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\begin{center}
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{\bf APPENDIX}
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\section{Official Criteria}
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\label{a:OfficialCriteria}
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In the following we summarize the tables for the official ``Robust,'' ``Loose,'' and ``Tight'' criteria
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\begin{table}[!tb]
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\caption{Thresholds and criteria applied for the official set of selection. We keep electron candidate which are below threshold with $f_{Brem} = $(P$_{in}$-P$_{out}$)/P$_{in}$.}
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\label{tab:OfficialCuts}
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\begin{center}
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\begin{tabular}{|c|c|c|c|c|c|c|} \hline
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& H/E & $\sigma_{\eta\eta}$ & $\Delta \phi_{in} $ & $\Delta \eta_{in} $ & E$_{seed}$/P$_{in}$ & Additional \\
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& & & & & & criteria\\ \hline
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Official Robust Barrel & $<$0.115 & $<$0.0140 & $<$0.090 &$<$0.090 & - & - \\ \hline
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Official Robust EndCap & $<$0.150 & $<$0.0275 & $<$0.092 &$<$0.105 & - & - \\ \hline\hline
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Official Loose Barrel & & & if(E$_{SC}$/P$_{in}<$1.5) & & & 0.8$\leq$E$_{SC}$/P$_{in}$\\
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And if $f_{Brem} <$ 0.06 & $<$0.100 & $<$0.0120 & $<$0.025 & $<$0.0045 & $>$0.91 & AND \\
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& & & else $<$0.09 & & & 0.2$\leq$$f_{Brem}$\\ \hline
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Official Loose Barrel & & & & & & 0.8$\leq$E$_{SC}$/P$_{in}$\\
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And if $f_{Brem}$ $\geq$ 0.06 & $<$0.115 & $<$0.0140 & $<$0.05 & $<$0.0090 & $>$0.11 & AND\\
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And 0.8$<$E$_{SC}$/P$_{in}<$1.2 & & & & & & 0.2$\leq$$f_{Brem}$\\ \hline
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Official Loose Barrel & & & if(E$_{SC}$/P$_{in}<$1.5) & & &0.8$\leq$E$_{SC}$/P$_{in}$\\
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And if $f_{Brem}$ $\geq$ 0.06 &$<$0.055 & $<$0.0115 &$<$0.053 & $<$0.0085 &$>$0.11 & AND \\
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And (E$_{SC}$/P$_{in}\geq$1.2) & & & else $<$0.090 & & & 0.2$\leq$$f_{Brem}$\\ \hline
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Official Loose EndCap & & & if(E$_{SC}$/P$_{in}<$1.5) & & & 0.8$\leq$E$_{SC}$/P$_{in}$\\
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And if $f_{Brem} <$ 0.06 & $<$0.120 & $<$0.0265 & $<$0.030 & $<$0.0068 & $>$0.85 & AND \\
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& & & else $<$0.092 & & & 0.2$\leq$$f_{Brem}$\\ \hline
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Official Loose EndCap & & & & & & 0.8$\leq$E$_{SC}$/P$_{in}$\\
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And if $f_{Brem}$ $\geq$ 0.06 & $<$0.145 & $<$0.0275 & $<$0.07 & $<$0.0105 & $>$0.00 & AND\\
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And 0.8$<$E$_{SC}$/P$_{in}<$1.2 & & & & & & 0.2$\leq$$f_{Brem}$\\ \hline
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Official Loose EndCap & & & if(E$_{SC}$/P$_{in}<$1.5) & & &0.8$\leq$E$_{SC}$/P$_{in}$\\
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And if $f_{Brem}$ $\geq$ 0.06 &$<$0.150 & $<$0.0265 &$<$0.092 & $<$0.0100 &$>$0.00 & AND \\
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And (E$_{SC}$/P$_{in}\geq$1.2) & & & else $<$0.092 & & & 0.2$\leq$$f_{Brem}$\\ \hline\hline
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Official Tight Barrel&&&if(E$_{SC}$/P$_{in}<$1.5)&&& 0.8$\leq$E$_{SC}$/P$_{in}$ AND\\
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And if $f_{Brem} <$ 0.06&$<$0.042&$<$0.0110&$<$0.016&$<$0.0030&$>$0.94&0.2$\leq$$f_{Brem}$ AND \\
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&&&else $<$0.09&&&E$_{SC}$/P$_{in}<0.9\times(1-f_{Brem})$ \\ \hline
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Official Tight Barrel&&& &&&0.8$\leq$E$_{SC}$/P$_{in}$ AND\\
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And if $f_{Brem}$ $\geq$ 0.06&$<$0.050&$<$0.0125&$<$0.032&$<$0.0055&$>$0.24&0.2$\leq$$f_{Brem}$ AND\\
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And 0.8$<$E$_{SC}$/P$_{in}<$1.2&&&&&&E$_{SC}$/P$_{in}<0.9\times(1-f_{Brem})$ \\ \hline
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Official Tight Barrel&&&if(E$_{SC}$/P$_{in}<$1.5) &&&0.8$\leq$E$_{SC}$/P$_{in}$ AND\\
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And if $f_{Brem}$ $\geq$ 0.06&$<$0.045& $<$0.0100& $<$0.0525& $<$0.0065&$>$0.11&0.2$\leq$$f_{Brem}$ AND\\
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And (E$_{SC}$/P$_{in}\geq$1.2)&&&else $<$0.090&&&E$_{SC}$/P$_{in}<0.9\times(1-f_{Brem})$ \\ \hline
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Official Tight EndCap&&&if(E$_{SC}$/P$_{in}<$1.5)&&& 0.8$\leq$E$_{SC}$/P$_{in}$ AND\\
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And if $f_{Brem} <$ 0.06&$<$0.037&$<$0.0252&$<$0.035&$<$0.0055&$>$0.83&0.2$\leq$$f_{Brem}$ AND\\
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&&&else $<$0.092&&& E$_{SC}$/P$_{in}<0.9\times(1-f_{Brem})$ \\ \hline
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Official Tight EndCap&&&&&&0.8$\leq$E$_{SC}$/P$_{in}$ AND\\
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And if $f_{Brem}$ $\geq$ 0.06&$<$0.055&$<$0.0265&$<$0.025&$<$0.0060&$>$0.24&0.2$\leq$$f_{Brem}$ AND\\
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And 0.8$<$E$_{SC}$/P$_{in}<$1.2&&&&&&E$_{SC}$/P$_{in}<0.9\times(1-f_{Brem})$ \\ \hline
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Official Tight EndCap&&&if(E$_{SC}$/P$_{in}<$1.5)&&&0.8$\leq$E$_{SC}$/P$_{in}$ AND\\
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And if $f_{Brem}$ $\geq$ 0.06&$<$0.050& $<$0.0260&$<$0.065& $<$0.0075&$>$0.11&0.2$\leq$$f_{Brem}$ AND\\
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And (E$_{SC}$/P$_{in}\geq$1.2)&&&else $<$0.092&&&E$_{SC}$/P$_{in}<0.9\times(1-f_{Brem})$ \\ \hline
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\end{tabular}
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\end{center}
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\end{table}
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