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\begin{flushright}
AMES-HET-97-09\\
NUHEP-TH-97-10\\
October 1997
\end{flushright}
\vspace{0.2cm}

\begin{center}
{\Large Probing top quark decay into light stop in the supersymmetric standard
model at the upgraded Tevatron}
\vspace{.2cm}
       
M. Hosch$^a$, R. J. Oakes$^b$, K. Whisnant$^a$, 
Jin Min Yang$^{b,}$\footnote{ On leave from Physics
Department, Henan Normal University, China}, 
Bing-Lin Young$^a$ and X. Zhang$^c$

 
\vspace{.2in}
\it
$^a$ Department of Physics and Astronomy, Iowa State University,\\
Ames, Iowa 50011, USA\\    
$^b$ Department of Physics and Astronomy, Northwestern University,\\
Evanston, Illinois 60208, USA\\
$^c$ CCAST (World Laboratory), P.O. Box 8730, Beijing 100080, and\\
Institute of High Energy Physics, Academia Sinica, Beijing 100039, China
\end{center}
\vspace{.2cm}

\begin{footnotesize}
\begin{center}\begin{minipage}{6in}
\baselineskip=0.25in

\begin{center} ABSTRACT\end{center}
 
We investigate the possibility of observing the exotic decay mode of the
top quark into the lightest stop ($\tilde t_1$) and neutralino
($\tilde\chi^0_1$) in the minimal supersymmetric standard model with
R-parity at the upgraded Tevatron. First we determine the allowed range
for the branching fraction $B(t\rightarrow \tilde t_1 \tilde\chi^0_1)$
in the region of parameter space allowed by the $R_b$ data and the CDF
$ee\gamma\gamma+{\large \not} \! E_T$ event, and then consider all
possible backgrounds and investigate the possibility of observing this
final state at the Tevatron. We find that this final state is
unobservable at Run 1. However, Run 2 can provide significant
information on this new decay mode of the top quark: either discover it,
or establish a strong constraint on the masses of $\tilde t_1$ and
$\tilde\chi^0_1$ given approximately by $M_{\tilde \chi^0_1} > M_{\tilde
t_1} - 6$~GeV.

\end{minipage}\end{center}
\end{footnotesize}
\vspace{.2cm}

PACS number: 14.65Ha; 14.80Ly
\end{titlepage}
\eject

\baselineskip=0.25in

\begin{center}{\large 1. Introduction} \end{center}

Because of its large mass, the top quark has the potential to be a
sensitive probe for new physics. In strongly interacting theories, such
as top condensation and extended technicolor, the top quark plays an
essential role in the electroweak symmetry breaking and in the
understanding of flavor physics. In weakly interacting theories, such as
supersymmetry (SUSY) [1], the heavy top quark provides a solution to the
electroweak symmetry breaking and makes it possible that the top quark may
decay into its lightest superpartner
\footnote{ Electroweak baryogenesis in SUSY requires a light stop to have a 
strong first order phase transition [2].}
($\tilde t_1$) plus the lightest neutralino ($\tilde \chi^0_1$).
Assuming that $\tilde t_1$ decays dominantly into $c \tilde \chi^0_1$,
this SUSY decay mode of the top quark will give rise to a new final
state in $t\bar t$ production at the Fermilab Tevatron, 
$t\bar t \rightarrow Wbc\tilde \chi^0_1 \tilde\chi^0_1$. 

