Search for rare decays of the $B_s$ Meson at the Tevatron
Ralf Patrick Bernhard
We report on searches for Flavor-Changing Neutral Current (FCNC) decays in \ppbar collisions at a \CME of 1.96 \tev~using up to 0.78~\fb of data, collected at the CDF and D\O~detectors respectively. The rare FCNC decays presented here are the searches for \bsdmm\ and \bsphimumu.
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\newcommand{\um}{\ensuremath{\mathrm{\mu m}}}
%\newcommand{\pp}{\ensuremath{p\overline{p}}}
%\newcommand{\pb}{\ensuremath{\mathrm{pb}^{-1}}}
%\newcommand{\fb}{\ensuremath{\mathrm{fb}^{-1}}}
\newcommand{\bs}{\ensuremath{B_s^0}}
\newcommand{\bd}{\ensuremath{B_d^0}}
\newcommand{\bsd}{\ensuremath{B_{s,d}^0}}
\newcommand{\bu}{\ensuremath{B^{+}}}
\newcommand{\mm}{\ensuremath{\mu^{+}\mu^{-}}}
\newcommand{\mmss}{\ensuremath{\mu^{\pm}\mu^{\pm}}}
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\newcommand{\brbsmm}{\ensuremath{\mathcal{B}(\bsmm)}}
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\newcommand{\bsphimumu}{\ensuremath{\bs \ra \phi \,\mu^+ \mu^-}}
\newcommand{\bdkstarll}{\ensuremath{B_d^0  \rightarrow K^\ast  \, \ell^+ \ell^-}}
\newcommand{\bukll}{\ensuremath{B^\pm  \rightarrow K^\pm \, \ell^+ \ell^-}}
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\begin{document}
\vspace*{4cm}
\title{Search for rare decays of the $B_s$ Meson at the Tevatron}

\author{Ralf Patrick Bernhard}

\address{Institute of Physics, Winterthurerstrasse 190,\\
8057 Z\"urich, Switzerland}

\maketitle

\vskip -5 cm
\centerline{\includegraphics[width = 4.4 cm]{Bernhard.eps} }
\vskip 0.5 cm
\abstracts{
We report on searches for Flavor-Changing Neutral Current (FCNC) decays in \ppbar collisions at a \CME of 1.96 \tev~using up to 0.78~\fb of data, collected at the CDF and D\O~detectors respectively. The rare FCNC decays presented here are the searches for \bsdmm\ and \bsphimumu.
}

\section{Introduction}
In the Standard Model (SM), Flavor-Changing Neutral Current (FCNC) decays are
highly suppressed and can only occur through higher order diagrams.
For example the  branching fractions of the FCNC decays \bsdmm\ have a 
%decay rate for the FCNC decay \bsmm is proportional to the
%CKM matrix element $\left|V_{ts}\right|^{2}$. The rate of \bdmm\ decays
%is further suppressed by the ratio of $\left|V_{td}/V_{ts}\right|^2$.
SM expectation~\cite{smbr} of
%for these branching fractions are
$\brbsmm=(3.42\pm0.54)\times10^{-9}$ and
$\brbdmm=(1.00\pm0.14)\times10^{-10}$. These predictions are about two orders
of magnitude smaller than the current experimental sensitivity.
However, new physics contributions can significantly enhance these branching
fractions. In the absence of an observation, any improvements 
to the limits can be used to set significant constraints on various
models beyond the SM.
The exclusive FCNC decay \bsphimumu\ is related to the quark-level transition of $b \rightarrow s\,
\ell^+\ell^-$. The long term goal is  study kinematic properties for these decay like the invariant di-muon mass distribution or the forward backward asymmetry.
%The corresponding decays \bdkstarll\ and \bukll\ have been already measured at $B$-factories and 
%were found to be consistent with the SM within the present experimental uncertainties. 
But also an observation of this decay or experimental upper limit on its rate will yield additional important information on the flavor dynamics of FCNC decays.

