Search for the Production of Single Sleptons through $R$-parity Violation in $p \bar{p}$ Collisions at $\sqrt{s}=$1.8 TeV
We report the first search for supersymmetric particles via $s$-channel production and decay of smuons or muon sneutrinos at hadronic colliders. The data for the two-muon and two-jets final states were collected by the D\O\ experiment, and correspond to an integrated luminosity of 94$\pm 5$ pb$^{-1}$. Assuming that $R$-parity is violated via the single coupling $\lambda^{\prime}_{211}$, the number of candidate events is in agreement with expectation from the standard model. Exclusion contours are given in the ($m_0,m_{1/2}$) and ($m_{\tilde{\chi}},m_{\tilde{\nu}})$ planes for $\lambda^{\prime}_{211}$=0.09, 0.08 and 0.07.
paper.tex
%\documentstyle[aps,twocolumn,psfig,floats]{revtex}  
\documentstyle[prl,aps,psfig]{revtex}  
\def \RPV {R-parity violating }
\def \susyq {supersymmetric }
\def \sugra {supergravity }
\newcommand{\rpv}{\mbox{$\not \hspace{-0.15cm} R_p$}}
\newcommand{\tab}{\begin{tabular}}
\newcommand{\etab}{\end{tabular}}

%\draft

\begin{document}
\preprint{D\O\ Paper XXXX}
\title{Search for the Production of Single Sleptons through $R$-parity Violation
in $p \bar{p}$ Collisions at $\sqrt{s}=$1.8 TeV}
\input{list_of_authors.texf}
\date{\today}
\maketitle
\vskip 2.0cm







\begin{abstract}
We report the first search for supersymmetric particles via $s$-channel 
production and decay 
of smuons or muon sneutrinos at hadronic colliders.
The data for the two-muon and two-jets final states were 
collected by the D\O\ experiment, and
correspond to an integrated luminosity of 94$\pm 5$ pb$^{-1}$.
Assuming that $R$-parity is violated via the single 
coupling $\lambda^{\prime}_{211}$, 
the number of candidate 
events  
is in agreement with expectation from the standard model. Exclusion 
contours are given in the ($m_0,m_{1/2}$) and ($m_{\tilde{\chi}},m_{\tilde{\nu}})$
planes for  $\lambda^{\prime}_{211}$=0.09, 0.08 and 0.07. 
\end{abstract}

%\pacs{PACS numbers: 12.60.Jv,11.30.Pb}

\twocolumn


%\section{Introduction }

Events with at least two muons and two hadronic jets in $p \bar{p}$ collisions 
provide a good sample in which
to search for new physics because the contribution from standard-model 
processes to such states is rather small. Any excess in such topologies can 
be attributed to a signal
from $R$-parity violating supersymmetry (SUSY), where $R$-parity 
is not conserved either in
the production or in the decay of sparticles.


$R$-parity of any particle \cite{rparity} is defined as $ R_p = (-1)^{3B+L+2S}$, 
where $B$,
$L$ and $S$ are the baryon, lepton and spin quantum numbers. 
$R_p$ equals $+1$ for SM particles and $-1$ for 
supersymmetric partners.
The conservation of $R$-parity is often assumed in experimental searches, 
because, without that, simultaneous lepton and baryon number
violation would lead to rapid proton decay. However, this argument can be
circumvented if
lepton and baryon number conservation are treated independently.   

In supersymmetry, $R$-parity violation (\rpv) can occur through
terms in the superpotential,
that are trilinear in quark and lepton superfields \cite{rparity}:
%
%
\begin{eqnarray}
\lambda _{ijk} L_i L_j \bar{E^c_k}+
\lambda ' _{ijk} L_i Q_j \bar{D^c_k}+ 
\lambda '' _{ijk} \bar{U_i^c} \bar{D_j^c} \bar{D_k^c} ,
\label{super}
\end{eqnarray}
%
%
where $i,j,$ and $k$ are family indices; $L$ and $Q$ are the SU(2)-doublet lepton and
quark superfields; $E$, $U$, and $D$ are the singlet-lepton, up-quark, 
and down-quark
superfields, respectively.

Such \rpv \ couplings offer the possibility of producing single 
\susyq particles \cite{Dim1}, which is not the case for
$R_p$-conserving supersymmetric
models, in which particles and sparticles are always produced in pairs.
Although the \rpv \ coupling constants are severely constrained by 
low-energy experimental bounds \cite{Drein,referbound}, $s$-channel
production and decay of sparticles can have a substantial cross section at lepton
and hadron colliders \cite{ourpap1,ourpap}.

