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\clearpage
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\section{Selection}
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\label{sec:eventSelection}
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In this section, we list the event selection, electron and muon objects selections, jets, \MET, and b-tagging selections
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used in this analysis. These selections are based on those recommended by the relevant POG's.
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\subsection{Event Selection}
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We require the presence of at least one primary vertex satisfying the standard quality criteria; namely,
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vertex is not fake, $\rm{ndf}\geq4$, $\rho<2$ cm, and $|z|<24$ cm.
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\subsection{Lepton Selection}
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Because Z $\rightarrow\ell\ell$ ($\ell=e,\mu$) is a final state with very little background,
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we restrict ourselves to events in which the Z boson decays to electrons or muons only.
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Therefore opposite sign leptons passing the identification and isolation requirements described below are required in each event.
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\begin{itemize}
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\item \pt $> 20$~GeV and $|\eta|<2.4$;
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\item Opposite-sign same-flavor (SF) ee and $\mu\mu$ lepton pairs (opposite-flavor (OF) e$\mu$ lepton pairs are retained in a control
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sample used to estimate the FS contribution);
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\item For SF events, the dilepton invariant mass is required to be consistent with the Z mass; namely $81<m_{\ell\ell}<101$ GeV.
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\end{itemize}
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\subsubsection{Electron Selection}
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The electron selection is the loose working point recommended by the E/gamma POG, as documented at~\cite{ref:Egamma}.
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Electrons with \pt $>$ 20 GeV and $|\eta|<2.4$ are considered.
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We use PF-based isolation with a cone size of $\Delta R<0.3$, using the effective area rho corrections documented at~\cite{ref:Egammaiso},
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and we require a relative isolation $<$ 0.15.
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Electrons in the transition region defined by $1.4442 < |\eta_{SC}| < 1.566$ are rejected.
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Electrons with a selected muon with \pt $>$ 10 GeV within $\Delta R<0.1$ are rejected.
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The electron selection requirements are listed in Table~\ref{table:electrons} for completeness.
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\begin{table}[htb]
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\begin{center}
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\caption{\label{table:electrons} Summary of the electron selection requirements.}
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\begin{tabular}{l|cc}
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\hline
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Quantity & Barrel & Endcap \\
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\hline
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$\delta\eta$ & $<0.007$ & $<0.009$ \\
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$\delta\phi$ & $<0.15$ & $<0.10$ \\
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$\sigma_{i\eta i\eta}$ & $<0.01$ & $<0.03$ \\
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H/E & $<0.12$ & $<0.10$ \\
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$d_{0}$ (w.r.t. 1st good PV) & $<0.02$ cm & $<0.02$ cm \\
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$d_{z}$ (w.r.t. 1st good PV) & $<0.2$ cm & $<0.2$ cm \\
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$|1/E-1/P|$ & $<0.05~\rm{GeV}^{-1}$ & $<0.05~\rm{GeV}^{-1}$ \\
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PF isolation / \pt & $<0.15$ & $<0.15$ \\
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conversion rejection: fit probability & $<10^{-6}$ & $<10^{-6}$ \\
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conversion rejection: missing hits & $\leq1$ & $\leq1$ \\
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\hline
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\end{tabular}
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\end{center}
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\end{table}
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\subsubsection{Muon Selection}
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We use the tight muon selection recommended by the muon POG, as documented at~\cite{ref:muon}.
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Muons with \pt $>$ 20 GeV and $|\eta|<2.4$ are considered. We use PF-based isolation with a cone size
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of $\Delta R<0.3$, using the $\Delta\beta$ PU correction scheme, and we require a relative isolation of $<$ 0.15.
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The muon selection requirements are listed in Table~\ref{table:muons} for completeness.
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\begin{table}[htb]
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\begin{center}
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\caption{\label{table:muons} Summary of the muons selection requirements.}
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\begin{tabular}{l|c}
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\hline
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Quantity & Requirement \\
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\hline
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muon type & global muon and PF muon \\
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$\chi^2/\rm{ndf}$ & $<10$ \\
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muon chamber hits & $\geq1$ \\
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matched stations & $\geq2$ \\
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$d_{0}$ (w.r.t. 1st good PV) & $<0.02$ cm \\
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$d_{z}$ (w.r.t. 1st good PV) & $<0.5$ cm \\
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pixel hits & $\geq1$ \\
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tracker layers & $\geq5$ \\
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\hline
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\end{tabular}
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\end{center}
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\end{table}
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\subsection{Photons}
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\label{sec:phosel}
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As will be explained later, it is not essential that we select real photons.
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What is needed are jets that are predominantly electromagnetic, well measured in the ECAL, and hence less likely to contribute to fake MET. We select photons with:
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\begin{itemize}
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\item \pt $ > 22$ GeV
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\item $|\eta| < 2$
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\item $H/E < 0.1$
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\item No matching pixel track (pixel veto)
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\item There must be a pfjet of \pt $ >$ 10 GeV matched to the photon within $dR < 0.3$.
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The matched jet is required to have a neutral electromagnetic energy fraction of at least 70\%.
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\item
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We require that the pfjet \pt matched to the photon satisfy
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(pfjet \pt - photon \pt) $>$ -5~GeV.
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This removes a few rare cases in which ``overcleaning" of a
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%ECAL recHit
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pfjet
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generates fake MET.
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\item We also match photons to calojets and require (calojet \pt - photon \pt) $>$ -5~GeV
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(the same requirement used for pfjets). This is to remove other rare cases in which fake
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energy is added to the photon object but not the calojet.
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\item We reject photons which have an electron of at least \pt $>$ 10 GeV
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within $dR < 0.2$
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in order to reject
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conversions from electrons from W decays which are accompanied by real MET.
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\item We reject photons which are aligned with the MET to within 0.14 radians in phi.
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\end{itemize}
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\subsection{MET}
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We use pfmet, henceforth referred to simply as \MET.
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\subsection{Jets}
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\label{sec:jetsel}
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\begin{itemize}
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\item PF jets with L1FastL2L3 corrections (MC), L1FastL2L3residual corrections (data).
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\item $|\eta| < 2.5$
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\item Passes loose PFJet ID
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\item \pt $ > 30$ GeV for determining the jet multiplicity, \pt $ > 15$ GeV for calculation of \Ht
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\item For the creation of photon templates, the jet matched to the photon passing the photon selection described above is vetoed
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\item For the dilepton sample, jets are vetoed if they are within $\Delta R < 0.4$
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from any lepton \pt $ > 20$~GeV passing analysis selection
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\item To reject PU jets, we require the jets to satisfy $\beta>0.2$, defined for each jet using the $d_Z$ of the tracks in the jet with
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respect to the primary vertex (see App.~\ref{sec:pujets} for further details).
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To calculate $\beta$ we take the sum of the $p_{T}^{2}$ of the tracks associated to PFCandidates in the jet
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that are consistent with originating from the primary vertex ($d_Z<0.5$~cm), and divide by the sum $p_{T}^{2}$ of all the tracks:
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\begin{equation}
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\beta = \frac{\Sigma_{i}^{\rm{d_z<0.5~cm}} (p_{T}^{i})^2}{\Sigma_{i}^{\rm{all}} (p_{T}^{i})^2}
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\end{equation}
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\item A jet is considered as ``b-tagged'' if it passes the above criteria and the CSV medium working point.
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\end{itemize}
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