A careful study of this final state is well motivated since
the presently allowed parameter space [3][4] of
the minimal supersymmetric standard model (MSSM), implied by
the $ee\gamma\gamma+{\large\not} \! E_T$ event at CDF [5] 
and the LEP $R_b$ data , will allow the top quark  
to have this new decay mode $t\rightarrow \tilde t_1 \tilde \chi^0_1$.
It is also implied in this scenario that
$M_{\tilde t_1} < M_{\tilde \chi^{\pm}_1}$ [3,4],
where $\tilde \chi^{\pm}_1$ is the lightest chargino, so the
decay $\tilde t_1 \rightarrow b\tilde \chi^+_1$ is not allowed. 
In the case that the $\tilde t_1$ is lighter than the next-to-lightest
neutralino $\tilde \chi^0_2$, $\tilde
l^{\pm}$ and $\tilde \nu$, the dominant decay of $\tilde
t_1$ is $\tilde t_1 \rightarrow c\tilde \chi^0_1$ via one loop processes
[6], with a branching fraction of almost 100\% \footnote{The four-body
decay mode $\tilde t_1 \rightarrow b\tilde \chi^0_1 f_1\bar f_2$ is
kinematically suppressed by both $\tilde \chi^{\pm}_1-$ and $W^{\pm}-$
propagators and thus its partial width is negligibly small.}. Therefore
searching for this final state may be a powerful tool for probing SUSY
at FNAL.

The possibility for detecting the $Wbc\tilde \chi^0_1 \tilde\chi^0_1$
final state in $t\bar t$ production was first discussed in Ref. [7]
where the focus was mainly on the background
$t\bar t\rightarrow W^-W^+b\bar b$. In this article, in the framework
of the MSSM with the lightest neutralino being the LSP, we will present a
detailed analysis including all the possible backgrounds. In particular,
we first determine the allowed range 
for $B(t\rightarrow \tilde t_1 \tilde \chi^0_1)$ in the region of parameter
space allowed by the $R_b$ data and the $ee\gamma\gamma+{\large \not} \!
E_T$ event at CDF, and then show what additional constraints can be imposed 
on the allowed parameter space if this final state is not observed
at the Tevatron. We find a lower bound of $0.07$ for 
$B(t\rightarrow \tilde t_1 \tilde \chi^0_1)$  in the
presently allowed parameter space [3][4], and, as a result, we find that
Run 2 can either discover this new decay mode or provide an
additional strong constraint given approximately by $M_{\tilde \chi^0_1} >
M_{\tilde t_1} - 6$~GeV. However, our results show that even if 
$B(t\rightarrow \tilde t_1 \tilde \chi^0_1)$ is as large as 0.5, it 
is unobservable at Run 1.   

This paper is organized as follows. In Sec.~2 we examine the range of
values for
$B(t\rightarrow \tilde t_1 \tilde \chi^0_1)$ in the region of parameter
space allowed by the $R_b$ data and the $ee\gamma\gamma+{\large \not} \!
E_T$ event.  In Sec.~3 we examine all possible backgrounds and
investigate the possibility of observing $t\bar t \rightarrow Wbc\tilde
\chi^0_1 \tilde \chi^0_1$ at the Tevatron.  And finally in Sec.~4 we
present a summary.

\vspace{.5cm}

\begin{center}{\large 2. Bounds for 
                 $B(t\rightarrow \tilde t_1\tilde \chi^0_1)$} 
\end{center}
\vspace{.5cm}