At $p \bar{p}$ colliders, either a sneutrino ($\tilde \nu$) or a charged
slepton ($\tilde l$) can be produced
in the $s$-channel via $\lambda '_{ijk}$ coupling.
In most SUSY models,
the slepton has two possible $R_p$-conserving gauge
decays: either into a chargino $\tilde{\chi}^{\pm}$ or a neutralino 
$\tilde{\chi}^0$.
These are favored over \rpv \  decay because of 
the small value of the coupling for the latter \cite{ourpap1}.
Consequently, for a single dominant
$\lambda '_{ijk}$ coupling, production of a slepton (smuon or muon sneutrino)
provides either a chargino or a neutralino,
together with either a charged lepton or a neutrino, in the final state.



In this Letter, we consider the resonant production of a muon
sneutrino or 
a smuon via $\lambda '_{211}$ coupling which leads to
a final state containing at least  two muons 
and two jets. From low-energy
measurements the $\lambda '_{211}$ coupling is constrained
to be less than $0.06 / 100 ({\rm GeV/c^2}) \times m_{\tilde{d_R}}$ 
\cite{limite},
where $m_{\tilde{d_R}}$ is the mass of the $\tilde{d_R}$-squark.
The lightest supersymmetric particle (LSP) is assumed to be the 
lightest neutralino. We also assume
that all sparticles cascade-decay into the neutralino, which decays through
the dominant \rpv \ $\lambda^{'}_{211}$ coupling.
Hence, ultimately, all SUSY particles decay into the 
lightest neutralino, which decays 
into two jets and a muon. 
The decay of the muon sneutrino into a muon and a
chargino, and of the smuon into a muon and a neutralino, therefore lead to at least
two muons and two jets in the final state. The decay of the smuon into a neutrino
and a chargino can also lead to the same topology, but only when the chargino decays into
muon+$X$, and for this reason the contribution of that channel is small (less than
5\% of the signal) and neglected in our analysis. The decay of the sneutrino
into a neutrino and a neutralino yields only one muon in the final state. 




%\section{Theoretical framework}
Our framework is
the so-called minimal \sugra model (mSUGRA),
which assumes the existence of a grand unified gauge theory and
family-universal boundary conditions on the supersymmetry breaking
parameters.
We choose the following five parameters that completely define the model:
$m_0$, the universal scalar mass at the unification scale $M_X$;
$m_{1/2}$, the universal gaugino mass at $M_X$;
$A=A_{t}=A_{b}=A_{\tau}$, the trilinear Yukawa coupling at $M_X$,
$sign(\mu)$, the sign of the Higgsino mixing parameter;
$\tan \beta=$ \mbox{$<H_u>/<H_d>$} where $<H_u>$ and
$<H_d>$ denote the vacuum expectation values of the two Higgs fields. The 
dependence of the cross section on different SUSY parameters can be found
in Ref. \cite{ourpap1}.


%\section{Cross sections}
%\section{Data Sample}

The data for this analysis were collected during the 1994-1995 Fermilab 
Tevatron running, at a center-of-mass energy of 1.8 TeV, and correspond to an 
integrated luminosity of 94$\pm 5$ pb$^{-1}$.
The D\O\ detector is described elsewhere
\cite{detD0}. Here, we outline the performance of the
components relevant to
this analysis.
Jets are identified using the energy deposited in the calorimeter, and 
reconstructed with a
cone algorithm in pseudorapidity ($\eta$) and azimuthal
angle ($\phi$) using a radius of 0.5. The calorimeter covers the region of
$| \eta |<4.0$, and provides a resolution for electrons and single hadrons 
($\sigma(E) /E$) of 
15\%$/ \sqrt E$ and 50\%$/ \sqrt E$, respectively.
Muons are detected using both tracking chambers (three layers
of proportional drift tubes ($|\eta| < 1.7$), 
one in front of, and two behind magnetized iron toroids) and
through ionization deposited in the calorimeter. The muon momentum resolution
is $\sigma (1/p) = 0.18 (p-2)/p^2 + 0.003$ (with $p$ in {\rm GeV}/$c$).

