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\Title{Measuring the $b$-jet tagging efficiency using samples of jets
          containing muons with ATLAS data}

\bigskip\bigskip

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

\begin{raggedright}  
{\it Christian Jung\index{Jung, C.},
on behalf of the ATLAS collaboration\\
TU Dortmund\\ Otto-Hahn-Strasse 4\\ 44221 Dortmund, Germany\\}
\bigskip\bigskip
\end{raggedright}
% \linenumbers
\section{Introduction}

% The identification of jets originating from the decay of long-lived $B$-hadrons is of great importance
% for the ATLAS physics program. Applications exist in various physics scenarios, e.g. in the identification of
% the decays of top quarks or the Higgs boson.
The identification of jets originating from the decay of $b$-hadrons is used in many physics channels like top quark and Higgs boson physics.

% In ATLAS \cite{Aad:2008zzm} there are several algorithms \index{$b$-tagging algorithm} to identify these jets which exploit the properties of tracks from
We describe several algorithms used in the ATLAS experiment \cite{Aad:2008zzm} to 
identify $b$-jets produced in pp collisions at $\unit[7]{TeV}$ center of mass energy.
These algorithms exploit the properties of tracks from
$b$-hadron decays and the existence of secondary vertices in jets to identify them.
An example for such an algorithm is the MV1 algorithm, a neural-net-based combination of three
 SV1, IP3D and JetFitter algorithms \cite{ATLAS_comm}.

% In order to use these algorithms it must be assured that they are correctly described by the simulation their performance must be measured in data.
In order for these algorithms to be used in the simulation they must be calibrated by measuring their efficiency in data.
% To allow a quantitative description of the $b$-tagging efficiencies those algorithms have to be calibrated and their performance is measured in data. 
% To allow a quantitative description of the $b$-tagging efficiencies
% One approach to measure the efficiency of these algorithms is to exploit the properties of the muons
% from decays of the $B$-hadrons: Due to the high mass of the bottom quark these muons will have a relatively
% high transverse momentum with respect to the axis of the jet in which they are, the so-called \ptrel\ variable. 
% This variable therefore is sensitive to the flavor of the jet and is uncorrelated to the decision of the $b$-tagging
% algorithm.
% Two analyses which use this variable to measure the efficiency of the $b$-tagging algorithms are presented, the \ptrel\ analysis and the System8 analysis.
One calibration approach is to exploit the fact that muons emerging from $b$-hadrons carry a relatively high transverse momentum with respect to the axis of the $b$-jet.
That variable \ptrel\ is sensitive to the flavour of the original quark and works independently of a specific $b$-tagging algorithm. 
Such calibrations are carried out in the so called \ptrel\ and system8 methods.

% \section{The \ptrel\ Method}
\section{Calibration Methods and Results}
In the \ptrel\ method template fits to the distribution of the muon \ptrel\ are performed before and after the tagging criterion
to obtain the number of $b$-jets before and after the decision. The efficiency is then the number of
$b$-jets after the tagging requirement divided by the original number of $b$-jets.
The templates for $b$- and $c$-jets are taken from simulation while the template for light-quark jets is
taken from data with the additional requirement that no jet in the event is tagged by a very efficient $b$-tagging
algorithm. 
The resulting light-quark jet sample has a about $(2-6)\%$ contamination of $b$-jets which needs to be corrected for.

% \section{The System8 Method}
The system8 method uses three criteria to split the jet sample into 8 different sub-samples to build a 
system of eight equations. One of the three criteria is the $b$-tagging algorithm which is to be calibrated.
Another one is a cut on the \ptrel\ of the muon inside the jet. The third criterion is the presence of
an opposite side $b$-tagged jet. 
In this method the $b$-tagging efficiency is one of the parameters in the set of equations. A key feature
of the method is that the only reliance on simulation it has comes from the correlation between the different
criteria.

% \section{Results}
\begin{figure}[htbp]
 \includegraphics[width=0.45\textwidth]{figures/MV170efficiencyPt.pdf}
 \includegraphics[width=0.5\textwidth]{figures/System8_bTagEff_MV170_DefaultFit.pdf}
 \caption{\label{eff} The $b$-tagging efficiency for the MV1 algorithm at a efficiency 
 of 70\% in simulation and measured by the \ptrel\ (left) and the system8 (right) methods  \cite{ATLAS_bTagEffMu:2012}. }
\end{figure}
Both methods calibrate jets which are based on an anti-$k_T$ algorithm with a cone size of 0.4 using
topological clusters in the ATLAS calorimeters. 
Muons are reconstructed by a statistical combination of the tracks from the muon spectrometer and the inner detector.
% Additional cuts are applied to reduce the number of fakes.
Additionally the muon is required to have a transverse momentum of at least $p_T > \unit[4]{GeV}$ and to be within the cone of a jet.
% The jet energy is corrected for the muon and the assumed neutrinos from the semileptonic $b$-decay momenta. The final
% jet is required to have a corrected transverse momentum of at least $p_T > \unit[20]{GeV}$.

As the $b$-tagging efficiency depends on the transverse momentum of the jet, the measurement is carried out
in several bins of $p_T$, varying from $\unit[20]{GeV}$ to $\unit[200]{GeV}$.
Figure \ref{eff} shows the efficiency for the MV1 $b$-tagging algorithm in simulation and the measurement with both methods.
% The efficiency of the working point was chosen to be 70\% in a top simulation sample.
The parameters of the algorithm were chosen such that it has 70\% $b$-tagging efficiency in a sample of $t\bar{t}$ simulated events.
Both methods show good agreement between data and simulation with a slightly lower efficiency
in data then in simulation.
The ratio of the efficiency in data and simulation is 
% sample independent and is 
used as a scale factor to correct the
simulation performance.





\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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%\cite{Morningstar:1997ff}
%\cite{Aad:2008zzm}
\bibitem{Aad:2008zzm} 
  ATLAS Collaboration,
  %``The ATLAS Experiment at the CERN Large Hadron Collider,''
  JINST {\bf 3}, S08003 (2008).
  %%CITATION = JINST,3,S08003;%%
  
\bibitem{ATLAS_comm}
ATLAS Collaboration, ATLAS-CONF-2011-102,
% Commissioning of the ATLAS high-performance b-tagging algorithms in the 7 TeV collision data,\ 
\url{http://cdsweb.cern.ch/record/1369219}

\bibitem{ATLAS_bTagEffMu:2012}
ATLAS Collaboration,\ ATLAS-CONF-2012-043,\ % Measurement of the b-tag Efficiency in a Sample of Jets Containing Muons with 5 $fb^{-1}$ of Data from the ATLAS Detector,
\url{http://cdsweb.cern.ch/record/1435197}


\end{thebibliography}

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