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%\subsection{Method validation}\label{sec:trackEff-validate}
\subsection{Results}\label{sec:trackEff-results}
The tracking efficiencies for the 2018 data-taking period obtained form data and from the simulation version Sim09h depending on pseudorapidity $\eta$, momentum $p$, number of primary vertices $N_{PV}$ and the number of hits in the \spd detector $N_{\spd hits}$ are shown in Figs.\,\ref{fig:trEff-eta}, \ref{fig:trEff-p}, \ref{fig:trEff-nPVs} and \ref{fig:trEff-nSPD}. All the shown track reconstruction efficiencies are 94\% or higher. The agreement between the track reconstruction efficiency obtained form the data sample and the simulation is very good. The two-dimensional correction table in momentum $p$ and pseudorapidity $\eta$ is given in \refFig{trEff-R}. The ratio is very close to one in all bins. The two-dimensional ratio for the Final method is made available as a correction table for physics analyses performed by the \lhcb collaboration.
The results for all the data-taking years 2011-2018 can be found at~Ref.\,\cite{Twiki-TrackCalib}. As all the results are consistent throughout the years, they are not shown in this work. Alternatively, more results are published in~Ref.\,\cite{TrackEff-FIG}.
\begin{figure}[hbt!] \centering \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/ETA_Velo.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/ETA_T.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/ETA_Long.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/ETA_Combined.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/ETA_Final.eps}\\ \vspace{-3pt} \captionof{figure}[Track reconstruction efficiency vs. pseudorapidity for 2018.]{Track reconstruction efficiency versus pseudorapidity $\eta$ for the 2018 data-taking period (25ns bunch spacing). Sim09h denotes the used version of the simulation software used by the \lhcb experiment. The track reconstruction efficiency is obtained using the \velo method (top left), the \T method (top right), the Long method (middle left), the Combined method (middle right), product of the \velo and \T method and the Final method (bottom), weighted average of the Long and Combined methods. The uncertainties are statistical only.}\label{fig:trEff-eta}\end{figure}
\begin{figure}[hbt!] \centering \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/P_Velo.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/P_T.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/P_Long.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/P_Combined.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/P_Final.eps}\\ \vspace{-3pt} \captionof{figure}[Track reconstruction efficiency vs. momentum for 2018.]{Track reconstruction efficiency versus momentum $p$ for the 2018 data-taking period (25ns bunch spacing). Sim09h denotes the used version of the simulation software used by the \lhcb experiment. The track reconstruction efficiency is obtained using the \velo method (top left), the \T method (top right), the Long method (middle left), the Combined method (middle right), product of the \velo and \T method and the Final method (bottom), weighted average of the Long and Combined methods. The uncertainties are statistical only.}\label{fig:trEff-p}\end{figure}
\begin{figure}[hbt!] \centering \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/nPVs_Velo.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/nPVs_T.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/nPVs_Long.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/nPVs_Combined.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/nPVs_Final.eps}\\ \vspace{-3pt} \captionof{figure}[Track reconstruction efficiency vs. the number of primary vertices for 2018.]{Track reconstruction efficiency versus the number of primary vertices $N_{PV}$ for the 2018 data-taking period (25ns bunch spacing). Sim09h denotes the used version of the simulation software used by the \lhcb experiment. The track reconstruction efficiency is obtained using the \velo method (top left), the \T method (top right), the Long method (middle left), the Combined method (middle right), product of the \velo and \T method and the Final method (bottom), weighted average of the Long and Combined methods. The uncertainties are statistical only.}\label{fig:trEff-nPVs}\end{figure}
\begin{figure}[hbt!] \centering \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/nSPDHits_Velo.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/nSPDHits_T.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/nSPDHits_Long.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/nSPDHits_Combined.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/nSPDHits_Final.eps}\\ \vspace{-3pt} \captionof{figure}[Track reconstruction efficiency vs. the number of hits in the \spd detector for 2018.]{Track reconstruction efficiency versus the number of hits in the \spd detector $N_{\spd hits}$ for the 2018 data-taking period (25ns bunch spacing). Sim09h denotes the used version of the simulation software used by the \lhcb experiment. The track reconstruction efficiency is obtained using the \velo method (top left), the \T method (top right), the Long method (middle left), the Combined method (middle right), product of the \velo and \T method and the Final method (bottom), weighted average of the Long and Combined methods. The uncertainties are statistical only.}\label{fig:trEff-nSPD}\end{figure}
\begin{figure}[hbt!] \centering \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/Ratio_Velo_P-ETA_pretty.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/Ratio_T_P-ETA_pretty.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/Ratio_Long_P-ETA_pretty.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/Ratio_Combined_P-ETA_pretty.eps} \includegraphics[width=0.48\textwidth]{TrackEff/PossibleCorrectResults/2018_25ns/Data2018_25ns_MC2018_25nsSim09h_WG/Ratio_Final_P-ETA_pretty.eps}\\ \vspace{-3pt} \captionof{figure}[Track reconstruction efficiency correction tables for 2018.]{Track reconstruction efficiency ratio of data to simulation in momentum $p$ and pseudorapidity $\eta$ for the 2018 data-taking period (25ns bunch spacing). Sim09h denotes the used version of the simulation software used by the \lhcb experiment. The track reconstruction efficiency is obtained using the \velo method (top left), the \T method (top right), the Long method (middle left), the Combined method (middle right), product of the \velo and \T method and the Final method (bottom), weighted average of the Long and Combined methods. The ratio for the Final method is made available as a correction table for physics analyses performed by the \lhcb collaboration. The uncertainties are statistical only. }\label{fig:trEff-R}\end{figure}
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