Events are required to satisfy a
$\mu~+$ jet or $\mu \mu~ +$ jet trigger. The trigger 
efficiency is 71\% and 50\% for central and forward muons, respectively.
Muons are required to have a transverse
momentum greater than 8 {\rm GeV}$/c$, and jets are required to have
transverse energy exceeding 15 {\rm GeV}.
We apply additional criteria to select two isolated muons and 
to eliminate cosmic-ray muons. If there are more than two isolated muons 
(which happens only rarely), only the two leading muons are used in the
ensuing analysis.



%\section{Monte Carlo Simulation}
%\subsection{Signal}
The signal topologies were generated with the SUSYGEN Monte Carlo 
program~\cite{SUSYGEN} using the cross sections computed in Refs.
\cite{ourpap1,ourpap} for a wide range of  ($m_0$, $m_{1/2}$) 
masses. 
For illustration purposes, we choose a reference point in the mSUGRA
parameter space: 
$m_0$=200\  {\rm GeV/c$^2$},  $m_{1/2}$=243 \  {\rm GeV/c$^2$},\ 
$\tan \beta =2$, $A=0$, and a negative sign for
$\mu$. These parameters predict the following sparticle masses:
$m_{\tilde{\nu}}$ =263 \  {\rm GeV/c$^2$} , $m_{\tilde{\mu}}$ =269 \  
{\rm GeV/c$^2$} ,
$m_{\tilde{\chi}_{1}^{\pm}}$ =207 \ {\rm GeV/c$^2$}, and
$m_{\tilde{\chi}_{1}^{0}}$ =102  \ {\rm GeV/c$^2$}. 
For $\lambda'=0.09$, the production
cross sections are $1.22$ pb and  $3.34$  pb for $\tilde \nu$ and
$\tilde \mu$ production, respectively. 


%\subsection{Backgrounds}

The dominant backgrounds are from $t\bar{t}$, $WW$+jets and $Z$+2\,jets events. The 
$t\bar{t}$ background was generated using PYTHIA  
\cite{PYTHIA}, with 
a cross section of 5.9 $\pm$ 1.7 pb \cite{top_xs}, the $Z$+2\, jets
background with VECBOS, \cite{vecbos} interfaced with the
ISAJET
fragmentation code \cite{isajet}, and a cross section of 9.7 $\pm$ 0.9 pb.
The $WW$+jets background was generated using PYTHIA \cite{PYTHIA}; 
it provides a much smaller background than 
the $t \bar{t}$ and $Z$+2 jets 
channels. The simulation of the detector was performed using both a full
and a parameterized simulation.



%\section{Analysis}


We use a neural network to discriminate signal from background 
in our analysis \cite{neural}
and we 
cross-check this with a more standard 
sequential analysis at several points of the
SUSY parameter space.
The following quantities are used as inputs to the neural network: the scalar sum of
the transverse energies of the two leading jets, the scalar sum of
the transverse momenta of the two leading muons, 
the distance in ($\eta$, $\phi$) 
space between the two muons, the dimuon mass,
the ($\eta$, $\phi$) distance between the most energetic muon and its 
nearest jet, the aplanarity and the sphericity of the two leading muons
and two leading jets in the laboratory frame
\cite{apla}.                               

%\subsection{Sequential Analysis}







%\subsection{Neural Network Analysis}

The output of the neural network is obtained separately for 
the sneutrino and the smuon channels. 
The signal-over-background ratio for the neural network is optimal
for an output cutoff of
$0.0$ for the $\tilde \nu$ and $-0.10$ for the 
$\tilde \mu$ analysis. 
  
%\section{Results}

%\subsection{Reference point}

For the reference point,  
$6.42 \pm 0.06$ $\tilde \nu$ and $\tilde \mu$ events are expected.
The estimated background of $1.01 \pm 0.02$  events is consistent with the two events 
observed in 
data. The details of the background estimate are given in Table I, with the quoted 
uncertainties being only statistical. 


%\subsection{Systematic Errors}

The systematic errors are shown in Table~\ref{sys_err}. 
The uncertainties due to jet energy scale and the measurement of the muon $p_T$ 
are deduced by varying the jet $E_T$ 
and muon $p_T$ by one standard deviation.
We use a fast version of the detector simulation
for most of the SUSY points, and the systematic
error associated with this procedure is also given in Table~\ref{sys_err}.
The last three lines give the final results for the number of events, the 
overall statistical error, and the overall systematic error. 
Using a Bayesian method to calculate the level of exclusion
\cite{Bayes}, 
our specific reference point is rejected at the 97.7\% C.L. 
for $\lambda^{\prime}_{211} = 0.09$.

