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\section{Event reconstruction} |
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\label{sec:eventReconstruction} |
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The four possible final states of \WZ |
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production with electrons and muons in the final state are studied, $\rm e^\pm \epem$, $\mu^\pm \epem$, $\rm e^\pm \mu^+\mu^-$ |
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and $\mu^\pm \mu^+\mu^-$. They are associated to four possible classes, |
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denoted as follows: |
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\begin{itemize} |
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\item $3e$: for \WZ events with $\W \to e \nu$ and $\Z\to \epem$. |
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\item $2e1\mu$: for \WZ events with $\W \to \mu \nu$ and $\Z\to \epem$. |
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\item $2\mu 1e$: for \WZ events with $\W \to e \nu$ and $\Z\to \mumu$. |
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\item $3\mu$: for \WZ events with $\W \to \mu \nu$ and $\Z\to \mumu$. |
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\end{itemize} |
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|
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\subsection{Trigger selection and efficiencies} |
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Events stemming from the three-lepton final states of $\WZ$ production |
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are collected by the electron and/or muon triggers. For each channel, |
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a minimun number of HLT requirements is chosen while keeping |
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the HLT efficiency for selected events close to 100\%. The same |
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HLT requirements are used for channels with the same Z decay mode: |
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\begin{itemize} |
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\item for $3e$ and $2e1\mu$: HLTSingleElectron or HLTDoubleElectronRelaxed |
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\item for $2\mu1e$ and $3\mu$: HLTSingleMuonIso |
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\end{itemize} |
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The HLT efficiencies for all modes for events passing the full |
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selection described in this section are given in table~\ref{tab:hlteff}. |
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\begin{table}[tbph] |
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\begin{center} |
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|
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\begin{tabular}{llc} \hline \hline |
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Channel & HLT selection & HLT efficiency \\ \hline |
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$3e$ & HLTSingleElectron or HLTDoubleElectronRelaxed & 0.996 \\ |
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$2e1\mu$ & HLTSingleElectron or HLTDoubleElectronRelaxed & 0.969 \\ |
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$2\mu 1e$ & HLTSingleMuonIso & 0.966 \\ |
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$3\mu$ & HLTSingleMuonIso & 0.994 \\ \hline \hline |
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\end{tabular} |
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|
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\end{center} |
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\caption{HLT Efficiencies, in percent, for all |
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the events in the generated phase space for events retained by |
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the complete event selection.} |
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\label{tab:hlteff} |
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\end{table} |
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\subsection{Lepton identification} |
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\label{sec:leptonId} |
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The requirements used for electron identification in this analysis are described |
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in~\cite{noteElectronID}. |
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Muon candidates are selected from global muons, which are reconstructed |
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combining measurements in the muon chambers and the central tracker. |
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An additional isolation criterion requires that the energy |
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measured in the calorimeters within a $\Delta R = 0.3$ cone around the |
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muon must be smaller than 3 GeV and the sum of the $p_t$ of tracks |
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within a $\Delta R = 0.25$ cone around the muon must be smaller than 2 |
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GeV. These cuts reduce the background from muons originated in |
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\b-quark decays of the $\Zbbbar$ background, which are close to tracks |
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and clusters from the other \b-quark decay products. |
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|
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%Figures~\ref{fig:muonisol} and ~\ref{fig:muonisoleffi} show the |
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%performance of the isolation cut. The distribution of the isolation |
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%variables for the $\Z\b\bbar(\epem\b\bbar)$ is particularly |
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%interesting, since muons only stem from \b-quark decays. |