It was found that in order to explain all of the presently available
low energy data the lightest mass eigenstate ($\tilde t_1$) of the stop
squarks is likely to be the right-stop ($\tilde t_R$) with mass of the
order of $M_W$ [4]. So we assume $\tilde t_1=\tilde t_R$ in our analyses. 
The interaction Lagrangian of top ($t$),  stop($\tilde t_1$) and neutralino 
($\tilde \chi^0_1$) is given by [8]
\begin{equation}
{\cal L}_{t\tilde t_1\tilde \chi^0_1}=-\sqrt 2 \bar t(AP_L
+BP_R) \tilde \chi^0_1 \tilde t_1 +H.c.,
\end{equation}
where $P_{L,R}=(1\mp \gamma_5)/2$ and
\begin{eqnarray}
A&=&-\frac{2}{3}e(N_{11}C_W+N_{12}S_W)
         +\frac{2}{3}\frac{gS_W^2}{C_W}(N_{12}C_W-N_{11}S_W),\\
B&=&-\frac{gM_tN_{14}}{2M_W\sin\beta}.
\end{eqnarray}
Here $S_W\equiv\sin\theta_W, C_W\equiv\cos\theta_W$, 
and $ N_{ij}$ are the elements of the $4\times4$ matrix $N$ 
which diagonalizes the neutralino mass matrix [1].
The decay  $t\rightarrow \tilde t_1 \tilde \chi^0_1$ has been 
calculated to one-loop level in Refs.~[9] and [10]. Here we neglect the
loop corrections, which are only on the order of 10\%; the partial
width is given at tree level by
\begin{eqnarray}
\Gamma(t\rightarrow \tilde t_1 \tilde \chi^0_1)&=&\frac{1}{16\pi M_t^3}
\lambda^{1/2}(M_t^2,M^2_{\tilde \chi^0_1},M^2_{\tilde t_1})\left [
(\vert A\vert^2+\vert B\vert^2)
(M_t^2+M^2_{\tilde \chi^0_1}-M^2_{\tilde t_1})\right.\nonumber\\
& & \left.+4Re(A^*B)M_tM_{\tilde \chi^0_1}\right ],
\end{eqnarray}
where $\lambda(x, y, z)=(x-y-z)^2-4yz$.

The parameters involved in 
$\Gamma(t\rightarrow \tilde t_1 \tilde \chi^0_1)$ are: 
\begin{equation}
M_{\tilde t_1},  M_2, M_1, \mu, \tan\beta,
\end{equation}
where $M_2$ and $M_1$ are gaugino masses corresponding to
$SU(2)$ and $U(1)$,  $\mu$ is the coefficient of
the $H_1H_2$ mixing term in the superpotential, and
$\tan\beta=v_2/v_1$ is the ratio of the vacuum expectation values 
of the two Higgs doublets.
If the $ee\gamma\gamma+{\large \not} \! E_T$ event is due to
$\tilde e_L$ pair production (depending on the scenario, the selectrons
decay into either $e\tilde\chi^0_2$ or $e\tilde\chi^0_1$, followed by
$\tilde\chi^0_2\rightarrow\tilde\chi^0_1\gamma$ or
$\tilde\chi^0_1\rightarrow\tilde G\gamma$, respectively, where
$\tilde G$ is the gravitino), 
the region of the parameter space allowed by both the 
$ee\gamma\gamma+{\large \not} \! E_T$
event and the $R_b$ data are given as [3]
\begin{eqnarray}
&50 \le M_1 \le 92 {\rm ~GeV},& 50 \le M_2 \le 105 {\rm ~GeV}, \nonumber\\
&0.75 \le M_2/M_1 \le 1.6,& -65 \le \mu \le -35 {\rm ~GeV}, \nonumber\\
&0.5 \le |\mu|/M_1 \le 0.95,& 1 \le \tan \beta \le 3, \nonumber\\
\label{el}
& 33 \le M_{\tilde \chi^0_1} \le 55 {\rm ~GeV},&
45 \le M_{\tilde t_1} \le 80 {\rm ~GeV}.
\end{eqnarray}
If the $ee\gamma\gamma+{\large \not} \! E_T$ event is due to
$\tilde e_R$ pair production, the allowed region is [3]
\begin{eqnarray}
&60 \le M_1 \le 85 {\rm ~GeV},& 40 \le M_2 \le 85 {\rm ~GeV}, \nonumber\\
&0.6 \le M_2/M_1 \le 1.15,& -60 \le \mu \le -35 {\rm~ GeV}, \nonumber\\
& 0.5 \le |\mu|/M_1 \le 0.8,& 1 \le \tan \beta \le 2.2, \nonumber\\
\label{er}
&32 \le M_{\tilde \chi^0_1} \le 50 {\rm~ GeV},&
45 \le M_{\tilde t_1} \le 80 {\rm~ GeV}.
\end{eqnarray}