\section{Search for the rare decays \bsdmm}

%The \dzero\ and CDF collaborations have published several papers describing
%searches for the rare \bsmm\ and \bdmm\ decays at Run II of the
%Tevatron~\cite{D0BsMMprl}~\cite{CDFBsMMprl}~\cite{CDFBsMMprl1}.
The most stringent published limits are a result of a combination~\cite{BsMMCombo} of the recent \dzero\ result~\cite{D0BsMMprl} using 0.3 \fb of data and the latest published limit from CDF~\cite{CDFBsMMprl} using 0.36 \fb of recorded data. 
%The most recent \dzero\  and CDF results have been combined~\cite{BsMMCombo}
%and yielded the most stringent published limits on both decay modes. 
The obtained limits  at 95\% C.L. were ${\cal B}(\bsmm) < 1.5 \times 10^{-7}$ and ${\cal B}(\bdmm) < 4.0 \times 10^{-8}$ respectively.

The used analysis procedure is similar in the \dzero and  CDF experiments.    
After a pre-selection step, special discriminating variables in an optimization procedure are used to further enhance the signal efficiency while reducing the expected background. Both collaborations employ a ``blind'' analysis strategy when choosing the
final selection criteria. As normalization the well measured and high statistics decay \bjk\ was used. 
In the following the most recent analyses from both experiments will be described. 

The strategy of the \dzero~collaboration is to use the already published analysis procedure~\cite{D0BsMMprl} for the data set recorded after  the first publication, to obtain a sensitivity. This obtained sensitivity is then combined with the already obtained limit. CDF used a published analysis procedure~\cite{CDFBsMMprl} as well and added more data to get an updated limit.
 
\dzero~used data collected by dimuon tiggers with two muons of opposite charge that form a
common secondary 3D-vertex with an invariant mass between 4.5 and 7.0 GeV/$c^2$. Each muon candidate had to have $p_T > 2.5~$GeV/$c$, $|\eta| < 2.0$ and a sufficient number of hits in the central
tracking station. To ensure a similar $p_T$ dependence of the $\mu^+\mu^-$ system in the signal and in
the normalization channel, $p_T^B$ had to be greater than 5~GeV/$c$.

For the \dzero analysis the following variables were found to exploit best the distinctive properties of the $B$ meson: the 3D Opening-Angle, \pting\ (here the decay
length vector is determined in three-dimensions), the $B$-candidate Isolation,
\iso, and the Transverse Decay Length Significance, $L_{2D}/\sigma_{L_{2D}}$.
%\dzero uses a Random Grid Search (RGS)~\cite{RGSearch} and an optimization procedure
%proposed by Punzi~\cite{Punzi} to find the optimal values of
%the discriminating variables by maximizing the ratio
%$P = \frac{\epsilon_{\bs}}{\frac{a}{2}+ \sqrt{N_{b}}}$.
%Here, $\epsilon_{\bs}$ is the reconstruction efficiency of the
%signal MC relative to the pre-selection and $N_{b}$ is the expected
%number of background events in the signal region, estimated by an interpolation from a likelihood fit to sideband data.
%The constant $a$ is the number of sigmas corresponding to the confidence
%level at which the signal hypothesis is tested and was set to $a=2$ corresponding to a hypothesis test at a 95\% C.L.
After optimizing the cuts and a linear interpolation of the sideband population for the data sample into the signal region we obtain an expected number of background events of 2.2$\pm$0.7. The remaining background distribution is shown
in Fig.~\ref{fig_background_box_closed} (left side). %It is to mention, that 
The values of the discriminating variables for this additional data set changed only slightly with respect to the previous analysis. The resulting sensitivity is calculated using the \bjk\  decay as normalization. The invariant mass distribution of the decay channel is shown in Fig.~\ref{fig_background_box_closed} (right side).
This yields a sensitivity including all the statistical and systematical uncertainties of
%\begin{center}
$\langle {\cal B}(B_s^0 \rightarrow \mu^+ \mu^-)\rangle < 3.0\,(3.7)\times 10^{-7}$
%\end{center}
at the 90\% (95\%) C.L.

