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\appendix |
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\section{Additional Cross Check on Background Estimation Studies} |
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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. It has to be noticed that due to a lack |
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of statistics in chowder soup, all bin with 0 events from chowder have |
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been modified in order to avoid to have an error at 0. The |
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corresponding error in the bin with no event correspond to the weight |
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of each process in Chowder soup. One can see that the errors are |
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large, and the fit is then not really constraint. |
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|
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\subsection{Further cross-checks} |
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The test described in the previous Section illustrate the robustness of the |
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matrix method to estimate the misidentification background correctly for varied |
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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 provide detailed information on the background extraction using the |
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default selection criteria, that without the requirement on the \W candidate |
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transverse mass, and finally using default selection criteria without subtracting |
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backgrounds that have no genuine \Z bosons. |
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|
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\subsubsection{Details on extracting background with matrix method} |
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|
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In Fig.~\ref{fig:AllFits} we provide dilepton mass fit information for each channel |
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for loose and tight \W lepton requirements using the full statistics of the CSA07 samples. |
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The fit is performed using an addition of a convolution of a Gaussian and Breit-Wigner function |
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and a line in order to fit the background. It has to be noticed that due to a lack |
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of statistics in ``Chowder soup'' sample, all bins with 0 events from the sample |
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have been modified in order to avoid to have a null uncertainty. The |
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corresponding uncertainty in the bin with no events correspond to the weight |
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of each process in the ``Chowder soup''. One can see that the uncertainties are |
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large, and the fit is not really constrained. |
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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/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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\caption{Invariant mass of \Z boson candidate for $3e$, $2e1\mu$, $2\mu1e$, and $3\mu$ |
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signatures (from top to bottom) for the lepton passing loose (left) and tight (right) identification |
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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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The linear fit takes into account not only the background with non-genuine |
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\Z boson but it also accounts for some part of the \Z+jets and |
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$Zb\bar{b}$ background as the $\gamma^*$ processes populate the sidebands as well. |
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However, the results are still consistent within errors, as it can be seen by comparison |
