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\begin{document}


\Title{Flavour Tagging at LHCb}

\bigskip\bigskip

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

\begin{raggedright}  

{\it Miriam Calvo Gomez\index{Calvo, M.}, on behalf of the LHCb Collaboration\\
Enginyeria La Salle\\
Universitat Ramon Llull\\
08022 Barcelona, SPAIN\\
miriam.calvo@cern.ch}
\bigskip\bigskip
\end{raggedright}


\section{Introduction}

LHCb is a heavy flavour experiment, mainly focused on beauty and charm physics, which performs precision measurements of CP violation and rare decays. The results shown here correspond to data samples up to 1 $fb^{-1}$ of proton proton collisions at $\sqrt{s} = 7~TeV$ collected in 2011. As $b\bar{b}$ pairs are produced in the same forward (or backward) region, the LHCb detector \cite{Jinst} is fully instrumented in the forward direction, covering a pseudorapidity range $2<\eta<5$. The requirements for CP measurements in the B sector are: a flexible and efficient trigger, a good particle identification and an excellent tracking and vertexing, conditions that the detector fulfills. 

Many LHCb measurements require the knowledge of the initial flavour ($b$ or $\bar b$) of the reconstructed $B^0_{d,s}$ mesons, such as $B^0-\bar{B}^0$ oscillations and time dependent CP asymmetries. The process of flavour identification is known as flavour tagging\index{Flavour Tagging} \cite{FT2007, FT2010, FT2011} and this will be detailed in the following sections.
Some examples of LHCb published results that use flavour tagging are: measurement of the $B_s$ oscillation frequency $\Delta m_s$ in $B_s^0\rightarrow D_s \pi$ ~\cite{Deltams2010, Deltams2011}; CP violating mixing phase, $\phi_s$ ~\cite{jpsiphi, jpsif0, jpsipipi, phis} and direct and mixing induced CP violation in $B\rightarrow hh$ ~\cite{b2hh}. 


\section{Flavour tagging}

Different type of taggers (algorithms) are used for the B flavour determination in LHCb. A schematic view of the possible sources of information are shown in Fig.~\ref{fig: tagscheme}. The one known as Same Side\index{Same Side tagger} (SS) tagger exploits the particle produced at the fragmentation process of the signal B: a pion in the case of $B^0$ or $B^+$ signal (or from a B** decay) and a kaon for $B_s^0$. The rest of taggers are those called Opposite Side\index{Opposite Side tagger} (OS) taggers. These exploit the decay products of the other b-hadron produced in the event: a lepton (electron or muon) from semileptonic B decays; a kaon from a $b\rightarrow c \rightarrow s$ chain and an overall charge of the secondary vertex. In any case, the charge of the tagger tags the flavour of the signal B.

\begin{figure}[htb]
\begin{center}
\epsfig{file=tagschema.eps, width=0.9\textwidth}
\caption{Schematic view of the different sources of information available to tag the initial flavour of a signal B candidate.}
\label{fig: tagscheme}
\end{center}
\end{figure}

Due to the possibility to select a wrong track to tag the event,  the tagging performance is not perfect. Moreover, as the opposite B can be neutral and oscillate, OS tagging algorithms have an intrinsic dilution.
In order to evaluate the performance, we define a tagging efficiency, $\epsilon_{tag}$, which is the fraction of events with a tagging decision; a wrong tag fraction, $\omega$, or mistag rate, which is the fraction of events with a wrong tagging decision and an effective efficiency, $\epsilon_{eff}$, or tagging power, which indicates the statistical precision of the sample, given by $\epsilon_{tag}(1-2\omega)^2$. 


%Example of typical OS performances in $B+\rightarrow J/\psiK+$ with 0.37 fb-1 2011 data

The flavour tagging performance can be evaluated in data using flavour-specific decay channels, known as control channels, as the decays: $B^+\rightarrow J/\psi K^+$, $B^0\rightarrow D^{*-}\mu^+\nu$, $B^0\rightarrow J/\psi K^{*0}$ and $B_s^0\rightarrow D_s^-\pi^+$. 
For $B^+$ the mistag can be estimated just comparing the flavour tagging decision with the observed (true) flavour. In case of neutral B,  $\omega$ can be determined from a fit to the time dependent mixing asymmetry, whose amplitude is proportional to the dilution factor $(1-2\omega)$. Fig.~\ref{fig: osc} shows the mixing asymmetry fits for $B^0\rightarrow D^{*-}\mu^+\nu$ and $B^0\rightarrow J/\psi K^{*0}$ using OS tagged events.   

