
 \section{Data}
For this analysis, data collected at $\sqrt{s} = 13$\,TeV during $2015\textendash2018$, corresponding to an integrated luminosity of 139\,fb$^{-1}$, are used. The backgroundevaluation is done with MC samples using full simulation produced in the three relevant simulation campaigns (MC16a, MC16d, and MC16e) and after being processes with the EXOT4 derivation. A complete list of samples is presented in Appendix~A. The main backgroundin this analysis is Z+jets. Processes such as $t\bar{t}$  and $t\bar{t}$ produces in associationwith vector bosons are sub-leading backgrounds, while small contributions are expected fromprocesses such as s single top, di-boson and $W$+jets. 
 
\section{$Z$+Jets Background}
For the description of the $Z$ boson production plus associated jets,the samples produced by\Sherpa~2.2.1 using the NNPDF3.0 NNLO PDF set are used. In order to ensure enough statistics in the high $P_{\rm T}$ range, the samples are produced in slices of the max($H_{\rm T}$, $p_{\rm T}(Z)$) and filteringthe heavy flavour composition. Samples produced with MADGRAPH, using the  NNPDF3.0 NLO PDF set and interfaced to  \Pythia~8  with theA14 NNPDF2.3LO tune for showering and are being used to assign a generator uncertanity.These samples are sliced in $H_{\rm T}$.

\section{SM $t\bar{t}$ and Single Top Background}
The SM $t\bar{t}$ background samples use the POWHEG method implemented in POWHEG-BOX v2 using the  NNPDF3.0 NLO PDF set. POWHEG-BOX was interfaced with  \Pythia~8 with the A14 set of tunable parameters for parton showering and hadronization. The $h_{\rm damp}$ parameter in  PowHEG-Box which controls matrix element to parton shower matching in and effectively regulates the high-$p_{\rm T}$
radiation, was set to 1.5$m_{t}$, where $m_{t} = 172.5$\,GeV. In this sample non all hadronic final states are considered, since the main contribution for the multileptonic topologies of the  analysis comes from the leptonic decays of $t\bar{t}$.  As much as possible for systematic uncertanity estimation, alternative generator weights with variations in the factorization and renormalization scales, shower tuning variations, as well as the choice of the PDF set are stored in the sample. For the shower tuning variations, the NLO radiation (scaled from $\times0.5$ up to $\times2.0$) as welll as the shower radiation  (using the A14 var3c eigentune) and NLO radiation was modified by changing the $h_{\rm damp}$  parameter to $h_{\rm damp}=1.5\times m_{t}$ and $3\times m_{t}$. Extra samples, simulated with AFII, have been used for additional systematics evaluation.  Showering uncertanities have been included using samples with the same generator and PDF set as the  nominal case by using HERWIG7 with the H7UE tune and for the showering. Generator systematics uncertanities are included using samples generated with aMC@NLO with  NNPDF3.0 NLO set and the showering done by  Pythia~8 with the A14 NNPDF2.3 LO tune.

The \textbf{singletop} background processes have been generated with POWHEG-BOX v1 and interfaced to Pythia~8 with Perugia2012 set of tunable paramaters.

\section{Di-Boson Background}
The contribution from diboson processes (i.e. $ZZ$, $WZ$ and $WW$) is evaluated using samples generated by \Sherpa~2.2.2 using the NNPDF3.0 NNLO PDF set.  

\section{SM $t\bar{t}$ with Associated Vector Bosons Background }
The samples for the production of a top anti-top quark pair in association with vector bosons are generated by a MC@NLO(for $t\bar{t}+W$ and $t\bar{t}+Z$ process) and MAGRAPH (for $t\bar{t}+WW$ processes) interfaced with \Pythia~8 for hadronization and using the NNPDF23LO PDF ser and the A14 tune. Processes with such as $t\bar{t}+W$,   $t\bar{t}+WW$ and  $t\bar{t}+Z$ with Z decaying to $\nu\bar{\nu}$, $q\bar{q}$ and $ll$, where $l= (e, \mu, \tau)$, are considered. Internal generator weights are used for the estimation of the modeling uncertanities.