\begin{figure}[h]
\begin{minipage}[c]{0.49\textwidth}
\begin{center}
  \includegraphics[width=\linewidth]{hMassBack_sens400.eps}
\end{center}
\end{minipage}
\begin{minipage}[c]{0.49\textwidth}
\begin{center}
   \includegraphics[width=\linewidth]{BuMass.eps}
\end{center}
\end{minipage}
  \caption{\label{fig_background_box_closed}The invariant mass
    distribution for the decay $\bsmm$ after optimized requirements on the discriminating variables on the left side. On the right side the invariant mass distribution of the normalization channel  \bjk\  is shown.}
\end{figure}

The obtained expected limit for the new data set is combined with the previous analysis~\cite{D0BsMMprl} using 0.3 \fb of data. 
%The previous finding yielded $4.3\pm1.2$ expected events while four events were finally observed in the signal region. 
The expected limit for the entire data set is thus a combination of two measurements: one actual measurement with observed events (old data) and one hypothetical experiment (new data) with all possible outcomes in the signal region weighted by their Poisson probability of occurrence, i.e., under the assumption of a background hypothesis only. We have used a Bayesian technique to combine the two experiments and include at this stage the uncorrelated uncertainties into the expected limit calculation. The background uncertainty, the uncertainty on the number of normalization events and the statistical error on the efficiencies are considered as uncorrelated.
The expected upper limit at the 90\% (95\%) C.L. for the entire D\O \ data set of 0.7 \fb is %then given by
\begin{eqnarray*}
\langle {\cal B}(B_s^0 \rightarrow \mu^+ \mu^-)\rangle < 1.9\,(2.3)\times 10^{-7}.
\end{eqnarray*}

The CDF detector has of two muon detectors with different acceptances.
Four layers of planar drift chambers (CMU) detect muon candidates with 
$p_T>1.4~\GeV/c$ and provide coverage in the pseudorapidity range 
$\left|\eta\right|<0.6$. The central muon extension (CMX) consists of conical 
sections of drift tubes and extends the coverage to $0.6<\left|\eta\right|<1.0$ 
for muon candidates with $p_T>2.0~\GeV/c$.  
The data used in the analysis are selected by two classes of dimuon 
triggers: for the CMU-CMU (U-U) triggers both muon candidates are reconstructed 
in the CMU chambers, while for the CMU-CMX (U-X) triggers one of the muon 
candidates is reconstructed in the CMX chambers.  
%The inclusion of the U-X 
%trigger increases the signal acceptance by about 50\%.  The details of the trigger 
%system and selection requirements can be found in Refs.~\cite{CDFBsMMprl1,CDFBpT}.  
%The invariant mass distribution of those events satisfying the trigger requirements
%and a loose set of track and muon quality criteria is shown in 
%figure~\ref{fig:CDFMmmTrig}.  The $J/\psi\ra\mm$ peak used for some of the 
%efficiency studies and in reconstructing the $B\ra J/\psi X$ normalization
%decays is evident.
Since they have different sensitivities, the U-U and U-X channels are treated separately, 
combining the results at the end.
The offline reconstruction begins by identifying two muon candidates of 
opposite charge which satisfy the online dimuon trigger requirements and  
with $p_{T}> 2\ (2.2) \;\GeV/c$.  
%To maintain as high an efficiency 
%as possible, we only explicitely require $\geq 3$ SVX $r-\phi$ hits on each 
%muon cadidate.  
The random combinatoric backgrounds are suppressed by requiring the vector sum 
of the muon transverse momenta to be $| \ptmm | > 4\;\GeV/c$.  
%This \ptmm\  requirement was optimized as part of the selection criteria.
%The remaining pairs of muon tracks are then refit under the constraint that they
%come from the same three-dimensional (3D) space point, and are required to 
%satisfy vertex fit quality criteria designed to remove poorly reconstructed
%vertices in the tail of the fit-$\chi^{2}$ distribution.
The 3D decay length is given by $\Lxyz=\vec{L}\cdot\pmm/|\pmm|$, 
where $\vec{L}$ is the displacement vector from the primary to the dimuon vertex.  
The primary vertex is determined using a constrained vertex fit of all  
tracks in the event, excluding the \mm\ pair and other secondary decay tracks.  
For each $B$-candidate the proper decay time $\tau=\Mmm\Lxyz/|\pmm|$ is estimated, where
\Mmm\ is the invariant mass and \pmm\ is the momentum vector of the dimuon system.
Additional background is reduced by demanding $\Lxyz < 1.0~\cm$, the 
uncertainty on $\Lxyz$ to be less than 150 \um, and  
$2\sigma_{\ctau} < \ctau <0.3~\cm$, where $\ctau=c\cdot \tau$ and $\sigma_{\ctau}$ 
is the total uncertainty on $\ctau$.  
%There are 22459 (14305) dimuon candidates 
%that fulfill all the above trigger and offline reconstruction requirements in the 
%U-U (U-X) channel.  At this stage, the data sample is dominated by 
%random combinatoric background.