In the region of Eq.(\ref{el})  we obtain 
\begin{equation} \label{bound1}
0.07\le B(t\rightarrow \tilde t_1\tilde \chi^0_1)\le 0.50,
\end{equation}
and in the region of Eq.(\ref{er}),
\begin{equation} \label{bound2}
0.10 \le B(t\rightarrow \tilde t_1\tilde \chi^0_1) \le 0.50.
\end{equation}
So, if  the $ee\gamma\gamma+{\large \not} \! E_T$ event is explained by 
the MSSM with the lightest neutralino being the LSP, the exotic decay
$t\rightarrow \tilde t_1\tilde \chi^0_1$ must occur at a branching 
ratio larger than 0.07. 

Upper bounds for this exotic decay of the top quark
can also be derived from the available data at FNAL.
Currently, the FNAL top quark pair production counting
rate is interpreted as a measurement of 
$\sigma(t\bar t)\times B^2(t\rightarrow bW)$. Since the final states
$t\bar t \rightarrow Wb\bar c\tilde \chi^0_1 \tilde \chi^0_1$ and
$t\bar t \rightarrow c\tilde \chi^0_1 \tilde \chi^0_1
\bar c\tilde \chi^0_1 \tilde \chi^0_1$ do not have enough leptons or
jets to be included in the dileptonic, leptonic or hadronic event samples,
they are invisible to the current counting experiments at FNAL. 
So the quantity $[1-B(t \rightarrow \tilde t_1\tilde \chi^0_1)]^2$,
which gives the fraction of events in which both the $t$ and
$\bar t$ decay normally
\footnote{ Here we assume that the only exotic decay mode
of top quark in R-parity conserving MSSM 
is $t \rightarrow \tilde t_1\tilde \chi^0_1$. If charged
Higgs is light enough, $t \rightarrow H^+ b$
is also possible;
its phenomenological implications at Tevatron have been studied [11].
The FCNC decays $t\rightarrow cZ, c\gamma, cg, ch$ are negligibly small
in R-parity conserving MSSM [12].},
should lie within the measured range of $\sigma[t\bar t]_{\rm exp}/
\sigma[t\bar t]_{\rm QCD}$. Note that in our analyses we neglected
the SUSY effects [13][14] in $t\bar t$ production and thus the
theoretical value of $\sigma[t\bar t]$ is given by the SM value 
$\sigma[t\bar t]_{\rm QCD}$. The production cross section measured by
CDF with an integrated luminosity of 110 pb$^{-1}$ is
$\sigma[t\bar t]_{\rm exp}=8.5^{+4.4}_{-3.4},6.8^{+2.3}_{-1.8},
10.7^{+7.6}_{-4.4}$pb in the dilepton, lepton+jets and all-hadronic 
channels, respectively [15]. The SM expectation for top mass of 175 GeV is
$\sigma[t\bar t]_{\rm QCD}=5.5^{+0.1}_{-0.4}$ pb [16]. 
By comparing $\sigma[t\bar t]_{\rm exp}$ from each channel with
$\sigma[t\bar t]_{\rm QCD}[1-B(t \rightarrow \tilde t_1\tilde \chi^0_1)]^2$,
we find that the $2\sigma$ upper bounds on
$B(t \rightarrow \tilde t_1\tilde \chi^0_1)$ for the various channels
are given by
\begin{equation} \label{bound3}
B(t\rightarrow \tilde t_1 \tilde \chi^0_1) 
\le \left \{ \begin{array}{ll} 0.44 & ~~{\rm dilepton~ channel}\\
                                 0.23 & ~~{\rm lepton+jets~ channel}\\
				 0.41 & ~~{\rm all-hadronic ~channel.}
               \end{array} \right.
\end{equation}
Here the upper bound from lepton+jets channel is comparable 
to the upper bound of 0.25 [7] obtained by a global fit to the 
available data. If the possible enhancement of $t\bar t$ production
cross section from gluino pair production is taken into account,
the upper bound for $B(t\rightarrow \tilde t_1 \tilde \chi^0_1)$ can
be relaxed to 0.5 [14].
\vspace{.5cm}

\begin{center}{\large 3. Observing 
                 $t\bar t \rightarrow Wbc\tilde \chi^0_1 \tilde \chi^0_1$
                 at the Tevatron} 
\end{center}
\vspace{.5cm}