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of the last two columns 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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Channel & $\Z+jets$ & $\Z b\bar{b}$ & $t\bar{t}$ & $\W+jets$ & Combined & Fit result \\ \hline |
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$3e$ Loose &7.1 & 2.9 & 1.1 & 0.4 & 1.5 & 1.5$ \pm $3.0 \\\hline |
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$3e$ Tight &2.0 & 1.2 & 0.6 & 0.4 & 1.0 & 1.1$ \pm $2.8 \\\hline |
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$2e1mu$ Loose &4.0 & 4.7 & 6.2 & 0.0 & 6.2 & 6.0$ \pm $4.1 \\\hline |
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$2e1mu$ Tight &0.0 & 0.1 & 0.7 & 0.0 & 0.7 & 1.0$ \pm $2.8 \\\hline |
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$2mu1e$ Loose &10.1 & 2.9 & 0.8 & 0.0 & 0.8 & 1.6$ \pm $3.1 \\\hline |
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$2mu1e$ Tight &1.8 & 1.3 & 0.6 & 0.0 & 0.6 & 1.0$ \pm $2.7 \\\hline |
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$3mu$ Loose &4.5 & 4.2 & 5.9 & 0.0 & 5.9 & 3.1$ \pm $3.5 \\\hline |
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$3mu$ Tight &0.1 & 0.3 & 0.3 & 0.0 & 0.3 & 0.5$ \pm $2.5 \\\hline |
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$2e1\mu$ Loose &4.0 & 4.7 & 6.2 & 0.0 & 6.2 & 6.0$ \pm $4.1 \\\hline |
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$2e1\mu$ Tight &0.0 & 0.1 & 0.7 & 0.0 & 0.7 & 1.0$ \pm $2.8 \\\hline |
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$2\mu 1e$ Loose &10.1 & 2.9 & 0.8 & 0.0 & 0.8 & 1.6$ \pm $3.1 \\\hline |
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$2\mu 1e$ Tight &1.8 & 1.3 & 0.6 & 0.0 & 0.6 & 1.0$ \pm $2.7 \\\hline |
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$3\mu$ Loose &4.5 & 4.2 & 5.9 & 0.0 & 5.9 & 3.1$ \pm $3.5 \\\hline |
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$3\mu$ Tight &0.1 & 0.3 & 0.3 & 0.0 & 0.3 & 0.5$ \pm $2.5 \\\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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} |
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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 on the \W lepton candidate.} |
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\label{tab:CompFit} |
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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}.The corresponding figure can be |
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seen~\ref{fig:FinalMatrix3e}~\ref{fig:FinalMatrix2e1mu}~\ref{fig:FinalMatrix2mu1e}~\ref{fig:FinalMatrix3mu} |
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for $3e$, $2e1\mu$, $2\mu1e$ and $3\mu$ channels respectively. |
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The comparison between estimated background and the MC truth information is provided |
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in Table~\ref{tab:FinalXCLoose} for ``Loose'' and \ref{tab:FinalXC} for ``Tight'' lepton candidates. |
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Within uncertainties the results agree with each other for every signature and every category of |
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\W lepton identification. The agreement between predicted and MC truth background |
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as function of the dilepton mass is given in Figs.~\ref{fig:FinalMatrix3e}-\ref{fig:FinalMatrix3mu} |
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for all four signal categories respectively. |
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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$ - ZZ -Zgamma &12.4$\pm$1.0 &8.7$\pm$0.0&13.1$\pm$0.9&10.6$\pm$0.0\\ \hline |
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$N^{non genuine Z}$ (Fit)&1.1$\pm$2.8&1.0$\pm$2.8&1.0$\pm$2.7&0.5$\pm$2.5\\ \hline |
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$N^{genuine Z}$ (matrix method)&3.2 $\pm$1.8&0.9 $\pm$1.1&4.6 $\pm$2.1&0.9 $\pm$1.1\\ \hline |
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$N^{WZ}$ & 8.2$\pm$3.5&7.7 $\pm$3.2 &7.6$\pm$3.5&9.6 $\pm$2.8\\ \hline |
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\WZ from MC &7.9&8.1& 9.0 &10.1\\ |
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|
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$N$ - \ZZ -\Z$\gamma$ &19.9$\pm$1.0&23.6$\pm$0.0&23.4$\pm$1.0&25.5$\pm$0.0\\ \hline |