\section{Reconstruction Cuts}

  \begin{table}[h!]
  \centering%
  \caption{Electron selection criteria.}
  \label{table:electron_criteria}
  \begin{tabular}{ |p{5cm}||p{7cm}|}  \hline	
 Feature  & Criterion  \\ \hline
 Pseudorapidity range   & ($|\eta| < 1.37 || < 1.52 < |\eta| < 2.47$) \\
 Energy calibration  & $\tt es2017\_R21\_PRE$ (ESModel) \\
 Transverse momentum & $p_{\rm T} > 28 GeV$\\\hline
 Object quality & Not from  a bad calorimeter cluster (\tt BADCLUSLECTRON) \\
                       & Remove clusters from regions with EMEC bad HV (2016 data only) \\\hline                                            
 Track to vertex association & $d_{0}^{\rm  BL}(\sigma) < 5$ \\
                                            & $|\Delta z_{0}^{\rm BL} \rm sin\,\theta| < 0.5$\,mm \\ \hline
 Identification & (\tt TightLH) \\
 Isolation & \tt None \\\hline \end{tabular}
\end{table}

  \begin{table}[h!]
  \centering%
  	\caption{Muon selection criteria.}
  	\label{table:muon_criteria}
    \begin{tabular}{ |p{5cm}||p{7cm}|}  \hline	
    Feature  & Criterion  \\ \hline
    Selection working point & \tt Medium \\
    Isolation working point & \tt FCTightTrackOnly \\
    Momentum calibration & Sagitta correction used \\
    $p_{\rm T}$ cut & 28\,GeV \\
    $|\eta|$ cut & $< 2.5$ \\
    $d_{0}$ significance cut & 3 \\
    $\Delta z_{0} \rm sin\,\theta$ cut & 0.5\,mm \\\hline \end{tabular}
  \end{table}

  \begin{table}[h!]
  \centering%
  	\caption{Jet selection criteria.}
  	\label{table:jet_criteria}
  	\begin{tabular}{| p{5.5cm} | p{9cm} |}\hline	
  		Feature  & Criterion  \\ \hline
  		\textit{R} parameter & 0.4 \\
  		Input constituent &  EMTopo \\
  		Analysis release number & 21.2.84 \\
  		\tt CalibArea tag & 00-04-82 \\
  		Calibration configuration & \tt JES\_MC16Recommedation\_Consolidated\_ EMTopo\_Apr2019\_Rel21 \\
  		Calibration sequence (Data) & \tt JetArea\_Residual\_EtaJES\_GSC\_Insitu \\
  		Calibration sequence (MC) & \tt JetArea\_Residual\_EtaJES\_GSC\_Smear \\\hline
  		& Selection requirements \\\hline
  	  	Observable & Requirement \\\hline
  		Jet cleaning & \tt LooseBad \\
  		$p_{\rm T}$  & 25\,GeV \\
  		$|\eta|$  & $< 4.5$ \\
  		JVT & $>0.59$ for $p_{\rm T} < 60$\,GeV, $|\eta| < 0.4$  \\\hline \end{tabular}
  \end{table}

    \begin{table}[h!]
    \centering
  	\caption{ $b$-tagging selection criteria.}
  	\label{table:bjet_criteria}
  	\begin{tabular}{|l| l|}\hline	
  		Feature  & Criterion  \\ \hline
  	    & EM Topo Jets \\\hline	
  		Jet collection & \tt AntiKt4EMTopo \\
  		Jet selection &  $p_{\rm T} > 25$\,GeV \\
  		                    & $|\eta| < 2.5$ \\
  		                    & JVT cut if applicable \\\hline                   
        Algorithm & \tt MV2c10 \\\hline
        Operating point & Fixed \\
                                 & Eff = 77 \\
         CDI  & \tt 2017-21-13TeV-MC16-CDI-2019-7-25\_v1 \\\hline \end{tabular}
  \end{table}


  \begin{table}[hbtp]
  \centering
  	\caption{ Overlap removal criteria.}
  	\label{table:overlap}
  	\begin{tabular}{| p{2.5cm} | p{2.5cm} | p{7cm} |}\hline	
  		Reject  & Against & Criteria \\ \hline
  		Electron & Electron & shared track, $p_{\rm T,1} <  p_{\rm T,2}$ \\
  		Muon & Electron & is Calo-Muon and shared ID track \\
  		Jet & Electron & $\Delta R < 0.2$ \\
  		Electron & Jet & $\Delta R < 0.4$ \\   
  		Jet & Muon & \tt NumTrack < 3 and (ghost-associated or $\Delta R < 0.2$) \\
  		                    && not a $b$-jet and  \tt NumTrack < 3 and  (ghost-associated or $\Delta R < 0.2$) \\
  		Muon & Jet &  $\Delta R < min(0.4,0.04+10 GeV/p_{\rm T}(\mu))$ \\    \hline \end{tabular}
  \end{table}