\vspace{10cm}

\begin{table}
\begin {center}
\tab{|l|l|}
$\tilde{\mu}$ & $3.93 \pm 0.05$\\
$\tilde{\nu}_\mu$ & $2.49 \pm 0.04$\\
Total expected signal & $6.42 \pm 0.06$ \\\hline 

$t\bar{t}$ & $0.27 \pm 0.01$ \\

$Z$+2jets & $0.73 \pm 0.02$ \\

$WW$ + jets & $0.01 \pm 0.00$ \\

Total background & $1.01 \pm 0.02$ \\\hline 

Data    &       2\\

CL    &      97.7\%\\
\etab
\caption{Number of events (expected) for the reference point 
for signal at $\lambda'=0.09$, 
for the 
background, and the number observed in the data after making all selections.}
\label{back-detail}
\end{center}
\end{table}


\begin{table}
\begin{center}
\tab{|l|c|c|c|}
 Source & Signal  &  $t \bar{t}$ & 
 $Z$+2 jets  \\\hline 
 Jet energy scale  & 2\% & 4\% & 5\% \\
 High $p_T^\mu$ efficiency & 1\% & 7\% & 4\% \\
 Cross section & 10\% & 30\% & 10\%\\
 Trigger simul. & 5\% & 5\% & 5\% \\
 Luminosity  & 5\% & 5\% & 5\% \\
 fast / full simul.  & 1\% & 1\% & 1\% \\\hline 
Total events & 6.42& 0.27 & 0.73 \\ 
Overall statistics & $\pm$ 0.06& $\pm$ 0.01 & $\pm$ 0.02 \\
Overall systematics & $\pm$ 0.80& $\pm$ 0.09 & $\pm$ 0.10 \\
\etab
\caption{Systematic uncertainties on signal and background, and  
the number of expected events, with their statistical and systematic errors.}
\label{sys_err}
\end{center}
\end{table}


%\subsection {Exclusion Contours}


To set 
exclusion contours, we scan the $(m_0$, $m_{1/2})$ plane for three 
values of the coupling constant 
$\lambda^{\prime}_{211} = 0.09,\ 0.08,\ 0.07 $, two values 
of $\tan \beta=2,\ 5$, all for  
$\rm{sign}(\mu) =-1$. For $\lambda' \ge 0.09$,
the coupling $100 \lambda' /m_{\tilde{d_R}}$ is almost completely excluded by earlier 
experiments \cite{limite} in our domain of sensitivity in $m_{\tilde{d_R}}$. The 
resulting exclusion contours at the 95\% C.L. 
are shown in Figs. \ref{contours_m} and 
\ref{contours_chi+} in the ($m_0$,\ $m_{1/2}$) plane. 
The most interesting feature, is 
the exclusion of  $m_{1/2}$ values up to 260 {\rm GeV/c$^2$} for 
$\tan \beta$=2 and $\lambda^{\prime}_{211} = 0.09$, and the exclusion 
of $\tilde \nu$ and $\tilde \mu$ with masses up to 280 {\rm GeV/c$^2$}.  

 
For low values of $m_0$ and $m_{1/2}$, the smuon mass is close to the chargino
or neutralino mass, the $p_T$ spectrum of the muons is soft, and the search
is inefficient. For $\mu>$0 and higher values of $\tan \beta$, the sensitivity of 
our reach is
expected to decrease due to the fact that
the photino component of the LSP becomes small, resulting in the decrease
of the branching fraction of the LSP into muons.
In addition, charginos and neutralinos become light, resulting in events
with softer muons and jets that fail the kinematic requirements.


%\section{Conclusions}

To conclude,
a search for single smuon and single muon sneutrino production 
in the mSUGRA 
model with R-parity violation, has been performed for the first  
time at the Tevatron. 
We exclude $m_{1/2}$ values up to 
260 \ {\rm GeV} (the excluded value of $m_{1/2}$ depends on the value
of $m_0$) and 
sneutrino and smuon masses up to 280 {\rm GeV}. The excluded domain in the ($m_0$,
$m_{1/2}$) plane
extends the region excluded using the dielectron channel \cite{diel}.

