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\title{New Results on the $B_c^{-}$ Meson at the Tevatron}

\author{M.~A.~Rahaman\address[MCSD]{University of Pittsburgh, Pittsburgh, PA 15260}%
        \thanks{Presented on behalf of the CDF and D$\O$ collaborations with support from the U.S. Department of Energy}}
       
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\runtitle{New Results on the $B_c^{-}$ Meson at the Tevatron}
\runauthor{M. A. Rahaman}

\begin{document}

\begin{abstract}
We present recent results on $B_c^{-}$ meson from the Tevatron. The $B_c^{-}$ meson has been 
observed in semileptonic decays, $B_c^{-} \rightarrow J/\psi{l^{-}}\nu{X}$, both by 
CDF and D$\O$ experiments at a significance larger than 5$\sigma$. The D$\O$ experiment has 
used the candidates in $B_c^{-} \rightarrow J/\psi{\mu^{-}}\nu{X}$ decay to extract 
the mass and lifetime of $B_c^{-}$ meson. The CDF experiment has used both electron and 
muon channel candidates in $B_c^{-} \rightarrow J/\psi{l^{-}}\nu{X}$ decays to measure the 
relative production times branching ratio with respect to $B^{-} \rightarrow J/\psi{K^{-}}$ 
decay and also measured the lifetime of $B_c^{-}$ meson in electron channel as 
$\tau(B_c^{-}) = 0.463_{-0.065}^{+0.073} \pm 0.036$ ps.
The CDF experiment has also observed $B_c^{-} \rightarrow J/\psi\pi^{-}$ decay with a 
significance exceeding 6.5$\sigma$ and has measured the mass of $B_c^{-}$ meson as 
$M(B_c^{-}) = 6276.5 \pm 4.0 \pm 2.7 MeV/c^2$.
     

\vspace{1pc}
\end{abstract}

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\section{Introduction}

\subsection{Tevatron in Run-II}
The Run-II data taking period at the Fermilab Tevatron collider began in
2001 with proton anti-proton collisions at energy $\sqrt{s} = 1.96$ TeV. Since then
data corresponding to a total integrated luminosity of about 1.6 $\rm{fb}^{-1}$ have been
collected.
It has also recorded highest ever instantaneous luminosity in any such hadron 
collider. The two interaction regions of Tevatron are instrumented with the CDF~\cite{cdfd05} and 
D$\O$~\cite{d0de06} detectors.
The state of art silicon tracking system at both CDF and D$\O$ detectors enable to reconstruct 
secondary vertices which is important ingredient to identify $B$ hardron decays. 

The Tevatron is a good source of all $B$ hadrons species including those not easily accessible at $B$ 
factories. The relatively large $b\bar{b}$ production cross section is an advantage to study $B$ physics 
at the Tevatron. However, the total inelastic cross section is proportionally 
large ($10^3$) as well. 
This makes it necessary to collect data with specific triggers. In particular, several of the 
$B_c^{-}$~\cite{conj00} 
decay modes contain a $J/\psi$ in the final state and $J/\psi$ is one of the most easily reconstructable 
decays owing to an efficient dimuon trigger giving high purity $J/\psi\rightarrow{\mu^{+}\mu^{-}}$ 
reconstruction both at CDF and D$\O$ experiments.

\subsection{The $B_c^{-}$ Properties}
The $B_c^{-}$ meson is the ground state of $b$ and $\bar{c}$ quarks which makes it a unique system with 
two heavy quarks of different flavors. The presence of both such quarks impacts on the the production,
decay and mass properties of the $B_c^{-}$ meson. Both color singlet and color octet states contribute
to the production of $B_c^{-}$ meson and separating the contributions suggests a softer $p_{T}$ 
distribution of $B_c^{-}$ compared to the other $B$ mesons~\cite{prod05}. 
The $B_c^{-}$ meson is expected to have decay properties that include both a shorter $c$-like lifetime 
and a large number of possible final states~\cite{deca04}. 
Finally, the measurement of the mass of $B_c^{-}$ is interesting to compare with theoretical 
predictions using potential models~\cite{pote04} and, more recent, the lattice QCD 
calculations~\cite{lqcd05}. All of these theoretical predictions require testing through 
experimental measurements.   