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$N^{non genuine \Z}$ (Fit)&1.5$\pm$3.0&6.0$\pm$4.1&1.6$\pm$3.1&3.1$\pm$3.5\\ \hline |
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$N^{genuine \Z}$ (matrix method)&10.1 $\pm$6.8&15.8 $\pm$8.4&14.5 $\pm$6.8&15.8 $\pm$5.7\\ \hline |
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$N^{\WZ}$ & 8.8$\pm$7.5&7.8$\pm$11.1&7.9$\pm$7.6&9.8 $\pm$7.4\\ \hline |
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\WZ from MC &8.1&9.0& 9.2 &11.3\\ |
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\hline |
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\end{tabular} |
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|
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\caption{Expected number of selected events for an integrated luminosity of 300 |
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pb$^{-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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pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV |
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with the full selection criteria applied but the requirement on the \W lepton which is |
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required to pass only ``Loose'' criteria.} |
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\label{tab:FinalXCLoose} |
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\end{center} |
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\end{table} |
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|
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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$ - ZZ -Zgamma &19.9$\pm$1.0&23.6$\pm$0.0&23.4$\pm$1.0&25.5$\pm$0.0\\ \hline |
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$N^{non genuine Z}$ (Fit)&1.5$\pm$3.0&6.0$\pm$4.1&1.6$\pm$3.1&3.1$\pm$3.5\\ \hline |
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$N^{genuine Z}$ (matrix method)&10.1 $\pm$6.8&15.8 $\pm$8.4&14.5 $\pm$6.8&15.8 $\pm$5.7\\ \hline |
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$N^{WZ}$ & 8.8$\pm$7.5&7.8$\pm$11.1&7.9$\pm$7.6&9.8 $\pm$7.4\\ \hline |
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\WZ from MC &8.1&9.0& 9.2 &11.3\\ |
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|
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\hline |
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$N$ - ZZ -Zgamma &12.4$\pm$1.0 &8.7$\pm$0.1 &13.1$\pm$0.9&10.6$\pm$0.0\\ \hline |
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$N^{non genuine Z}$ (Fit)&1.1$\pm$2.8&1.0$\pm$2.8&1.0$\pm$2.7&0.5$\pm$2.5\\ \hline |
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$N^{genuine Z}$ (matrix method)&3.2 $\pm$1.8&0.9 $\pm$1.1&4.6 $\pm$2.1&0.9 $\pm$1.1\\ \hline |
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$N^{WZ}$ & 8.2$\pm$3.5&7.7 $\pm$3.2 &7.6$\pm$3.5&9.6 $\pm$2.8\\ \hline |
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\WZ from MC &7.9&8.1& 9.0 &10.1\\ \hline |
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\end{tabular} |
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|
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\caption{Loose Sample: Expected number of selected events for an integrated luminosity of 300 |
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pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.} |
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\label{tab:FinalXCLoose} |
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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 for |
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the full selection criteria applied.} |
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\label{tab:FinalXC} |
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\end{center} |
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\end{table} |
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|
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\begin{figure}[hbt] |
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\begin{center} |
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\scalebox{0.8}{\includegraphics{figs/MatrixMethod3eLooseTightZmassMWtCut.eps}} |
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\caption{Result of Matrix Method application for $3e$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.} |
