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\Title{Study of the ATLAS muon identification efficiency in the presence of high pile-up}

\bigskip\bigskip

%+\addtocontents{toc}{{\it D. Reggiano}}
%+\label{ReggianoStart}

\begin{raggedright}  

{\it William Spearman, on behalf of the ATLAS Collaboration\index{Spearman, W.}\\
Department of Physics\\
Harvard University\\}
%17 Oxford Street\\
%Cambridge, MA 02138, USA}
\bigskip\bigskip
\end{raggedright}



%\section{Introduction}


%Di-muon decays of $J / \psi$ mesons and Z bosons have been used to study the muon reconstruction and identification efficiency of the ATLAS detector~\cite{ATLAS} as a function of the muon transverse momentum, from $p_{T}=4$ GeV to $p_{T}=100$ GeV, and the number of inelastic collisions per event. The results show a steep efficiency turn-on curve reaching its plateau value of 100\% at $p_{T} \approx 6$ GeV and no dependence of the muon reconstruction efficiency on pile-up. The studies also reveal that the use of inner detector tracks allows us to distinguish between isolated muons and non-isolated muons produced in jets with high separation power even at the highest pile-up levels.


%Recently, F.  A. Mesmer \index{Mesmer} has reported evidence of a profound influence of magnets on a variety of aspects of human and animal physiology~\cite{Mesmer}.  Numerous authors have claimed to reproduce certain of the phenomena reported by Mesmer~\cite{diCenzo,Muller}, but there is little understanding of the precise mode of action of the magnetic influence.  In this article, I will present evidence that mesmeric influence can disrupt the lethal action of sodium cyanide (NaCN) when modulated by a sequence of high-pitched tones.  After a description of the phenomenon, I will comment on the implications for the nature of the magnetic coupling.

%\footnote{Tag-and-probe works by selecting events produced by a resonance.  Tight selection criteria are applied to one of the decay particles, the tag.  A looser set of selection criteria is then applied to the other decay particle, the probe.  The looseness of this selection means that an unbiased sample of probes has been selected which can then be used to measure certain properties such as reconstruction efficiency or isolation efficiency} 

%\section{Method}

%The muon identification efficiency of the ATLAS detector~\cite{ATLAS} at the Large Hadron Collider (LHC) has been measured using di-muon events from the $J / \psi$ and $Z$ resonances.  The measurements were performed on the data collected in 2011.  The muon reconstruction efficiency was measured at low transverse momentum ($p_{T}$) using the $J / \psi$ sample and at high $p_{T}$ using the $Z$ sample.  The reconstruction efficiency was measured using an unbiased sample of muons selected by choosing events with a combined (CB) muon\footnote{A combined muon is the statistical combination of an inner detector track with a track in the muon spectrometer.}, called the tag, and a calo-tagged (CT) inner detector (ID) track, known as the probe.  The isolation efficiency and its dependence on pile-up was determined using an unbiased sample of probes from the $Z$ resonance selected by requiring events with one well isolated CB muon, the tag, and one CB muon without isolation requirements, the probe.  In both cases, the tag and probe are required to be oppositely charged and to form an invariant mass near the mass of the $J / \psi$ or $Z$.   Details for the $J / \psi$ and $Z$ measurements can be found in~\cite{Jpsi_2010_Measurement} and ~\cite{Z_2010_Measurement} respectively. 


The muon reconstruction and isolation efficiency of the ATLAS detector~\cite{ATLAS} at the Large Hadron Collider have been measured using the data collected in 2011.  An unbiased sample of muons is selected, using tag-and-probe on the $J / \psi$ and $Z$ resonances, to measure these efficiencies.  The tag-and-probe method selects events with one well reconstructed muon, the tag, and one loose opposite charge muon, the probe, that form an invariant mass near the mass of the resonance.  The specific selections on the probes are tuned to provide a high purity sample of muons that will not bias the efficiency being measured.  In both reconstruction efficiency measurements, a combined (CB) muon\footnote{A combined muon is the statistical combination of an inner detector track with a track in the muon spectrometer.} is chosen as tag.  For the muon reconstruction efficiency, measured at low transverse momentum ($p_{T}$) using the $J / \psi$ sample~\cite{Jpsi_2010_Measurement} and at high $p_{T}$ using the $Z$ sample~\cite{Z_2010_Measurement}, a calo-tagged\footnote{Calo-tagging selects inner detector tracks whose energy deposition in the calorimeter is consistent with that of a minimum ionizing particle.} inner detector track was used as probe.  For the isolation efficiency, a CB muon was used as probe.  

