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\Title{Measuring the $b$-jet tagging efficiency on $c$-jets containing $D^{*+}$ mesons with ATLAS data}

\bigskip\bigskip

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

\begin{raggedright}  

{\it Andrea Ferretto Parodi, on behalf of the ATLAS Collaboration\index{Ferretto Parodi, A.}\\
INFN Sezione di Genova \& Universit\`a degli Studi di Genova\\
Via Dodecaneso 33, 16146 Genova - ITALY}
\bigskip\bigskip
\end{raggedright}



\section{Introduction}

    The identification of jets originating from $b$-quarks ($b$-tagging) is a crucial tool for the ATLAS~\cite{atlas} physics program at the LHC, both for precision measurements and in searches for new particles. One important ingredient when using $b$-tagging in physics analyses is the determination of the probability to mistakenly $b$-tag a jet originating from a $c$-quark ($c$-tag efficiency). The optimal sample for measurements of the $c$-tag efficiency would be a clean sample of jets originating from $c$-quarks. The sample of jets associated to reconstructed $D^{*+}$ mesons (through the decay chain $D^{*+}\to D^0 \pi^+ \to K^- \pi^+\pi^+$) is quite close to this ideal case since most $D^{*+}$ mesons originate from $c$-quark hadronization. The $c$-tag efficiency has been measured by comparing the reduction in the yield of $D^{*+}$ mesons before and after the $b$-tagging requirement of the associated jet. The contamination from $D^{*+}$ mesons that originate from $b$-hadron decays has been taken into account using a fit to the $D^0$ pseudo-proper time distribution.

%\section{Data sample and flavour composition}
\section{Flavour composition and $c$-tag efficiency}


  The data sample has been collected by ATLAS during 2011, using events selected by single jet triggers, and corresponds to a total integrated luminosity $\L\simeq 5 \mbox{ fb}^{-1}$. %Background is subtracted from the signal region by normalizing it to the fitted background fraction in the signal region.
Signal and background regions are defined as the region within $3\sigma$ of the $\Delta m$ peak center and the region above 150 MeV respectively (Fig.~1a).
 
The discriminating variable to identify beauty and charm components is the $D^0$ pseudo-proper time:
$ t(D^0) = \mbox{sign}(\mathbf{L_{xy}}\cdot \mathbf{p_T(D^0)}) \cdot m_{D^0} \cdot \frac{L_{xy}(D^0)}{p_{\mathrm T}(D^0)}$.
The beauty component $F_b(t)$ is modelled as the convolution of two exponential functions with the resolution function, while the charm component $F_c(t)$ is modelled as a single exponential function convolved with the resolution. The beauty component $f_b$ is fitted as: $ F(t) = f_b \cdot F_b(t) + (1-f_b) \cdot F_c(t) $. The fit is done on background subtracted data (Fig.~1b), obtained by subtracting the background $t(D^0)$ distribution, normalized to the fitted background fraction in the $\Delta m$ signal region, from the signal $t(D^0)$ distribution.

  
\begin{figure}[htb]
\begin{center}
\epsfig{file=fig_01d.eps,height=1.7in}
\epsfig{file=fig_02a.eps,height=1.7in}\\
%\epsfig{file=img/fig_01b.eps,height=1.3in}
(a) \hskip 6cm (b)  %\hskip 4cm (c) 
\caption{(a) $\Delta m$ distribution of the $D^{*+}$ candidates associated with a jet of transverse momentum between 90 and 140 GeV. (b) Fitted $D^0$ pseudo-proper time distribution on background subtracted $D^{*+}$ samples in jet $p_{\mathrm T}$ bin 20--30 GeV~\cite{dstar}.      }
\label{fig:magnet}
\end{center}
\end{figure}


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%\begin{tabular}{l|ccc}  
%Patient &  Initial level($\mu$g/cc) &  w. Magnet &  
%w. Magnet and Sound \\ \hline
% Guglielmo B.  &   0.12     &     0.10      &     0.001  \\
% Ferrando di N. &  0.15     &     0.11      &  $< 0.0005$ \\ \hline
%\end{tabular}
%\caption{Blood cyanide levels for the two patients.}
%\label{tab:blood}
%\end{center}
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%\section{Measuring the $c$-tag efficiency}

The $c$-tag efficiency can be obtained as:
$ \epsilon_c = \frac{\epsilon_{D^*}-f_b\epsilon_b}{1-f_b}          $,
where $f_b$ is the fitted beauty fraction, $\epsilon_{D^*}$ accounts for the $D^*$ mesons yield reduction when applying the $b$-tagging selection, and $\epsilon_b$ is the  $b$-tagging efficiency measured by independent analyses~\cite{ptrel}. Results are presented for the MV1 tagging algorithm at $70\%$ efficiency (Fig.~2). % as both $c$-tag absolute efficiencies and data-to-MC scale factors.
  A complete list of results and systematic uncertainties is available in~\cite{dstar}. Scale factors ($SF=\epsilon_c^{\mathrm{data}}/\epsilon_c^{\mathrm{sim}}$) are consistent with unity for all the taggers and operating points with uncertainties varying, depending on the jet $p_{\mathrm{T}}$, from 10\% to 40\%.

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\caption{The $c$-tag efficiency in data and simulation (left) and the data-to-simulation scale factor (right)~\cite{dstar}.}
\label{fig:magnet}
\end{center}
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%\bigskip
%I am grateful to Don Alfonso d'Alba for certain services essential to 
%this investigation.
%

\vspace*{-1.5cm}
\begin{thebibliography}{99}

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\bibitem{atlas}
ATLAS Collaboration, JINST {\bf 3} S08003 (2008).
\bibitem{ptrel}
ATLAS Collaboration,~ATLAS-CONF-2012-043,~http://cdsweb.cern.ch/record/1435197.
\bibitem{dstar}
 ATLAS Collaboration,~ATLAS-CONF-2012-039,~http://cdsweb.cern.ch/record/1435193.
 %%CITATION = TAADD,23,2647;%%

%\bibitem{Muller}
%For an exhaustive review of the Prussian literature, see A. D. M\"uller,
%in Workshop on Action at a Distance, F. Eisenschmidt, ed. (Springer,
%Berlin, 1774).
%
%\bibitem{daPonte}
%
%L. da Ponte, Trans. N. Y. Acad. Sci., {\bf 3}, 27 (1795).
%%%CITATION = TNYAA,3,27;%%


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%
%\speaker{D. Giovanni (University of Seville)}  My analysis indicates that the
%recovery of the two gentlemen is due simply to their embrace of the masculine
%principle and has nothing to do with magnetism at all.  Could you comment on 
%this?
%
%\speaker{Reggiano} Professor Giovanni has discussed this hypothesis in several
%forums, but, I do not believe there is anything in print.  I understand that
%he is spending his time in other pursuits.
%
%\speaker{D. Anna (University of Seville)}  In fact, my colleague Giovanni 
%has expressed opposite opinions on this question at various times, depending
%on the audience.  All of these testosterone-based theories are, of course,
%nonsense.
%
%\endDiscussion
 
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