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\scalebox{0.62}{\includegraphics{figs/MatrixMethod3eLooseTightZmassMWtCut.eps}} |
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\caption{Comparison between background predicted with matrix method and MC truth information for the |
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$3e$ channel as a function of the \Z boson candidate invariant mass for loose (a, c) and tight (b, d) requirements |
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on the \W lepton for background (a, b) and signal (c, d).} |
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\label{fig:FinalMatrix3e} |
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\end{center} |
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\end{figure} |
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|
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\begin{figure}[hbt] |
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\begin{center} |
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\scalebox{0.8}{\includegraphics{figs/MatrixMethod2e1muLooseTightZmassMWtCut.eps}} |
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\caption{Result of Matrix Method application for $2e1\mu$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.} |
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\label{fig:FinalMatrix2e1mu} |
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\scalebox{0.62}{\includegraphics{figs/MatrixMethod2e1muLooseTightZmassMWtCut.eps}} |
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\caption{ |
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Comparison between background predicted with matrix method and MC truth information for the |
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$2e1\mu$ channel as a function of the \Z boson candidate invariant mass for loose (a, c) and tight (b, d) requirements |
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on the \W lepton for background (a, b) and signal (c, d).} |
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\label{fig:FinalMatrix2e1mu} |
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\end{center} |
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\end{figure} |
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|
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\begin{figure}[hbt] |
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\begin{center} |
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\scalebox{0.8}{\includegraphics{figs/MatrixMethod2mu1eLooseTightZmassMWtCut.eps}} |
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\caption{Result of Matrix Method application for $2\mu1e$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.} |
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\scalebox{0.62}{\includegraphics{figs/MatrixMethod2mu1eLooseTightZmassMWtCut.eps}} |
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\caption{Comparison between background predicted with matrix method and MC truth information for the |
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$2\mu 1e$ channel as a function of the \Z boson candidate invariant mass for loose (a, c) and tight (b, d) requirements |
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on the \W lepton for background (a, b) and signal (c, d).} |
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\label{fig:FinalMatrix2mu1e} |
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\end{center} |
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\end{figure} |
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|
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\begin{figure}[hbt] |
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\begin{center} |
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\scalebox{0.8}{\includegraphics{figs/MatrixMethod3muLooseTightZmassMWtCut.eps}} |
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\caption{Result of Matrix Method application for $3\mu$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.} |
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\scalebox{0.62}{\includegraphics{figs/MatrixMethod3muLooseTightZmassMWtCut.eps}} |
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\caption{Comparison between background predicted with matrix method and MC truth information for the |