To enhance signal and background separation CDF constructs a multivariate
likelihood ratio based on the input variables: \iso, \pting, and
\ctau\ probability $P(\ctau)=e^{-\ctau/c\tau_{B_{s(d)}}}$, where
$\tau_{B_{s(d)}}$ is the world average $B_{s(d)}$ lifetime.  CDF uses the
$P(\ctau)$ variable instead of $\ctau$ in constructing the likelihood
ratio because the $P(\ctau)$ distribution is nearly flat, and therefore
better behaved in the likelihood.  The likelihood ratio is then defined to be
\begin{equation}\label{eq:LH}
  L_R = \frac{\prod_{i} \mathbf{P}_{s}(x_{i})}
       {\prod_{i} \mathbf{P}_{s}(x_{i})
      + \prod_{i} \mathbf{P}_{b}(x_{i})},
\end{equation}
where $x_1=\iso$, $x_2=\pting$, $x_3=P(\ctau)$, and $\mathbf{P}_{s(b)}(x_{i})$
is the probability that a signal (background) event has an observed $x_i$.
The probability distributions for the signal events are obtained from the signal
MC and the background distributions are taken from the data
sidebands. An example of the likelihood ratio for the U-U channel is shown in Fig~\ref{fig:CDFBsMMResults} (left side). 
The optimization of the analysis is based on the {\it{a priori}} expected $90\%$~C.L. upper limit on \brbsdmm.  The expected limit for a given set of optimization requirements is computed by summing the $90\%$~C.L. limits over all possible observations $N_o$, weighted by the corresponding Poisson probability when expecting $N_b$ background events.
A scan over a range of $L_R$ requirements
the optimal value was determined to be $L_R>0.99$.  With the optimized selection requirements, 
the expected number of background events in 0.78 \fb for \bs\ in a signal region of $\pm 60~\MeV/c^2$ 
($\pm 2.5\sigma_{M}$) around the world average \bs\ mass~\cite{pdg} is
$N_{b}$ is $0.88\pm0.30$ [$0.39\pm0.21$]  for the U-U [U-X] channel. The expected number of background events in a $\pm 60~\MeV/c^2$  
signal region around the \bd\  is estimated to be $N_{b}$ is $1.86\pm0.34$ [$0.59\pm0.21$]  in the U-U [U-X] channel.
%is the same in the \bs\ and \bd\ 
%search windows.  Within the signal region of $\pm 60~\MeV/c^2$ 
%($\pm 2.5\sigma_{M}$) around the world average \bs\ or \bd\ mass~\cite{pdg}, 
%$N_{b}$ is $0.88\pm0.30$ [$0.39\pm0.21$] .U-U [U-X] channel
%and the
%single-event-sensitivity is $(1.0\pm0.2) \times 10^{-7}$ 
%[$(1.5\pm0.3) \times 10^{-7}$] for the U-U [U-X] channel.  
Using these criteria 1 [0] and 2 [0] events are observed in the U-U [U-X] channel of the  \bs\ and \bd\ signal boxes respectively which is consistent
with the background expectations. 
%we observe no events inside either the \bs\ or \bd\ signal box 
%as 
shown in Fig.~\ref{fig:CDFBsMMResults} (right side). 
%Using Eq.~\ref{eq:brbsmm} and 
Combining the U-U and U-X channels taking into
account the correlated uncertainties, 90\% (95\%) C.L. limits can be derived to be
\begin{eqnarray*}
\brbsmm &<& 8\times 10^{-8} (1.0\times 10^{-7}) \, \, \, {\rm and} \\
\brbdmm &<& 2.3\times 10^{-8} (3.0\times 10^{-8}).  
\end{eqnarray*}