\subsection{The $B_c^{-}$ in Run-I} 
The observation of $20.4_{-5.5}^{+6.2}$ signal events in a combined electron and muon channel by
CDF at Run-I marked the discovery of the $B_c^{-}$ meson~\cite{runi98}. From these events, CDF measured
the mass and lifetime of $B_c^{-}$ as $M(B_c^{-})~=~6.4~\pm~0.39~\pm~0.13~MeV/c^2$ and
$\tau(B_c^{-}) = 0.46_{-0.16}^{+0.18} \pm 0.03$ ps respectively. In addition, the relative production 
cross section times the branching ratio of $B_c^{-}\rightarrow{J/\psi{l^{-}}\nu{X}}$ with respect
to $B^{-}\rightarrow{J/\psi{K^{-}}}$ decay was determined as
${\cal{R}} = 0.132_{-0.037}^{+0.041}\pm0.031_{-0.020}^{+0.032}$ with the assumption of hard $p_{T}$ 
spectrum. These measurements were crude, yet were indication that the study of 
$B_c^{-}$ properties would be very interesting at Tevatron Run-II. 

\section{Measurements of the $B_c^{-}$ properties}
At Run-II both CDF and D$\O$ experiments have studied the $B_c^{-}$ properties. The results are 
reported in the following sections.

\subsection{Results from D$\O$ experiment}
The D$\O$ experiment has analyzed data of total integrated luminosity of 0.21 $\rm{fb}^{-1}$ in
three muon final state, $B_c^{-}\rightarrow{J/\psi\mu^{-}\nu{X}}$, 
where $J/\psi~\rightarrow~\mu^{+}\mu^{-}$. 
The D$\O$ experiment observes 231 candidates including signal and residual backgrounds~\cite{d0resu}. The backgrounds are studied in a
$J/\psi$ + track control sample. The backgrounds are broadly divided in two categories:
prompt background coming from prompt $J/\psi$ plus fake muon and non-prompt background
coming from $J/\psi$ from $B$ mesons plus fake muon. Monte Carlo methods are used to perform
a combined likelihood (${\cal{L}}$) fit with or without the assumption of signal component. The background
only fit is poor compared with the addition of signal component. The difference in 
$-2log{\cal{L}}$ between signal + background fit and background only fit is 60 for 5 degrees of freedom. 
Figure~\ref{fig:d0plot} shows the mass and pseudo-proper time distributions for $B_c^{-}$ 
candidates in D$\O$ data with contribution of prompt and non-prompt backgrounds. 

\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.5\textwidth]{./d0plot.eps}
\caption{The invariant mass (upper) and pseudo-proper time (lower) distributions of $B_c^{-}~\rightarrow~{J/\psi\mu^{-}\nu{X}}$ decay in D$\O$ data with signal and background contributions.}
\label{fig:d0plot}
\end{center}
\end{figure}
 
The fit, where
signal component is included, estimates $95 \pm 12 \pm 11$ signal candidates. 
A combined likelihood fit is performed under a variety of mass hypothesis to extract mass 
and lifetime of $B_c^{-}$ meson. A full 2D fit to the
$-2log{\cal{L}}$ returned by the fit at different mass hypothesis estimates the mass
and lifetime as $M(B_c^{-})~=~5.95_{-0.13}^{+0.14}~\pm~0.34~MeV/c^2$ and 
$\tau(B_c^{-}) = 0.448_{-0.096}^{+0.123} \pm 0.121$ ps respectively. 

\subsection{Results from CDF experiment}
CDF has analyzed data in semileptonic decays, $B_c^{-}\rightarrow{J/\psi{l^{-}}\nu{X}}$, both
electron and muon channels, and 
also in the hadronic decay, $B_c^{-} \rightarrow J/\psi\pi^{-}$, where $J/\psi\rightarrow\mu^{+}\mu^{-}$ 
and $l=e, \mu$. 