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$3\mu$ channel as a function of the \Z boson candidate invariant mass for loose (a, c) and tight (b, d) requirements |
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on the \W lepton for background (a, b) and signal (c, d).} |
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\label{fig:FinalMatrix3mu} |
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\end{center} |
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\end{figure} |
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|
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|
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+ |
\clearpage |
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\subsubsection{Background estimation without the \W boson transverse mass requirement} |
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|
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Check on Without MWtCut Samples~\ref{tab:FitNoMWt} (Linear Fit): |
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We also estimate background to the \WZ signal for the selection criteria without |
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the requirement on the transverse \W boson candidate mass. The results of |
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extraction of the background sources without real \Z boson are given in Table~\ref{tab:FitNoMWt}. |
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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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$3mu$ 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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\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.} |
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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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In table~\ref{tab:FinalNoMWtCut}, the final results are presented if |
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we remove the cut on the W transverse mass. Everthing is still in |
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perfect agreement... The corresponding figure can be |
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seen~\ref{fig:FinalMatrix3eNoWtCut}~\ref{fig:FinalMatrix2e1muNoWtCut}~\ref{fig:FinalMatrix2mu1eNoWtCut}~\ref{fig:FinalMatrix3muNoWtCut} |
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for $3e$, $2e1\mu$, $2\mu1e$ and $3\mu$ channels respectively. |
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The comparison between the estimated and MC truth backgrounds is given |
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in Tables~\ref{tab:FinalNoMWtCutLoose} and {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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\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$ - ZZ -Zgamma &35.9505$\pm$7.12087&15.9252$\pm$0.00840717&40.1673$\pm$5.70847&17.967$\pm$0.00420358\\ \hline |
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$N^{non genuine Z}$ (Fit)&3.76001$\pm$3.52367&1.45461$\pm$3.15729&4.10686$\pm$2.52845&0.750563$\pm$2.77128\\ \hline |
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$N^{genuine Z}$ (matrix method)&18.7345 $\pm$6.09299&8.35304 $\pm$6.61818&23.4279 $\pm$7.47204& 8.86174 $\pm$7.06819\\ \hline |
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$N^{WZ}$ &10.0951 $\pm$7.97988&7.56371 $\pm$7.47561&11.031 $\pm$8.8933& 9.10106 $\pm$7.62906\\ \hline |
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\WZ from MC &11.6&12.3& 13.3 &14.9\\ |
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|
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$N$ - \ZZ -\Z$\gamma$ &75.3$\pm$7.3&146.6$\pm$0.0&90.4$\pm$5.9&156.9$\pm$0.0\\ \hline |
| 185 |
> |
$N^{non genuine \Z}$ (Fit)&6.6$\pm$4.2&16.9$\pm$5.5&6.9$\pm$4.4&11.0$\pm$5.0\\ \hline |
| 186 |
> |
$N^{genuine \Z}$ (matrix method)&58.5 $\pm$14.4&139.2 $\pm$20.3&73.2 $\pm$14.9& 147.7 $\pm$14.7\\ \hline |
| 187 |
> |
$N^{\WZ}$ &9.5$\pm$16.4&7.4 $\pm$27.0&11.3 $\pm$17.0& 9.2 $\pm$19.0\\\hline |
| 188 |
> |
\WZ from MC &12.0&14.2& 13.6 &17.2\\ |
| 189 |
|
\hline |
| 190 |
|
\end{tabular} |
| 191 |
< |
|
| 192 |
< |
\caption{Expected number of selected events for an integrated luminosity of 300 |
| 193 |
< |
pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.} |
| 194 |
< |
\label{tab:FinalNoMWtCut} |
| 191 |
> |