\begin{figure}[h]
\begin{minipage}[c]{0.49\textwidth}
\begin{center}
  \includegraphics[width=\linewidth]{Dlhood_SBvsBG_031606.eps}
\end{center}
\end{minipage}
\begin{minipage}[c]{0.49\textwidth}
\begin{center}
   \includegraphics[width=\linewidth]{DCMUX_Open_MvL90_031506.eps}
\end{center}
\end{minipage}
  \caption{\label{fig:CDFBsMMResults} Signal and background distribution of the likelihood ratio for the U-U channel on the left side. Invariant mass distribution versus the event likelihood with the signal boxes indicated on the right side.}
\end{figure}

\section{Search for the rare decays \bsphimumu}
The decay \bsphimumu\ is an exclusive FCNC in the \bs\ meson system. 
%An observation of this decay or experimental upper limit on its rate will yield additional important information on the flavor dynamics of FCNC decays. 
Within the SM, the decay rate for the \bsphimumu\ decay, neglecting the interference effects with the much stronger \bjf\ and \bpf\ resonance decays, is predicted to be of the order of $1.6\times 10^{-6}$~(see Ref.~\cite{geng}) with about 30\% uncertainty due to poorly known form factors. 

A search for this rare decay is performed by the \dzero collaboration and uses about 0.45~\fb~of data. The event pre-selection starts by requiring exactly two muons fulfilling quality cuts on the number of hits in the muon system and the two additional charged particle tracks to form a good vertex. The invariant mass of the two muons is required to be within
$0.5<m_{\mu^+\mu^-}<4.4$~GeV/$c^2$. In this mass region, the $J/\psi(\rightarrow \mu^+\mu^-)$ and $\psi(2S)(\rightarrow \mu^+\mu^-)$ resonances are excluded to discriminate against dominant resonant decays. 
%The rejected mass region then covers $\pm 5 \sigma$ wide windows around the resonance masses.
The $\chi^2/d.o.f.$ of the two-muon vertex is required to be less than
10.  %a sufficient number of hits in the tracking detectors.
The tracks that are matched to each muon are required to have
a sufficient number of hits in the tracking detectors 
%at least three (four) measurements in the SMT (CFT) 
and the transverse momentum of each of the muons is required to be greater
than 2.5~GeV/$c$ with $|\eta|<2.0$ to be well inside the fiducial
tracking and muon detector acceptances.
%In order to select well-measured secondary vertices,
%we define the two-dimensional decay length $L_{xy}$ in the plane
%transverse to the beamline, and require its uncertainty $\delta
%L_{xy}$ to be less than 0.15~mm. $L_{xy}$ is calculated
%as $L_{xy}=\frac{\vec{l}_{vtx}\cdot \vec{p}_T^B}{p_T^B}$, where $p_T^B$ is the
%transverse momentum of the candidate $\bs$, and $\vec{l}_{vtx}$ represents
%the vector pointing from the primary vertex to the secondary vertex. The uncertainty on the transverse decay length, $\delta L_{xy}$, is calculated by taking into account the
%uncertainties in both the primary and secondary vertex positions. The
%primary vertex itself is found for each event using a beam-spot
%constrained fit as described in Ref.~\cite{delphi}.
The number of $\bsphimumu$ candidates is further
reduced by requiring $p_T^B>5~$GeV/$c$ and asking the $\bs$
candidate vertex to have $\chi^2 < 36$ with 5 $d.o.f.$ The two
tracks forming the $\phi$ candidate are further required to have
$p_T>0.7$~GeV/$c$ and their invariant mass within the range $1.008