Under the assumption that the top (or anti-top) decays via the normal weak
interactions to $Wb$, the anti-top (top) decays to $\tilde t_1
\tilde \chi^0_1$, and the light stop decays to $c\tilde\chi^0_1$, then
the final state of interest is $Wbc\tilde\chi^0_1\tilde\chi^0_1$.
Due to the large QCD backgrounds, it is very difficult
to search for the signal from the hadronic decays of $W$ at the Tevatron.
We therefore look for events with the leptonic decay of the $W$.
Thus, the signature of this process is an energetic charged lepton,
one $b$-quark jet, one light $c$-quark jet, plus missing $E_{T}$ from
the neutrino and the unobservable ${\chi^0_1}^\prime$s.
We assumed silicon vertex tagging of the $b$-quark jet
with $50 \%$ efficiency and the probability of 0.4\% for a light quark
jet to be mis-identified as a $b$-jet.
The potential SM backgrounds are:
\begin{itemize}
\begin{description}
\item[{\rm(1)}] $bq (\bar q) \rightarrow tq'(\bar q')$;
\item[{\rm(2)}] $q\bar q' \rightarrow W^* \rightarrow t\bar b$;
\item[{\rm(3)}] $Wb\bar b$;
\item[{\rm(4)}] $Wjj$;
\item[{\rm(5)}] $t\bar t\rightarrow W^-W^+b\bar b$;
\item[{\rm(6)}] $gb\rightarrow tW$;
\item[{\rm(7)}] $qg\rightarrow q't\bar b$.
\end{description}
\end{itemize}
The quark-gluon process (7) can occur with a W-boson intermediate state
in either the t-channel or the s-channel. We found backgrounds (6) and
(7) to be negligible since they have an extra jet, and can mimic our
signal (before $b$-tagging) only if a jet is missed in the detector. The
background process (5) can mimic our signal if both $W$'s decay leptonically
and one charged lepton is not detected, which we assumed to occur if
the lepton pseudo-rapidity and transverse momentum satisfy $\eta(l)>3$
and $p_T(l)<10$ GeV, respectively.

To simulate the detector acceptance,  we made a series of
basic cuts on the transverse momentum ($p_{T}$), the pseudo-rapidity
($\eta$), and the separation in the azimuthal angle-pseudo-rapidity plane
(~$\Delta R= \sqrt{(\Delta \phi)^2 + (\Delta \eta)^2}~ )$ between a jet and 
a lepton or between two jets. These cuts are chosen to be
\begin{eqnarray}
p_T^l, ~p_T^{\rm jet},~
p_T^{\rm miss}&\ge& 20 \rm{~GeV} ~,\\
\eta_{\rm jet},~\eta_{l} &\le& 2.5 ~,\\
\Delta R_{jj},~\Delta R_{jl} &\ge& 0.5 ~.
\end{eqnarray}
Further simulation of detector effects is made
by  assuming a Gaussian smearing of the energy of the final state
particles, given by:
\begin{eqnarray}
\Delta E / E & = & 30 \% / \sqrt{E} \oplus 1 \% \rm{,~for~leptons~,} \\
             & = & 80 \% / \sqrt{E} \oplus 5 \% \rm{,~for~hadrons~,}
\end{eqnarray}
where $\oplus$ indicates that the energy dependent and independent
terms are added in quadrature and $E$ is in GeV.