% Di-muon events coming from a resonance were selected by requiring one well-reconstructed muon, the tag, and one opposite charge particle, the probe, forming an invariant mass with the tag near the mass of the resonance.  Specific selections are placed on the probes to ensure that they provide a high quality sample of unbiased muons which can be used to measure specific efficiencies.  Both reconstruction and isolation efficiencies used a combined (CB) muon\footnote{A combined muon is the statistical combination of an inner detector track with a track in the muon spectrometer.} as tag.  For the muon reconstruction efficiency, a calo-tagged (CT) inner detector (ID) track was used as probe and for the isolation efficiency, a CB muon was used as probe.  The efficiencies are then measured on these unbiased probe samples\footnote{Details for the $J / \psi$ and $Z$ measurements can be found in~\cite{Jpsi_2010_Measurement} and ~\cite{Z_2010_Measurement} respectively}.  

%The muon reconstruction efficiency was measured at low transverse momentum ($p_{T}$) using the $J / \psi$ sample and at high $p_{T}$ using the $Z$ sample. 

%o select an unbiased sample of muons to be used for to measure efficiency, a tag-and-probe is used  which The reconstruction efficiency was measured using an unbiased sample of muons selected by choosing events with a combined (CB) muon\footnote{A combined muon is the statistical combination of an inner detector track with a track in the muon spectrometer.}, called the tag, and a calo-tagged (CT) inner detector (ID) track, known as the probe.  The isolation efficiency and its dependence on pile-up was determined using an unbiased sample of probes from the $Z$ resonance selected by requiring events with one well isolated CB muon, the tag, and one CB muon without isolation requirements, the probe.  In both cases, the tag and probe are required to be oppositely charged and to form an invariant mass near the mass of the $J / \psi$ or $Z$.   Details for the $J / \psi$ and $Z$ measurements can be found in~\cite{Jpsi_2010_Measurement} and ~\cite{Z_2010_Measurement} respectively. 

%\footnote{Certain details have changed for the 2011 analyses with respect to the 2010 analyses.  Most notably, both analyses use the single muon trigger with $p_{T}$ threshold of $18$ GeV. Furthermore, the $J / \psi$ measurement relies on a muon + inner detector track trigger with a $p_{T}$ threshold for the muon of $6$ GeV and a $p_{T}$ threshold for the track of $3.5$ GeV.}  
%In order to measure the muon reconstruction efficiency at high pile-up and the dependence of the muon isolation efficiency on pile-up for the ATLAS detector~\cite{ATLAS}, a tag-and-probe method was used on the $J / \psi$ and $Z$ samples for 2011 LHC data and Monte Carlo~\cite{ATLAS_Simulation}.  Candidate events were required to have one fully reconstructed muon, the tag, matched to a triggered muon\footnote{The trigger used for the $J / \psi$ analysis is a muon + ID track trigger with a muon $p_{T}$ threshold of $6$ GeV and a track $p_{T}$ threshold of $3.5$ GeV.  The $Z$ analysis uses tag muons matched to a single muon trigger with $p_{T}$ threshold of $18$ GeV.} and one inner detector (ID) track, the probe, which forms an invariant mass with the tag consistent with the mass of the $J$/$\psi$ or $Z$\footnote{For the $Z$ isolation efficiency study, the probe is also required to be a fully reconstructed muon.}.  For the $J / \psi$ measurement~\cite{Jpsi_2010_Measurement}, background subtraction is performed by fitting the tag-probe invariant mass distribution with a Gaussian signal+polynomial background and for the $Z$ measurement~\cite{Z_2010_Measurement}, background subtraction is done using Monte Carlo.  
%The ATLAS muon reconstruction efficiency was measured using tag and probe on di-muon resonances.  Both the $J / \psi$ and $Z$ For low $p_{T}$, from $4$ GeV $ \leq p_{T} \leq 30$ GeV, the efficiency was measured using a tag-and-probe method with background subtraction on the $J / \psi$ resonance.  For $p_{T} \geq 15$ GeV, the Z tag and probe is used to measure efficiencies.