%\section*{Acknowledgments}
We thank G. Moreau, M. Chemtob, R. Peschanski and C. Savoy for useful discussions.
\input{acknowledgement_paragraph.texf}

\begin{thebibliography}{99}
 
\input{list_of_visitor_addresses.texf}

\bibitem{rparity} P. Fayet, Phys. Lett. B{\bf 69}, 489 (1977);
G. Farrar and P. Fayet, Phys. Lett. B{\bf 76}, 575 (1978).
\bibitem{Dim1} S. Dimopoulos and L. J. Hall, Phys. Lett. B{\bf 207}, 210
(1988); H. Dreiner and G. G. Ross, Nucl. Phys. B{\bf 365},
597 (1991).
\bibitem{Drein} H. Dreiner, in
{\em Perspectives on Supersymmetry},
ed. by G. L. Kane, World Scientific, 1998, Singapore, hep-ph/9707435;
R. Barbier $et~ al.$, hep-ph/9810232.
\bibitem{referbound} B. C. Allanach, A. Dedes, H. K. Dreiner,
Phys. Rev. D{\bf 60}, 075014 (1999).
\bibitem{ourpap1}
F. D\'eliot, G. Moreau, C. Royon, Eur. Phys. J. C{\bf 19}, 155 (2001)
\bibitem{ourpap}
F. D\'eliot, G. Moreau, C. Royon, E. Perez and M. Chemtob,
Phys. Lett. B{\bf 475}, 184 (2000); H. Dreiner, P. Richardson and M. H. Seymour,
hep-ph/0007228.
\bibitem{limite} B. C. Allanach, A. Dedes, H. K. Dreiner,
Phys. Rev. D{\bf 60}, 075014 (1999).
\bibitem{SUSYGEN} SUSYGEN 3.0/06,
N. Ghodbane $et~ al.$,
lyoinfo\-.in2p3\-.fr\-/susygen\-/susygen3.html.
\bibitem{detD0} D\O\ Collaboration, S. Abachi $et~ al.$, Nucl. Instrum. Methods
Phys. Res.
A{\bf 338}, 185 (1994) and references therein.
\bibitem{PYTHIA} T. Sj\"{o}strand, Comp. Phys. Comm. {\bf 82}, 74 (1994);
S. Mrenna, Comp. Phys. Comm. {\bf 101}, 232 (1997).
\bibitem{top_xs} D\O\ Collaboration, B. Abbott $et~ al.$, 
Phys. Rev. Lett. {\bf 79}, 1203 (1997).
\bibitem{vecbos} F. A. Berends, H. Kuijf, B. Tausk and W. T. Giele, 
Nucl. Phys. B{\bf 357}, 32 (1991). 
\bibitem{isajet} H. Baer, F. E. Paige, S. D. Protopopescu and X. Tata, in
$Proceedings~ of~ the~
Workshop~ on~ Physics~ at~ Current~$ $Accelerators~ and~ the~ Supercolliders~$, 
edited in Argonne Accel. Phys. 0703 (1993) 720.
\bibitem{neural} For more information about the neural network, see
http://schwind.home.cern.ch/schwind/MLPfit.html
\bibitem{apla} D\O\ Collaboration, B. Abbott $et~ al.$, 
Phys. Rev. D{\bf 60}, 012001 (1999).
\bibitem{Bayes} I. Bertram $et~ al.$, Fermilab-TM-2104 (2000).
\bibitem{diel} D\O\ Collaboration, B. Abbott $et~ al.$, Phys. Rev. Lett.  {\bf 83} 
4476 (1999).


\end{thebibliography}

\newpage


\begin{figure}
\begin{center}
\psfig{figure= mdemi_m0_09_08_07_bh_v3.eps,height=7cm}
\psfig{figure= mdemi_m0_tanb5_bh_v3.eps,height=7cm}  
\end{center}
\caption{Exclusion contours at the 95\% C.L. in the ($m_0$, $m_{1/2}$) 
plane. The top figure shows the exclusion contours for $\tan \beta =2$,
$\lambda^{\prime}_{211}=$0.09, 
0.08 and 0.07. The bottom figure shows the exclusion contour for 
$\tan \beta=5$, but only for $\lambda^{\prime}_{211}=0.09$, because the smaller 
couplings do not provide a region of 95\% C.L. exclusion. }
\label{contours_m}
\end{figure}                                                                      