<m_{\phi} < 1.032~$GeV/$c^2$. In analogy to the search for the decay \bsmm the same discriminating variables and optimization procedure is used to enhance the sensitivity. The optimal values of the discriminating variables yield after a linear interpolation of the sidebands into the mass window signal region, 
%the expected number of background events is 
1.6$\pm$0.4 expected background events as shown in Fig.~\ref{fig_background_bsphimumu} (left side). Upon examining the data in the mass region, zero candidate events are observed in the signal region, consistent with the background events as
estimated from sidebands. The Poisson probability of observing zero events for an expected background of $1.6\pm0.4$ is $p=0.22$.
In the absence of an apparent signal, a limit on the branching fraction ${\cal B}(\bsphimumu)$ can be computed by normalizing the upper limit on
the number of events in the $B^0_s$ signal region to the number of reconstructed $\bjf$ events.
The mass spectrum of the reconstructed $\bjf$ after all cuts is shown in Fig.~\ref{fig_background_bsphimumu} (right side).
%Including he statistical and systematic uncertainties 
%can be included
%in the limit calculation by integrating over
%probability functions that parameterize the uncertainties. We
%use a prescription~\cite{conrad} where we construct a frequentist
%confidence interval with the Feldman and Cousins~\cite{feldman}
%ordering scheme for the MC integration. The background is modeled as a
%Gaussian distribution with its mean value equal to the expected number
%of background events and its standard deviation equal to the background
%uncertainty. 
Including statistical and systematic uncertainties, without including the uncertainty on the measured branching fraction of the decay $\bjf$, the Feldman and Cousins (FC) limit is
\begin{eqnarray*}
\frac{{\cal B}(\bsphimumu)}{{\cal B}(\bjf)} <4.4\,(3.5)\,\times 10^{-3}
\end{eqnarray*}

at the 95\% (90\%) C.L. respectively. Taking a Bayesian approach with a flat prior and the
uncertainties treated as Gaussian distributions in the integration, an
upper limit of ${\cal B}(\bsphimumu)/{\cal B}(\bjf) <7.4 \,(5.6)
\times 10^{-3}$ at the 95\% (90\%) C.L., respectively was found.
Using only the central value of the world average branching fraction~\cite{pdg} of
${\cal B}(\bjf) = (9.3 \pm 3.3)\,\times 10^{-4}$, the FC limit
corresponds to ${\cal B}(\bsphimumu) < 4.1\,(3.2)\,\times 10^{-6}$ at
the 95\% (90\%) C.L. respectively. This is presently the most stringent upper bound and has been recently submitted to PRL~\cite{Abazov:2006qm}.

\begin{figure}[h]
\begin{minipage}[c]{0.49\textwidth}
\begin{center}
  \includegraphics[width=\linewidth]{BsMuMuPhiRGS.eps}
\end{center}
\end{minipage}
\begin{minipage}[c]{0.49\textwidth}
\begin{center}
\includegraphics[width=\linewidth]{BsJpsiPhiMassRGSMuMuPhiPRL.eps}
\end{center}
\end{minipage}
  \caption{\label{fig_background_bsphimumu}The invariant mass
    distribution for the decay $\bsphimumu$ on the left side.
    %after optimized
    %requirements on the discriminating variables. The solid line shows the sidebands background interpolation into the signal region.}
	On the right side the invariant mass distribution of the normalization channel $\bjf$ is shown.
}
\end{figure}


\section*{References}
\begin{thebibliography}{99}
%\bibitem{qconj}
%Throughout this section inclusion of charge conjugate modes is implicit.