%The use a control channel with similar topology and trigger and selection requirements to the CP channel is recommended, in order to reduce systematics.

\begin{figure}[htb]
\begin{center}
\epsfig{file=OS_asym_dstarmunu.eps, width=0.45\textwidth}
\epsfig{file=Bd_OS_tagged_asym.eps, width=0.45\textwidth}
\caption{Raw mixing asymmetry of $B^0\rightarrow D^{*-}\mu^+\nu$ (left) and $B^0\rightarrow J/\psi K^{*0}$ (right) when using the combination of all OS taggers for 0.37 $fb^{-1}$. Black points are data and red line is the result of the fit. The lower plots show the pull of the residuals with respect to the fit.}
\label{fig: osc}
\end{center}
\end{figure}

\section{Optimization and calibration}

Flavour tagging algorithms were initially designed studying simulated events~\cite{FT2007}. 
For each tagger, the tagging particle is selected requiring several cuts on kinematic and geometrical observables (such as $IP/\sigma, p, p_T$) and particle identification discriminators.
In the case of SS taggers, also proximity to the signal B is required.
If several candidates for the same tagger exist, the one with highest $p_T$ is selected.
An optimization of the selection cuts with real data has been performed using several control channels, in order to maximize the tagging power ~\cite{FT2010, FT2011}. For OS the main control channel used is $B^+\rightarrow J/\psi K^+$ and the other channels are used as a cross check.

The taggers make individual decisions about the flavour with varying accuracy, which is evaluated by means of a Neural Net (NNet).
The NNet uses as input some properties of the tagger and of the event (B $p_T$, number of interactions, ...), providing an estimate of the mistag probability ($\eta$) for each event. As this NNet was trained on MC samples, a calibration has to be performed on real data.
The predicted mistag is calibrated with a linear fit using the measured $\omega$ in a control channel: $\omega = p_0 + p_1 (\eta-<\eta>)$.

In case more than one tagger give a response, the final decision and predicted mistag are obtained combining the individual decisions and calibrated predicted mistag ($\eta_c$). 
Due to the correlation among taggers (mainly between secondary vertex charge  and other OS taggers) the OS predicted mistag needs to be calibrated in data.

The OS calibration is performed with $B^+\rightarrow J/\psi K^+$ and validated using other control channels~\cite{phis} (as $B^0\rightarrow J/\psi K^{*0}$ and $B^0\rightarrow D^-\pi^+$), as shown in Fig.~\ref{fig: calib}. 
%The systematic uncertainties estimated taking into account: signal B flavour, tag decision, B field polarity, run period, nPV, fit model and control channel.
This calibrated per-event mistag can be used directly in the time-dependent CP fits.

\begin{figure}[htb]
\begin{center}
\epsfig{file=OScalib_jpsik.eps, width=0.45\textwidth}
\epsfig{file=OScalib_jpsikstar.eps, width=0.45\textwidth}
\caption{Measured OS mistag as a function of the predicted mistag probability, $\eta_c$, for $B^+\rightarrow J/\psi K^+$ (left) and $B^0\rightarrow J/\psi K^{*0}$ (right) with 1 $fb^{-1}$ data sample. The solid red line corresponds to a linear fit. In the right plot the calibration obtained from the $B^+\rightarrow J/\psi K^+$ sample is superimposed as a blue shaded area, corresponding to a $\pm 1\sigma$ variation.}
\label{fig: calib}
\end{center}
\end{figure}

%Alternatively, an average mistag can be used. For instance, when no calibration is available. 
%In this case, the use of 5 tagging categories of increasing mistag improves the tagging power by ~30\% with respect using only one. 
%$\eta$ is used to classify the events in categories.