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|
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The significance of the muon impact parameter in the plane |
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transverse to the beam, $S_{IP}$, discriminates against leptons from |
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heavy-quark decays in all Standard Model background processes. This |
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variable is defined as the ratio between the measured impact parameter |
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and its uncertainty: $S_{IP}=IP/\sigma_{IP}$, and is required to |
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satisfy $S_{IP}<3$. This requirement is applied only for muons |
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and not for electrons. For electrons, the dominant background |
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comes from fake electrons and not from heavy quark decays. |
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|
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\subsection{\WZ candidate selection} |
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\subsection{Signal extraction} |
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\subsection{\WZ candidate selection} |
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Events are accepted if they contain at least three charged leptons, |
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either electrons or muons, with $p_t > 15\,\mathrm{GeV}$ and $| \eta | < 2.5$ for |
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electrons,$| \eta | < 2.4$ for muons. |
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as discussed in~\ref{sec:leptonId}. |
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The \WZ candidate selection proceeds from building all possible |
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\Z-boson candidates from same-flavour opposite-charge lepton pairs. |
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For $\Z \to ee$ decays, electrons have to fullfil the loose requirements |
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defined in~\cite{noteElectronID}. |
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Events are retained if the mass of this \Z-boson candidate is |
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within 20 GeV of the Z-boson mass,$m_Z$. The event is |
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rejected if a second Z candidate is found. This second Z candidate is done |
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with all possible same-flavour opposite-charge combinations which are left |
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after removing the two leptons already used for the first Z candidate. This |
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veto on the presence of a second Z helps to suppress $ZZ$ events. The invariant |
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mass distribution for accepted \Z candidates is shown in |
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Figure~\ref{fig:zcandidates}. |
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|
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% and the \Z mass resolution is shown in |
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%Figure~\ref{fig:dzmass}. |
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After the \Z-boson candidate is identified, the lepton associated |
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to the \W-boson decay is chosen from the remaining electrons and muons |
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in the event that have not been used for reconstructing the \Z-boson. |
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Electrons are required to pass the tight criteria described in |
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\cite{noteElectronID}. If the event contains more than three leptons, |
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the highest $p_t$ is chosen as the one from the \W-boson decay, and |
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the additional leptons are not considered further. |
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The transverse momentum of this lepton is required to be larger |
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than 20 GeV. This last requirement is effective in rejecting |
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the \Zbbbar and \Zjets backgrounds, and the cut value is chosen in |
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the range that maximises the significance as shown in |
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Figure~\ref{fig:s_vs_wlpt}. |
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|
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An additional requirement on the isolation between electron and muons is applied |
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for the $2\mu 1e$ channel, by demanding $\Delta R$ between the electron associated |
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to the \W-decay and any of the two muons associated to the \Z-decay be greater than |
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0.1. This requirement allows to suppress the contributions of $\Z \to \mu\mu$ |
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decays, where one of the two muons radiates a photon which is reconstructed |
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as electrons, possibly after conversion, which shows up as a peak at around 60 GeV |
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in the Z mass distribution, as shown in figure~\ref{fig:Z2mu1e_60GeVPeak}. |
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|
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The expected number of events passing the various steps of the selection |
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is listed in Tables~\ref{tab:sel-effA} and~\ref{tab:sel-effB}. |
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Table~\ref{tab:wz-effimatrix} lists the final selection efficiency for |