\bibitem{smbr}
  G.~Buchalla and A.~J.~Buras,  Nucl.\ Phys.\ {\bf B400}, 225 (1993);
  A.J.~Buras, Phys.\ Lett.\ B {\bf{566}}, 115 (2003).

\bibitem{BsMMCombo}
  R. Bernhard {\it et al.}, hep-ex/0508058.

\bibitem{D0BsMMprl}
 \dzero\ Collaboration, V.~Abazov {\it{et al.}},
 Phys.\ Rev.\ Lett.\ {\bf{94}}, 071802 (2005); A preliminary result using 300 \pb is described in \dzero note 4733-CONF (2005).

\bibitem{CDFBsMMprl}
 CDF Collaboration, A.~Abulencia {\it{et al.}},
 Phys.\ Rev.\ Lett.\ {\bf{95}}, 221805 (2005).

%\bibitem{CDFBsMMprl1}
%  CDF~Collaboration, D.~Acosta {\it{et al.}},
%  Phys.\ Rev.\ Lett.\ {\bf{93}}, 032001 (2004).

\bibitem{pdg}S.~Eidelman {\it et al.}, Phys. Lett. B  {\bf 592}, 1 (2004).

\bibitem{geng} C.~Q.~Geng and C.~C.~Liu, J.~Phys.~G {\bf 29}, 1103 (2003).

\bibitem{Abazov:2006qm}
  V.~M.~Abazov {\it et al.}  [D0 Collaboration],
  %``Search for the rare decay B0/s $\to$ Phi mu+ mu- with the D0 detector,''
  hep-ex/0604015.
  %%CITATION = HEP-EX 0604015;%%

\end{thebibliography}

\end{document}

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% End of moriond.tex  %
%%%%%%%%%%%%%%%%%%%%%%

hep-ex0605065.extracted_bib
\begin{thebibliography}{99}
%\bibitem{qconj}
%Throughout this section inclusion of charge conjugate modes is implicit.

\bibitem{smbr}
  G.~Buchalla and A.~J.~Buras,  Nucl.\ Phys.\ {\bf B400}, 225 (1993);
  A.J.~Buras, Phys.\ Lett.\ B {\bf{566}}, 115 (2003).

\bibitem{BsMMCombo}
  R. Bernhard {\it et al.}, hep-ex/0508058.

\bibitem{D0BsMMprl}
 \dzero\ Collaboration, V.~Abazov {\it{et al.}},
 Phys.\ Rev.\ Lett.\ {\bf{94}}, 071802 (2005); A preliminary result using 300 \pb is described in \dzero note 4733-CONF (2005).

\bibitem{CDFBsMMprl}
 CDF Collaboration, A.~Abulencia {\it{et al.}},
 Phys.\ Rev.\ Lett.\ {\bf{95}}, 221805 (2005).

%\bibitem{CDFBsMMprl1}
%  CDF~Collaboration, D.~Acosta {\it{et al.}},
%  Phys.\ Rev.\ Lett.\ {\bf{93}}, 032001 (2004).

\bibitem{pdg}S.~Eidelman {\it et al.}, Phys. Lett. B  {\bf 592}, 1 (2004).

\bibitem{geng} C.~Q.~Geng and C.~C.~Liu, J.~Phys.~G {\bf 29}, 1103 (2003).

\bibitem{Abazov:2006qm}
  V.~M.~Abazov {\it et al.}  [D0 Collaboration],
  %``Search for the rare decay B0/s $\to$ Phi mu+ mu- with the D0 detector,''
  hep-ex/0604015.
  %%CITATION = HEP-EX 0604015;%%

\end{thebibliography}