\subsubsection{$B_c^{-}\rightarrow{J/\psi{l^{-}}\nu{X}}$ decay in CDF}
In the semileptonic decays, $B_c^{-}\rightarrow{J/\psi{l^{-}}\nu{X}}$, CDF has used 
data of total integrated luminosity of 0.36 $\rm{fb}^{-1}$ where about 2.7 M $J/\psi$ decays are selected.
A third track, identified as muon or electron, is added to $J/\psi$ to reconstruct the $B_c^{-}$ meson. 

In $B_c^{-}\rightarrow{J/\psi{\mu^{-}}\nu{X}}$ decay, a total of 106 candidates are observed including
signal and backgrounds~\cite{cdfmuo}. Both $J/\psi$ + track and $B^{-}~\rightarrow~{J/\psi{K^{-}}}$ samples 
are used to understand the background compositions. The fake muon background is estimated from the 
$J/\psi$ + track sample where the third track is misidentified as muon. The fake probability is estimated by 
studying $D^{0}\rightarrow{K^{-}\pi^{+}}$ and $\Lambda^{0}\rightarrow{p\pi^{-}}$ samples. The composition of 
K, $\pi$ and $p$ in $J/\psi$ + track sample are estimated using PID quantities ($ToF$ and $dE/dX$) 
at the CDF. The number of fake muons is then calculated by multiplying the fake probability with the composition.
The $b\bar{b}$ background
is estimated using Pythia Monte Carlo normalized to $B^{-}\rightarrow{J/\psi{K^{-}}}$ data. Finally,
the sideband events of $J/\psi$ are used, to estimate the contribution coming from
fake $J/\psi$ events. These three background processes are estimated to contribute approximately
16 (fake-$\mu$), 13 ($b\bar{b}$) and 17 (fake $J/\psi$) events resulting
in a 5.2$\sigma$ excess of signal consisting of $60.0 \pm 12.6$ candidates. 
Figure~\ref{fig:cdfmass} shows the invariant mass distribution of $J/\psi\mu$
obtained from CDF data with background contribution. 
The production cross section times branching ratio of $B_c^{-}~\rightarrow~J/\psi{\mu^{-}}\nu{X}$ decay
with respect to $B^{-}\rightarrow{J/\psi{K^{-}}}$ decay is measured as, 
${\cal{R}} = 0.249 \pm 0.045 \pm 0.069_{-0.033}^{+0.082}$ with $p_{T}(B) > 4$ GeV/c and $|y| < 1$.

\begin{figure}[t]
%\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.5\textwidth]{./BcYield2.eps}
\caption{The invariant mass distributions of $J/\psi\mu$ in CDF data with background contribution.}
\label{fig:cdfmass}
\end{center}
\end{figure}

CDF has also studied the $B_c^{-}\rightarrow{J/\psi{e^{-}}\nu{X}}$ decay and selected a total
179 candidates including signal and backgrounds~\cite{cdfele}. The backgrounds in this channel are 
further complicated by the presence of conversion photon in addition to the fake-$e$, $b\bar{b}$ 
and fake-$J/\psi$ backgrounds. 
During the reconstruction, the events which are tagged to be as photon conversion are rejected. 
The residual conversion is estimated from the $J/\psi$ + tagged sample using the conversion finding 
efficiecy obtained from Monte Carlo. The conversion background contributes 
approximately 15 out of total 64 background events resulting in an excess of $114.9 \pm 15.5 \pm 13.6$ 
$B_c^{-}$ signal candidates which corresponds to a significance of 5.9$\sigma$. The measurement of
the production cross section times branching ratio of $B_c^{-}~\rightarrow~J/\psi{e^{-}}\nu{X}$ decay
with respect to $B^{-}~\rightarrow~{J/\psi{K^{-}}}$ decay is measured as,
${\cal{R}}~=~0.282~\pm~0.038~\pm~0.035~\pm~0.065$ with $p_{T}(B) > 4$ GeV/c and $|y| < 1$.       