\vspace{10cm}

\begin{figure}
\begin{center}
\psfig{figure= chargi_mass_09_08_07_bh_v3.eps,height=7cm}
\psfig{figure= chargi_tanb5_bh_v3.eps,height=7cm}  
\end{center}
\caption{Exclusion contours at the 95\% C.L. in the 
($m_{\tilde \mu}$/$m_{\tilde \nu}$, $m_{\chi^+}$) plane. The top figure is for
$\tan \beta=2$, and three values of $\lambda^{\prime}_{211}$, while the 
bottom figure is for $\tan \beta=5$ and $\lambda^{\prime}_{211}=0.09$.
We give all contour plots as a function of the sneutrino mass. Because,
for any given set of parameters,
the sneutrino mass is very close to the smuon mass, 
the smuon contour plots lie very close to the
sneutrino results, and are therefore not shown.
}
\label{contours_chi+}
\end{figure}                                                                      



 
\end{document}










hep-ex0207100.extracted_bib
\begin{thebibliography}{99}
 
\input{list_of_visitor_addresses.texf}

\bibitem{rparity} P. Fayet, Phys. Lett. B{\bf 69}, 489 (1977);
G. Farrar and P. Fayet, Phys. Lett. B{\bf 76}, 575 (1978).
\bibitem{Dim1} S. Dimopoulos and L. J. Hall, Phys. Lett. B{\bf 207}, 210
(1988); H. Dreiner and G. G. Ross, Nucl. Phys. B{\bf 365},
597 (1991).
\bibitem{Drein} H. Dreiner, in
{\em Perspectives on Supersymmetry},
ed. by G. L. Kane, World Scientific, 1998, Singapore, hep-ph/9707435;
R. Barbier $et~ al.$, hep-ph/9810232.
\bibitem{referbound} B. C. Allanach, A. Dedes, H. K. Dreiner,
Phys. Rev. D{\bf 60}, 075014 (1999).
\bibitem{ourpap1}
F. D\'eliot, G. Moreau, C. Royon, Eur. Phys. J. C{\bf 19}, 155 (2001)
\bibitem{ourpap}
F. D\'eliot, G. Moreau, C. Royon, E. Perez and M. Chemtob,
Phys. Lett. B{\bf 475}, 184 (2000); H. Dreiner, P. Richardson and M. H. Seymour,
hep-ph/0007228.
\bibitem{limite} B. C. Allanach, A. Dedes, H. K. Dreiner,
Phys. Rev. D{\bf 60}, 075014 (1999).
\bibitem{SUSYGEN} SUSYGEN 3.0/06,
N. Ghodbane $et~ al.$,
lyoinfo\-.in2p3\-.fr\-/susygen\-/susygen3.html.
\bibitem{detD0} D\O\ Collaboration, S. Abachi $et~ al.$, Nucl. Instrum. Methods
Phys. Res.
A{\bf 338}, 185 (1994) and references therein.
\bibitem{PYTHIA} T. Sj\"{o}strand, Comp. Phys. Comm. {\bf 82}, 74 (1994);
S. Mrenna, Comp. Phys. Comm. {\bf 101}, 232 (1997).
\bibitem{top_xs} D\O\ Collaboration, B. Abbott $et~ al.$, 
Phys. Rev. Lett. {\bf 79}, 1203 (1997).
\bibitem{vecbos} F. A. Berends, H. Kuijf, B. Tausk and W. T. Giele, 
Nucl. Phys. B{\bf 357}, 32 (1991). 
\bibitem{isajet} H. Baer, F. E. Paige, S. D. Protopopescu and X. Tata, in
$Proceedings~ of~ the~
Workshop~ on~ Physics~ at~ Current~$ $Accelerators~ and~ the~ Supercolliders~$, 
edited in Argonne Accel. Phys. 0703 (1993) 720.
\bibitem{neural} For more information about the neural network, see
http://schwind.home.cern.ch/schwind/MLPfit.html
\bibitem{apla} D\O\ Collaboration, B. Abbott $et~ al.$, 
Phys. Rev. D{\bf 60}, 012001 (1999).
\bibitem{Bayes} I. Bertram $et~ al.$, Fermilab-TM-2104 (2000).
\bibitem{diel} D\O\ Collaboration, B. Abbott $et~ al.$, Phys. Rev. Lett.  {\bf 83} 
4476 (1999).


\end{thebibliography}