%\subsection{$J$/$\psi$ Method}

%To measure the muon reconstruction efficiency at low $p_{T}$, a tag and probe was performed using the $J$/$\psi$ resonance.  To select $J / \psi$ candidates, events were required to have one fully reconstructed muon, known as the tag, and one track, the probe, which forms an invariant mass with the tag\footnote{Such events are selected by a muon + track trigger.  The muon $p_{T}$ threshold of this trigger is $6$ GeV and the track $p_{T}$ threshold is $3.5$ GeV} consistent with the mass of a $J$/$\psi$.  Background subtraction was performed by fitting the invariant mass of the candidate tag-probe pairs is fitted with a polynomial background plus a Gaussian signal.  The efficiency is then calculated by dividing the number of events in the signal gaussian for reconstructed tag-probe pairs by the total number of events in the signal Gaussian for all tag-probe pairs.  


%\subsection{$Z$ Method}

%In the tag-and-probe method, $Z \rightarrow \mu^{+} \mu^{-}$ decays are selected by requiring two oppositely charged isolated inner detector (ID) tracks with a di-muon invariant mass near the mass of the Z boson. One track, the �tag muon�, is required to be a a combined (CB) muon and to have fired a trigger\footnote{Events for the $Z$ tag and probe measurement are selected by a single muon trigger with a $p_{T}$ threshold of $18$ GeV.}. The other track is then referred to as the �probe."  The matching efficiency is the fraction of ID probes which can be associated to a CB or ST muon. The background is numerically subtracted by taking the number of background events from MC.   

%\section{Results}

%Figure~\ref{fig:pT_eff} shows the ATLAS muon reconstruction efficiency versus $p_{T}$ for the $J / \psi$ efficiency measurement on the left and the $Z$ measurement on the right.  The results are compatible in the $p_{T}$ overlap region and the plateau efficiency which begins around $6$ GeV continues through the entire $p_{T}$ range of the $Z$ measurement.   Both plots show the efficiency for the final two run periods of the 2011 data-taking.  Combined (CB) and Combined+Segment Tagged (CB+ST) reconstruction efficiency is shown for the $J / \psi$ measurement while only the CB+ST efficiency is shown for the $Z$ measurement.  

%\begin{figure}[htbp]
%\begin{center}
%\begin{tabular}{cc}
%\includegraphics[width=70mm]{fig02.eps} &
%\includegraphics[width=70mm]{fig11a.eps} \\
%\end{tabular}
%\caption{Efficiency versus $p_{T}$ for the $J / \psi$ (left) and $Z$ (right) efficiency measurements.  }
%\label{fig:pT_eff}
%\end{center}
%\end{figure}
% ($s.f. \equiv \epsilon_{data}/ \epsilon_{MC}$)


\begin{figure}[htb]
\begin{center}
\epsfig{file=fig05.eps,width=70mm}
\caption{Combined muon data/MC efficiency scale factor comparison between the $J/ \psi$ and $Z$ measurements for $p_{T}$ range of $10$ GeV $ < p_{T} \leq 15$ GeV for the $J / \psi$ measurement and $15$ GeV $< p_{T} \leq 20$ GeV for the $Z$ measurement~\cite{Jpsi_2011_Measurement}.}
\label{fig:JpsiZcomp}
\end{center}
\end{figure}



Figure~\ref{fig:JpsiZcomp} shows the scale factors, calculated by dividing the efficiency in data by the efficiency in Monte Carlo, comparing the $Z$ and $J / \psi$ measurements versus the pseudo-rapidity\footnote{Where $\eta = - ln \left[ tan \left( \frac{ \theta}{2} \right) \right]$ and $\theta$ is the polar angle of the particle from the beam line.}, $\eta$.  The results show good agreement between the $J / \psi$ and $Z$ measurements.  The track and calorimetric isolation\footnote{Relative isolation is when the sum of the track momentum or calorimeter energy deposition around the given particle in a specific cone does not exceed a certain threshold.  For this analysis, track isolation is defined by $\sum p_{T} \left( \Delta R < 0.3 \right) / p_{T} < 0.15$ and calorimeter isolation is defined by $\sum E_{T} \left( \Delta R < 0.3 \right) / p_{T} < 0.14$} efficiency versus the number of reconstructed vertices per event is seen in Figure~\ref{fig:IsolationEff}.  The pile-up\footnote{The term pile-up refers to multiple interactions per bunch crossing.  Accordingly, high pile-up events are those with many reconstructed vertices.} corrected calorimeter isolation efficiency displays a small dip in efficiency at high pile-up.  The track isolation efficiency, on the other hand, remains constant at even the highest levels of pile-up.  