\caption{Expected number of selected events for an integrated luminosity of 300 \invpb |
| 192 |
> |
for the signal and estimated background for 81 GeV $< M_Z < $ 101 GeV and for ``Loose'' |
| 193 |
> |
\W lepton.} |
| 194 |
> |
\label{tab:FinalNoMWtCutLoose} |
| 195 |
|
\end{center} |
| 196 |
|
\end{table} |
| 197 |
|
|
| 199 |
|
\begin{center} |
| 200 |
|
\begin{tabular}{lcccc} \hline \hline |
| 201 |
|
& 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline |
| 202 |
< |
$N$ - ZZ -Zgamma &75.3302$\pm$7.2764&146.642$\pm$0.0336287&90.4007$\pm$5.87661&156.943$\pm$0.0252215\\ \hline |
| 203 |
< |
$N^{non genuine Z}$ (Fit)&6.58354$\pm$4.18822&16.9415$\pm$5.45238&6.90489$\pm$4.44438&10.9672$\pm$4.95535\\ \hline |
| 204 |
< |
$N^{genuine Z}$ (matrix method)&58.5455 $\pm$14.4155&139.217 $\pm$20.2565&73.2121 $\pm$14.8922& 147.696 $\pm$14.674\\ \hline |
| 205 |
< |
$N^{WZ}$ &9.50837 $\pm$16.3918&7.39079 $\pm$26.9642&11.312 $\pm$17.0061& 9.22217 $\pm$18.977\\\hline |
| 206 |
< |
\WZ from MC &12.0&14.2& 13.6 &17.2\\ |
| 193 |
< |
|
| 202 |
> |
$N$ - \ZZ -\Z$\gamma$ &36.0$\pm$7.1&15.9$\pm$0.0&40.2$\pm$5.7&18.0$\pm$0.0\\ \hline |
| 203 |
> |
$N^{non genuine \Z}$ (Fit)&3.8$\pm$3.5&1.5$\pm$3.2&4.1$\pm$2.5&0.8$\pm$2.8\\ \hline |
| 204 |
> |
$N^{genuine \Z}$ (matrix method)&18.7 $\pm$6.1&8.4 $\pm$6.6&23.4 $\pm$7.5& 8.9 $\pm$7.1\\ \hline |
| 205 |
> |
$N^{\WZ}$ &10.1 $\pm$8.0&7.6 $\pm$7.5&11.0 $\pm$8.9& 9.1 $\pm$7.6\\ \hline |
| 206 |
> |
\WZ from MC &11.6&12.3& 13.3 &14.9\\ |
| 207 |
|
\hline |
| 208 |
|
\end{tabular} |
| 209 |
< |
|
| 210 |
< |
\caption{Loose Sample: Expected number of selected events for an integrated luminosity of 300 |
| 198 |
< |
pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.} |
| 199 |
< |
\label{tab:FinalNoMWtCutLoose} |
| 209 |
> |
\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.} |
| 210 |
> |
\label{tab:FinalNoMWtCut} |
| 211 |
|
\end{center} |
| 212 |
|
\end{table} |
| 213 |
|
|
| 214 |
< |
\begin{figure}[hbt] |
| 215 |
< |
\begin{center} |
| 216 |
< |
\scalebox{0.8}{\includegraphics{figs/MatrixMethod3eLooseTightZmassNoCutMWt.eps}} |
| 217 |
< |
\caption{Before M$_T$(W) criteria: Result of Matrix Method application for $3e$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.} |
| 218 |
< |
\label{fig:FinalMatrix3eNoWtCut} |
| 219 |
< |
\end{center} |
| 220 |
< |
\end{figure} |
| 221 |
< |
|
| 222 |
< |
\begin{figure}[hbt] |
| 223 |
< |
\begin{center} |
| 224 |
< |
\scalebox{0.8}{\includegraphics{figs/MatrixMethod2e1muLooseTightZmassNoCutMWt.eps}} |
| 225 |
< |
\caption{Before M$_T$(W) criteria: Result of Matrix Method application for $2e1\mu$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.} |
| 226 |
< |
\label{fig:FinalMatrix2e1muNoWtCut} |
| 227 |
< |
\end{center} |
| 228 |
< |
\end{figure} |
| 229 |
< |
|
| 230 |
< |
\begin{figure}[hbt] |
| 231 |
< |
\begin{center} |
| 232 |
< |
\scalebox{0.8}{\includegraphics{figs/MatrixMethod2mu1eLooseTightZmassNoCutMWt.eps}} |
| 233 |
< |
\caption{Before M$_T$(W) criteria: Result of Matrix Method application for $2\mu1e$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.} |
| 223 |
< |
\label{fig:FinalMatrix2mu1eNoWtCut} |
| 224 |
< |
\end{center} |
| 225 |
< |
\end{figure} |
| 214 |
> |
\subsubsection{Performance of the matrix method without background categorization} |
| 215 |
> |
The performance of the matrix method depends on the validity of the following two assumptions: |
| 216 |
> |
the $p_{fake}$ should describe the probability of misidentified jets passing loose criteria to also |
| 217 |
> |
pass tight lepton requirements, and there must be only one misidentified lepton. If the former |
| 218 |
> |
challenge can be tackled by estimating $p_{fake}$ in the sample with the jet composition similar |
| 219 |
> |
to that of the major \WZ background (\W+jets in this case), then the latter can be safely assumed |
| 220 |
> |
if the sources of backgrounds with multiple leptons are suppressed. The latter can be checked |
| 221 |
> |
with data by measuring comparing \W+jets cross-section measured in data with MC truth information |
| 222 |
> |
and estimating the \W+jets background to the \WZ signal. As total $\W+jets$ background to |
| 223 |
> |
\WZ signal is very small, we can neglect background contribution with multiple misidentified leptons |
| 224 |
> |
to the signal. |
| 225 |
> |
|
| 226 |
> |
Therefore, with small data sample, it might be a good approximation not to divide instrumental |