\section{Performances}
After the optimization and calibration performed with the control channels, Table~\ref{tab: perfcc} shows the tagging power using OS taggers and the event-per-event mistags in some control channels with 0.37~$fb^{-1}$~\cite{FT2011} and Table~\ref{tab: perf} the performance in some CP-channels with 1.0 $fb^{-1}$ 2011 data~\cite{jpsif0, jpsipipi, phis}. Some differences in performance among channels are expected due to different trigger and selection requirements.

\begin{table}[b]
\begin{center}
\begin{tabular}{l|c}  
Channel & $\epsilon_{tag}(1-2\omega)^2 (\%)$ \\ \hline
 $B^+\rightarrow J/\psi K^+$  &   $2.10\pm0.08\pm0.24$ \\
$B^0\rightarrow J/\psi K^{*0}$  &  $2.09 \pm 0.09\pm 0.24$\\
 $B^0\rightarrow D^{*-}\mu^+\mu$  &  $2.53 \pm 0.10 \pm 0.27$ \\ \hline
 \end{tabular}
\caption{OS effective efficiency for some control channels measured with 0.37~$fb^{-1}$.}
\label{tab: perfcc}
\end{center}
\end{table}

\begin{table}[th]
\begin{center}
\begin{tabular}{l|c}  
Channel & $\epsilon_{tag}(1-2\omega)^2 (\%)$ \\ \hline
 $B_s^0\rightarrow J/\psi \phi$  &   $2.29\pm0.07\pm0.26$ \\
$B_s^0\rightarrow J/\psi f_0(980)$  &  $2.12 \pm 0.26$\\
 $B_s^0\rightarrow J/\psi \pi \pi$  &  $2.43 \pm 0.08 \pm 0.26$ \\ \hline
\end{tabular}
\caption{OS effective efficiency for some CP-channels, used for several measurements of $\phi_s$ in LHCb with 1~$fb^{-1}$.}
\label{tab: perf}
\end{center}
\end{table}

The SS$\pi$ tagger was already used together with OS taggers in 2010 measurements as $\Delta m_d$ with $B^0\rightarrow D^-\pi^+$~\cite{Deltamd} and $\sin(2\beta)$ with $B^0\rightarrow J/\psi K_s^0$~\cite{sin2b}. The tagging power for SS$\pi$ is around 1\%.

The performance of SSK was initially optimized using prompt $D_s^+\rightarrow \phi \pi^+$, due to the low event yield of the main control channel $B_s^0\rightarrow D_s^-\pi^+$. The SSK has been used in the $\Delta m_s$ measurement with $B_s^0\rightarrow D_s^-\pi^+$~\cite{Deltams2011}, where a clear oscillation is seen with only this tagger, as seen in Fig.~\ref{fig: ssk} and obtaining a tagging power of ($1.3\pm 0.4$)\%. The corresponding $\epsilon_{eff}$ is ($4.3\pm1.0$)\% when using both OS and SSK.
A new optimization and calibration has been performed with $B_s^0\rightarrow D_s^-\pi^+$ and the whole 2011 data sample, 1 $fb^{-1}$, to be used for next updates. 

\begin{figure}[htb]
\begin{center}
\epsfig{file=SSK_only.eps, width=0.45\textwidth}
\epsfig{file=SSK_OS.eps, width=0.45\textwidth}
\caption{Mixing asymmetry for $B_s^0\rightarrow D_s^-\pi^+$ candidates as a function of decay time, modulo ($\frac{2\pi}{\Delta m_s}$), for a fit using only the SSK tagger (left) and the combination of OS and SS taggers (right).}
\label{fig: ssk}
\end{center}
\end{figure}

\section{Summary}
Flavour tagging is a fundamental ingredient for B physics measurements in LHCb.
An optimization and calibration of the OS and SS$\pi$ tagging algorithms have been performed with $B^+\rightarrow J/\psi K^+$ data and validated with
other control channels. The SSK optimization and calibration with $B_s^0\rightarrow D_s^-\pi^+$ required the whole 1 $fb^{-1}$ and is going to be used in next updated measurements. 