\begin{figure}[htb]
\begin{center}
\begin{tabular}{cc}
\includegraphics[width=70mm]{fig14a.eps} &
\includegraphics[width=70mm]{fig14c.eps} \\
\end{tabular}
\caption{Track isolation (left) and pile-up corrected calorimeter isolation (right) efficiencies versus the number of reconstructed vertices~\cite{Z_2011_Measurement}.}
\label{fig:IsolationEff}
\end{center}
\end{figure}

%In conclusion, di-muon decays of $J / \psi$ mesons and Z bosons have been used to study the muon reconstruction efficiency scale factors for the ATLAS detector as a function of $\eta$ and the isolation efficiency versus the number of reconstructed vertices per event. The results show good agreement between the $J / \psi$ and $Z$ measurements and they reveal that the track isolation efficiency remains constant at even the highest levels of pile-up.

%In conclusion, di-muon decays of $J / \psi$ mesons and Z bosons have been used to study the muon reconstruction and identification efficiency of the ATLAS detector~\cite{ATLAS} as a function of the muon transverse momentum, from $p_{T}=4$ GeV to $p_{T}=100$ GeV, and the number of inelastic collisions per event. The results show a steep efficiency turn-on curve reaching its plateau value of 100\% at $p_{T} \approx 6$ GeV. The studies also reveal that the track isolation efficiency remains constant at even the highest levels of pile-up.



\begin{thebibliography}{99}

%%
%%  bibliographic items can be constructed using the LaTeX format in SPIRES:
%%    see    http://www.slac.stanford.edu/spires/hep/latex.html
%%  SPIRES will also supply the CITATION line information; please include it.
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\bibitem{ATLAS}
ATLAS Collaboration, JINST {\bf3 S08003} (2008).

%\bibitem{ATLAS_Simulation}
%ATLAS Collaboration, Eur. Phys. J. C {\bf C70} (2010) 823�874.
%The ATLAS Collaboration, \textit{The ATLAS Simulation Infrastructure}, Eur. Phys. J. C {\bf C70} (2010) 823�874, \url{arXiv:1005.4568 [hep-ex]. http://arxiv.org/abs/1005.4568}.

\bibitem{Jpsi_2010_Measurement}
ATLAS Collaboration, ATLAS-CONF-2012-125.
%, \url{https://cdsweb.cern.ch/record/1474642}.
%The ATLAS Collaboration, \textit{A measurement of the muon reconstruction efficiency in 2010 ATLAS data using jpsi decays}, ATLAS-CONF-2012-125, \url{https://cdsweb.cern.ch/record/1474642}.

\bibitem{Z_2010_Measurement}
ATLAS Collaboration, ATLAS-CONF-2011-063.
%, \url{https://cdsweb.cern.ch/record/1345743}.
%The ATLAS Collaboration, \textit{Muon reconstruction efficiency in reprocessed 2010 LHC proton-proton collision data recorded with the ATLAS detector}, ATLAS-CONF-2011-063, \url{https://cdsweb.cern.ch/record/1345743}.


\bibitem{Jpsi_2011_Measurement}
ATLAS Collaboration, ATL-COM-MUON-2012-013, \url{https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/MUON/PublicPlots/2011/May_2012/}.
%The ATLAS Collaboration, \textit{Muon Reconstruction Efficiency using $J / \psi$}. ATL-COM-MUON-2012-013, \url{https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/MUON/PublicPlots/2011/May_2012/index.html}.

\bibitem{Z_2011_Measurement}
ATLAS Collaboration, ATL-COM-PHYS-2011-1640, \url{https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/MUON/PublicPlots/2011/Dec/}.
%Muon Combined Performance Working Group, \textit{Pile-up Dependence of the ATLAS Muon Performance}. ATL-COM-PHYS-2011-1640, \url{https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/MUON/PublicPlots/2011/Dec/index.html}.

\end{thebibliography}
\end{document}