| 227 |
> |
background into genuine \Z boson and fake \Z boson categories, but apply the matrix method |
| 228 |
> |
directly to the dilepton |
| 229 |
> |
invariant mass after the physics backgrounds are subtracted. This results in smaller |
| 230 |
> |
systematic uncertainties associated with the fit. We follow this procedure and provide the |
| 231 |
> |
comparisons between predicted and true MC backgrounds |
| 232 |
> |
in Tables~\ref{tab:FinalNoFitLoose} and \ref{tab:FinalNoFit} for ``Loose'' and ``Tight'' |
| 233 |
> |
\W lepton, respectively. |
| 234 |
|
|
| 227 |
– |
\begin{figure}[hbt] |
| 228 |
– |
\begin{center} |
| 229 |
– |
\scalebox{0.8}{\includegraphics{figs/MatrixMethod3muLooseTightZmassNoCutMWt.eps}} |
| 230 |
– |
\caption{Before M$_T$(W) criteria: Result of Matrix Method application for $3\mu$ channel for Invariante mass of \Z boson candidate plot (a) and (c) when the lepton pass the loose criteria, (b) and (d) when the lepton pass the tight criteria. (a) and (b) represent the estimation of the background, (c) and (d) represent estimation of signal.} |
| 231 |
– |
\label{fig:FinalMatrix3muNoWtCut} |
| 232 |
– |
\end{center} |
| 233 |
– |
\end{figure} |
| 234 |
– |
|
| 235 |
– |
|
| 236 |
– |
WIHTOUT FITTING: |
| 235 |
|
\begin{table}[h] |
| 236 |
|
\begin{center} |
| 237 |
|
\begin{tabular}{lcccc} \hline \hline |
| 238 |
|
& 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline |
| 239 |
< |
$N$ - ZZ -Zgamma &12.4437$\pm$0.992046 &8.69811$\pm$0&13.1255$\pm$0.937399&10.5715$\pm$0\\ \hline |
| 240 |
< |
$N^{genuine Z}$ (matrix method)&3.21939 $\pm$1.56769&15.8043 $\pm$0.691583&4.63515 $\pm$1.91862&0.945652 $\pm$1.12544\\ \hline |
| 241 |
< |
$N^{WZ}$ &8.23222 $\pm$1.56769&7.78552 $\pm$0.691583&7.55297 $\pm$1.91862&9.62584 $\pm$1.12544\\ \hline |
| 242 |
< |
\WZ from MC &7.9&8.1& 9.0 &10.1\\ |
| 245 |
< |
|
| 239 |
> |
$N$ - \ZZ -\Z$\gamma$ &19.9$\pm$1.0&23.6$\pm$0.0&23.4$\pm$1.0&25.5$\pm$0.0\\ \hline |
| 240 |
> |
$N^{genuine \Z}$ (matrix method)&10.1 $\pm$0.6&0.9 $\pm$1.0&14.5 $\pm$0.9&15.8 $\pm$0.7\\ \hline |
| 241 |
> |
$N^{\WZ}$ &8.8 $\pm$0.6&7.7 $\pm$1.0&7.9 $\pm$0.9&9.8 $\pm$0.7\\ \hline |
| 242 |
> |
\WZ from MC &8.1&9.0& 9.2 &11.3\\ |
| 243 |
|
\hline |
| 244 |
|
\end{tabular} |
| 245 |
< |
|
| 246 |
< |
\caption{Expected number of selected events for an integrated luminosity of 300 |
| 247 |
< |
pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.} |
| 251 |
< |
\label{tab:FinalNoFit} |
| 245 |
> |
\caption{Expected number of events for an integrated luminosity of 300 \invpb for the signal |
| 246 |
> |
and estimated background for 81 GeV $< M_Z < $ 101 GeV with ``Loose'' \W lepton criteria.} |
| 247 |
> |
\label{tab:FinalNoFitLoose} |
| 248 |
|
\end{center} |
| 249 |
|
\end{table} |
| 250 |
|
|
| 252 |
|
\begin{center} |
| 253 |
|
\begin{tabular}{lcccc} \hline \hline |
| 254 |
|
& 3e &2e1$\mu$ &2$\mu$1e &3$\mu$\\ \hline |
| 255 |
< |
$N$ - ZZ -Zgamma &19.9098$\pm$1.00886&23.5941$\pm$0.00420358&23.3592$\pm$0.95001&25.5227$\pm$0.00420358\\ \hline |
| 256 |
< |
$N^{genuine Z}$ (matrix method)&10.0606 $\pm$0.621487&0.948261 $\pm$1.03651&14.4848 $\pm$0.885223&15.7609 $\pm$0.692575\\ \hline |
| 257 |
< |
$N^{WZ}$ &8.84029 $\pm$0.62148&7.74985 $\pm$1.03651&7.92435 $\pm$0.885223&9.75762 $\pm$0.692575\\ \hline |
| 258 |
< |
\WZ from MC &8.1&9.0& 9.2 &11.3\\ |
| 263 |
< |
|
| 264 |
< |
\hline |
| 255 |
> |
$N$ - \ZZ -\Z$\gamma$ &12.4$\pm$1.0 &8.7$\pm$0&13.1$\pm$0.9&10.6$\pm$0.0\\ \hline |
| 256 |
> |
$N^{genuine \Z}$ (matrix method)&3.2 $\pm$1.6&15.8 $\pm$0.7&4.6 $\pm$1.9&0.9 $\pm$1.1\\ \hline |
| 257 |
> |
$N^{\WZ}$ &8.2 $\pm$1.6&7.8 $\pm$0.7&7.6 $\pm$1.9&9.6$\pm$1.1\\ \hline |
| 258 |
> |
\WZ from MC &7.9&8.1& 9.0 &10.1\\ \hline |
| 259 |
|
\end{tabular} |
| 260 |
< |
|
| 261 |
< |
\caption{Loose Sample: Expected number of selected events for an integrated luminosity of 300 |
| 262 |
< |
pb$^{-1}$ for the signal and estimated background with 81 GeV $< M_Z < $ 101 GeV.} |
| 269 |
< |
\label{tab:FinalNoFitLoose} |
| 260 |
> |
\caption{Expected number of events for an integrated luminosity of 300 \invpb for the signal |
| 261 |
> |
and estimated background for 81 GeV $< M_Z < $ 101 GeV and ``Tight'' \W lepton requirement.} |
| 262 |
> |
\label{tab:FinalNoFit} |
| 263 |
|
\end{center} |
| 264 |
|
\end{table} |
| 265 |
+ |
The agreement between estimated and MC true backgrounds is excellent. |