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the different generated \W and \Z decays. It can be seen there that \WZ\ |
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events with both the \W and the \Z boson decaying into electrons or muons |
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almost always get reconstructed with the correct flavour. It is to be |
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noted in addition that each of our four selection channels gets a small |
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contribution from $W \to \tau \to e/\mu$ decays as one would expect. The |
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selection efficiency for these events is however smaller which is mostly due |
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to the \pt cut on the third lepton, since the \pt spectrum of electrons or |
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muons from $W \to \tau \to e/\mu$ decays is softer. |
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|
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\begin{table}[p] |
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\begin{center} |
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|
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\begin{tabular}{lcccc} \hline |
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Step & WZ & Z+jets & TTbar+jets & bbll\\ \hline |
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All events & 546 & 1.2679e+06 & 17556.1 & 72770.4 \\ |
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Found $Z \to ee$ & 219.517 (40.2045 \%) & 520695 (41.0674 \%) & 3474.61 (19.7914 \%) & 29563.3 (40.6254 \%) \\ |
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Z loose electron ID & 219.517 (100 \%) & 520695 (100 \%) & 3474.61 (100 \%) & 29563.3 (100 \%) \\ |
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Z Lepton Pt cut & 216.371 (98.5671 \%) & 515556 (99.0131 \%) & 3289.22 (94.6645 \%) & 29109.9 (98.4665 \%) \\ |
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Z Lepton $eta$ cut & 216.371 (100 \%) & 515556 (100 \%) & 3289.22 (100 \%) & 29109.9 (100 \%) \\ |
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Z Lepton IP cut & 206.797 (95.5751 \%) & 492205 (95.4707 \%) & 3011.11 (91.5448 \%) & 27833.5 (95.6153 \%) \\ |
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Found $W \to e$ & 42.8968 (20.7434 \%) & 301.116 (0.061177 \%) & 14.8797 (0.494158 \%) & 173.054 (0.621745 \%) \\ |
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W Lepton $\eta$ cut & 42.8968 (100 \%) & 301.116 (100 \%) & 14.8797 (100 \%) & 173.054 (100 \%) \\ |
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W Lepton Pt cut & 35.6425 (83.0889 \%) & 86.9864 (28.8879 \%) & 9.30549 (62.5383 \%) & 23.9385 (13.833 \%) \\ |
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W tight electron ID & 35.6425 (100 \%) & 86.9864 (100 \%) & 9.30549 (100 \%) & 23.9385 (100 \%) \\ |
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Passes HLT & 35.4852 (99.5587 \%) & 85.9427 (98.8002 \%) & 9.30549 (100 \%) & 23.4938 (98.1424 \%) \\ |
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Z mass window & 31.7106 (5.8078 \%) & 54.1554 (0.00427126 \%) & 3.2585 (0.0185605 \%) & 17.046 (0.0234243\%) \\ |
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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}{lcccc} \hline |
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Step & WZ & Z+jets & TTbar+jets & bbll\\ \hline |
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All events & 546 & 1.2679e+06 & 17556.1 & 72770.4 \\ |
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Found $Z \to ee$ & 219.517 (40.2045 \%) & 520695 (41.0674 \%) & 3474.61 (19.7914 \%) & 29563.3 (40.6254 \%) \\ |
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Z electron ID loose & 219.517 (100 \%) & 520695 (100 \%) & 3474.61 (100 \%) & 29563.3 (100 \%) \\ |
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Z Lepton Pt cut & 216.371 (98.5671 \%) & 515556 (99.0131 \%) & 3289.22 (94.6645 \%) & 29109.9 (98.4665 \%) \\ |
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Z Lepton $eta$ cut & 216.371 (100 \%) & 515556 (100 \%) & 3289.22 (100 \%) & 29109.9 (100 \%) \\ |
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Z Lepton IP cut & 206.797 (95.5751 \%) & 492205 (95.4707 \%) & 3011.11 (91.5448 \%) & 27833.5 (95.6153 \%) \\ |
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Found $W \to \mu$ & 57.1892 (27.6547 \%) & 5982.86 (1.21552 \%) & 815.122 (27.0705 \%) & 3808.22 (13.6821 \%) \\ |
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W Lepton $\eta$ cut & 57.1695 (99.9656 \%) & 5964.1 (99.6865 \%) & 815.122 (100 \%) & 3805.62 (99.9319 \%) \\ |
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W $\mu$ isolation & 52.1367 (91.1967 \%) & 2754.29 (46.1811 \%) & 85.5097 (10.4904 \%) & 1328.18 (34.9004 \%) \\ |
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W muon isolation & 39.8889 (76.5083 \%) & 22.2149 (0.806557 \%) & 18.8521 (22.0468 \%) & 16.6013 (1.24993 \%) \\ |
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Passes HLT & 38.7683 (97.1907 \%) & 21.2077 (95.466 \%) & 16.5627 (87.8556 \%) & 16.1566 (97.3214 \%) \\ |
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Z mass window & 34.6399 (6.34429 \%) & 17.3805 (0.00137081 \%) & 5.4405 (0.0309891 \%) & 14.0814 (0.0193505 \%) \\ |
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\hline |
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\end{tabular} |
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|
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\begin{tabular}{lcccc} \hline |
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Step & WZ & Z+jets & TTbar+jets & bbll\\ \hline |
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All events & 546 & 1.2679e+06 & 17556.1 & 72770.4 \\ |
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Found $Z \to \mu\mu$ & 326.484 (59.7955 \%) & 748256 (59.0152 \%) & 14081.6 (80.2087 \%) & 43207.1 (59.3746 \%) \\ |