OS taggers have been already used in several published LHCb results, with an effective efficiency that goes from 2.1\% to 3.5\%, depending on the decay.
SS taggers have also been used in a few measurements. The SS$\pi$ effective efficiency is approximately 1\% and the SSK effective efficiency is 1.3\% (with a preliminary optimization).


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%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
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%\caption{Blood cyanide levels for the two patients.}
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%bigskip
% I am grateful to 



\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.
%%
\bibitem{Jinst}
A.~A.~Alves, Jr. {\it et al.}  [LHCb Collaboration],
  %``The LHCb Detector at the LHC,''
  JINST {\bf 3} (2008) S08005.
  %%CITATION = JINST,3,S08005;%%
\bibitem{FT2007}
M. Calvi et. al., 
%''Flavour tagging performances in LHCb'',
 CERN-LHCb-2007-058. 
\bibitem{FT2010}
LHCb Collaboration, 
%''Optimization and calibration of the LHCb flavour tagging performance using 2010 data'', 
LHCb-CONF-2011-003.
\bibitem{FT2011}
R.~Aaij {\it et al.}  [LHCb Collaboration],
  %``Opposite-side flavour tagging of B mesons at the LHCb experiment,''
  Eur.\ Phys.\ J.\ C {\bf 72} (2012) 2022
  [arXiv:1202.4979 [hep-ex]].
  %%CITATION = ARXIV:1202.4979;%%
\bibitem{Deltams2010}
R.~Aaij {\it et al.}  [LHCb Collaboration],
  %``Measurement of the B^0_s - \bar{B}^0_s oscillation frequency Delta m_s in B^0_s -> D_s^-(3) pi decays,''
  Phys.\ Lett.\ B {\bf 709} (2012) 177
  [arXiv:1112.4311 [hep-ex]].
  %%CITATION = ARXIV:1112.4311;%%
\bibitem{Deltams2011}
LHCb Collaboration, 
%''Measurement of $\Delta m_s$ in the decay $B_s\rightarrow D_s(KK\pi)\pi$  using opposite-side and same-side algorithms'',
LHCb-CONF-2011-050.
\bibitem{jpsiphi}
R.~Aaij {\it et al.}  [LHCb Collaboration],
  %``Measurement of the CP-violating phase phi_s in the decay Bs->J/psi phi,''
  Phys.\ Rev.\ Lett.\  {\bf 108} (2012) 101803
  [arXiv:1112.3183 [hep-ex]].
  %%CITATION = ARXIV:1112.3183;%%
\bibitem{jpsif0}
R.~Aaij {\it et al.}  [LHCb Collaboration],
  %``Measurement of the CP violating phase $\phi_s$ in $\bar{B}^0_s -> J/\psi f_0(980)$,''
  Phys.\ Lett.\ B {\bf 707} (2012) 497
  [arXiv:1112.3056 [hep-ex]].
  %%CITATION = ARXIV:1112.3056;%%
\bibitem{jpsipipi}
R.~Aaij {\it et al.}  [LHCb Collaboration], 
%''Measurement of $\phi_s$ in $B_s\rightarrow J/\psi \pi^+\pi^-$ decays,''
LHCb-PAPER-2012-006 [arXiv:1204.5675v2 [hep-ex]].
\bibitem{phis}
LHCb Collaboration, 
%''Tagged time-dependent angular analysis of $B_s\rightarrow J/\psi\phi$ decays at LHCb.'',
LHCb-CONF-2012-002.
\bibitem{b2hh}
LHCb Collaboration, 
%''Measurement of time-dependent CP violation in charmless two body decays,''
LHCb-CONF-2012-007. 
\bibitem{Deltamd}
LHCb Collaboration, 
%''Measurement of $\Delta m_d$ in $B^0\rightarrow D^-(K^+\pi^-\pi^-) \pi^+$,''
LHCb-CONF-2011-010.
\bibitem{sin2b}
LHCb Collaboration,
%''Search for CP violation in $B^0\rightarrow J/\psi K_s^0$ decays with first LHCb data'',
LHCb-CONF-2011-004.


\end{thebibliography}

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