The lifetime of the $B_c^{-}$ meson is also measured in the $B_c^{-}\rightarrow{J/\psi{e^{-}}\nu{X}}$ decay
mode~\cite{cdfect}. To have convenient parameterization of decay length, the lifetime related 
requirements have been relaxed during event selection compared to the $\cal{R}$ analysis. The decay 
lenght is corrected by a factor, $K=(m(B)/p_{T}(B))/(m(J/\psi{e})/p_{T}(J/\psi{e}))$, 
obtained from Monte Carlo to account for the missing particles. 
Figure~\ref{fig:cdfctau} shows the psedo-proper decay length distribution obtained from CDF data with
signal and bacground contributions. 
From an unbinned likelihood fit, the lifetime of the $B_c^{-}$ meson is measured as
$\tau(B_c^{-})~=~0.463~_{-0.065}^{+0.073}~\pm~0.036$ ps.

%\begin{figure}[t]
\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.5\textwidth]{./lifetime_fit_jpsie2.eps}
\caption{The pseudo-proper decay length distributions of $B_c^{-}\rightarrow{J/\psi{e^{-}}\nu{X}}$ decay 
in CDF data with signal and background contributions.}
\label{fig:cdfctau}
\end{center}
\end{figure}

\subsubsection{$B_c^{-} \rightarrow J/\psi\pi^{-}$ decay in CDF}
CDF reported initial evidence of $B_c^{-}\rightarrow{J/\psi\pi^{-}}$ decay 
with 0.36 $\rm{fb}^{-1}$~\cite{cdfpio}.
Recently, CDF has analysed data of total integrated luminosity of 1.1 $\rm{fb}^{-1}$ in 
$B_c^{-} \rightarrow J/\psi\pi^{-}$ decay using an independent analysis and has measured 
the mass of $B_c^{-}$ meson~\cite{cdfpin}. The analysis cuts are optimized in an unbiased way 
on the reference $B^{-}\rightarrow{J/\psi{K}^{-}}$ decay using first 0.36 $\rm{fb}^{-1}$ of data 
and the sideband background events below 5.5 $GeV/c^2$. The optimized cuts are then applied to
analyse $B_c^{-} \rightarrow J/\psi\pi^{-}$ decay. The selection requirements include the $K$ 
candidate must have an impact parameter significantly displaced from the primary vertex while 
simultaneously pointing toward the vertex formed by the two muons of $J/\psi$. 
A small excess of events is observed in this
analysis with 0.36 $\rm{fb}^{-1}$ data and with accumalation of full 1.1 ${\rm{fb^{-1}}}$ data, the 
excess becomes more significant. A fit to the data of 1.1 $\rm{fb}^{-1}$ with Gaussian signal and linear
background gives $49.1 \pm 9.7$ $B_c^{-}$ signal events over a background of 34.1 events
which corresponds to a significance larger than 6.5$\sigma$ based upon simulations that include 
random fluctuations over a wide search window. Figure~\ref{fig:cdfjpsipi} shows the invariant
mass distribution of $J/\psi\pi$ candidates in a mass window 5.6 to 7.2 $\rm{GeV/c^2}$.
An unbinned likelihood fit is used to extract the mass of the $B_c^{-}$ meson as
$M(B_c^{-}) = 6276.5 \pm 4.0 \pm 2.7~MeV/c^2$ compared to the prediction from lattice QCD calculation
of $M(B_c^{-})_{LAT} = 6304 \pm 12_{-0}^{+18}~MeV/c^2$.   
 
\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.5\textwidth]{./psipiv3.eps}
\caption{The invariant mass distributions of $J/\psi\pi$ 
in CDF data of 1.1 $\rm{fb}^{-1}$.}
\label{fig:cdfjpsipi}
\end{center}
\end{figure}

\section{Summary and Conclusions}
Both CDF and D$\O$ experiments at Tevatron have studied the $B_c^{-}$ meson properties from the RUN-II data.
The D$\O$ experiment has measured the lifetime and the mass of the $B_c^{-}$ meson in tri-muon channel. 
The CDF experiment has analysed data in semileptonic decays both in $e$ and $\mu$ channels and 
measured the production cross section times branching ratio with respect to 
$B^{-}\rightarrow{J/\psi{K}^{-}}$ decay and also measured the lifetime in $e$-channel. 
The mass of the $B_c^{-}$ meson has been measured in hadronic decay channel which is 
already challenging the prediction of Lattice QCD calculation. 


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\end{thebibliography}

\end{document}