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Z muon isolation & 282.27 (86.4575 \%) & 669556 (89.4822 \%) & 4201.52 (29.837 \%) & 37959.1 (87.8538 \%) \\ |
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Z Lepton $eta$ cut & 282.27 (100 \%) & 669547 (99.9987 \%) & 4200.47 (99.975 \%) & 37959.1 (99.9998 \%) \\ |
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Z Lepton Pt cut & 274.249 (97.1584 \%) & 657267 (98.1659 \%) & 3626.81 (86.3429 \%) & 36945.8 (97.3306 \%) \\ |
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Z Lepton IP cut & 249.792 (91.0824 \%) & 603257 (91.7827 \%) & 3125.35 (86.1737 \%) & 33937.7 (91.8581 \%) \\ |
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Found $W \to e$ & 51.9401 (20.7933 \%) & 797.766 (0.132243 \%) & 20.4415 (0.654055 \%) & 228.342 (0.672826 \%) \\ |
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W Lepton $\eta$ cut & 51.9401 (100 \%) & 797.766 (100 \%) & 20.4415 (100 \%) & 228.342 (100 \%) \\ |
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W tight electron ID & 51.9401 (100 \%) & 797.766 (100 \%) & 20.4415 (100 \%) & 228.342 (100 \%) \\ |
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W Lepton Pt cut & 43.2703 (83.3081 \%) & 519.647 (65.1378 \%) & 15.0823 (73.7829 \%) & 55.14 (24.148 \%)\\ |
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Passes HLT & 41.8745 (96.7742 \%) & 490.859 (94.46 \%) & 13.533 (89.7275 \%) & 54.2506 (98.3871 \%) \\ |
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Z mass window & 37.5298 (6.87358 \%) & 63.522 (0.00501 \%) & 5.02282 (0.02861 \%) & 20.0105 (0.0274981 \%) \\ |
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\hline |
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\end{tabular} |
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|
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\begin{tabular}{lcccc} \hline |
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Step & WZ & Z+jets & TTbar+jets & bbll\\ \hline |
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All events & 546 & 1.2679e+06 & 17556.1 & 72770.4 \\ |
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Found $Z \to \mu\mu$ & 326.484 (59.7955 \%) & 748256 (59.0152 \%) & 14081.6 (80.2087 \%) & 43207.1 (59.3746 \%) \\ |
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Z muon isolation & 282.27 (86.4575 \%) & 669556 (89.4822 \%) & 4201.52 (29.837 \%) & 37959.1 (87.8538 \%) \\ |
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Z Lepton $eta$ cut & 282.27 (100 \%) & 669547 (99.9987 \%) & 4200.47 (99.975 \%) & 37959.1 (99.9998 \%) \\ |
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Z Lepton Pt cut & 274.249 (97.1584 \%) & 657267 (98.1659 \%) & 3626.81 (86.3429 \%) & 36945.8 (97.3306 \%) \\ |
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Z Lepton IP cut & 249.792 (91.0824 \%) & 603257 (91.7827 \%) & 3125.35 (86.1737 \%) & 33937.7 (91.8581 \%) \\ |
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Found $W \to \mu$ & 73.015 (29.2303 \%) & 7135.7 (1.18286 \%) & 774.076 (24.7677 \%) & 4435.51 (13.0696 \%) \\ |
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W Lepton $\eta$ cut & 72.956 (99.9192 \%) & 7110.07 (99.6409 \%) & 774.076 (100 \%) & 4432.32 (99.9282 \%) \\ |
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W $\mu$ isolation & 66.724 (91.4578 \%) & 3382.99 (47.5803 \%) & 78.3017 (10.1155 \%) & 1560.97 (35.2178 \%) \\ |
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W muon isolation & 50.1118 (75.1031 \%) & 6.25174 (0.184799 \%) & 5.8096 (7.41951 \%) & 20.6775 (1.32466 \%) \\ |
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Passes HLT & 49.7972 (99.3723 \%) & 6.25174 (100 \%) & 5.8096 (100 \%) & 20.6034 (99.6416 \%) \\ |
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Z mass window & 45.1576 (8.27062 \%) & 4.9976 (0.000394162 \%) & 1.683 (0.00958638 \%) & 18.3059 (0.0251557 \%) \\ |
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\hline |
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\end{tabular} |
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\caption{Expected number of signal and background events passing the different |
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selections steps in the \WZ, \ttbar and \Zbbbar samples for an integrated luminosity |
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of 1 \invfb.} |
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\label{tab:sel-effA} |
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\end{center} |
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\end{table} |
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|
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\subsection{Systematic uncertainties} |
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|
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\subsection{Signal extraction} |
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|
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\input D0Matrix |
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\input zjetbackground |
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|
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|
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\subsection{Systematic uncertainties} |
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\input Sys |
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\begin{figure}[bt] |
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\begin{center} |
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\scalebox{0.8}{\includegraphics{figs/mtw_by_channel.eps}} |
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\caption{W transverse mass for the four signal categories. |
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The distributions show the number of expected events |
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for $1 fb^{-1}$. Only events with 81.1 GeV $< M_Z < $ 101.1 GeV are shown.} |
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\label{fig:mtw} |
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\end{center} |
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\end{figure} |