In order to substantially reduce the background, we apply a cut
on the transverse mass defined by
$m_T = \sqrt{ (P_T^l+P_T^{\rm miss})^2
- (\vec P_T^l+\vec P_T^{\rm miss})^2}.$
Without smearing, $m_T$ is always less than $M_W$ (and peaks just below
$M_W$) if the only missing energy comes from a neutrino from W decay,
which is the case for most of the background events (single top, Wbb,
Wjj). Smearing pushes some of this above $M_W$. For the signal $m_T$
is spread about equally above and below $M_W$, due to the extra missing
energy of the neutralinos. Therefore we also require
\begin{equation}
m_T > 90 GeV.
\end{equation}

The results with different cuts are shown in Table 1. For convenience
the numerical results shown are obtained without including the
appropriate branching ratios; the actual cross sections are found by
multiplying the given values by the branching fraction factors
$x=B(t \rightarrow c\tilde\chi^0_1\tilde\chi^0_1)$ and
$1-x=B(t\rightarrow bW)$. The products of the appropriate branching
fractions in each case are given in the last column of Table~1.
In our numerical evaluation, we assumed $M_t=175$ GeV,
$\sqrt s=1.8$ TeV and an integrated luminosity of 0.1 fb$^{-1}$ for Run 1,
and $\sqrt s=2$ TeV and an integrated luminosity of 10 fb$^{-1}$ for Run 2.
  
At Run 1,  with the basic and $m_T$ cuts the number of background events
is always less than 1, and the number of signal events is always less than
9 for any value of $x=B(t\rightarrow \tilde t_1 \tilde \chi^0_1)$ allowed
by Eq.(\ref{bound1}) or (\ref{bound2}). Thus the signal is unobservable
at Run 1 under the criteria $S \ge 3 \sqrt{B+S}$, which corresponds to
the 95\% confidence level (C.L.) if we assume
Poisson statistics. The $m_T$ cut hurts the signal, but, as we pointed
out above,  it reduces the background much more than the signal. Even
when the $m_T$ cut is relaxed, this final state is unobservable at Run 1.  

At Run 2  this signal is observable even for quite small values of 
$B(t\rightarrow \tilde t_1 \tilde \chi^0_1)$. In Fig.~1 we show
$B(t\rightarrow \tilde t_1 \tilde \chi^0_1)$ versus $M_{\tilde \chi^0_1}$
for the signal to be observable at 95\% C.L. The region
above each curve is the corresponding observable region. From this figure
we can see that for $B(t\rightarrow \tilde t_1 \tilde \chi^0_1)>0.07$
(the minimum value allowed by Eqs.~8 and 9), Run 2 can detect this
signal at 95\% C.L. if (approximately) $M_{\tilde \chi^0_1} \le
M_{\tilde t_1} - 5$~GeV. This means that if this signal is not
observed at Run 2, an additional constraint, given approximately by
\begin{equation}
M_{\tilde \chi^0_1} > M_{\tilde t_1} - 5 {\rm~GeV},
\end{equation}
can be placed on the region of Eq.(\ref{bound1}) allowed by the $R_b$
data and the $ee\gamma\gamma+{\large \not} \! E_T$ event at 95\% C.L. 

In Fig.~2 we present $B(t\rightarrow \tilde t_1 \tilde \chi^0_1)$
versus $M_{\tilde \chi^0_1}$ for the signal to be observable under
the stricter discovery criteria $ S \ge 5 \sqrt{B}$. 
In this case we see that if this signal is not observed at Run 2 the
additional constraint of approximately
\begin{equation}
M_{\tilde \chi^0_1} > M_{\tilde t_1} - 6 {\rm~GeV},
\end{equation}
can be placed on the allowed region of Eq.(\ref{bound1}).

Note that a lower limit of 67 GeV for $\tilde t_1 $ has been obtained 
from the direct search for $\tilde t_1 \rightarrow c\tilde \chi^0_1$
under the restriction $M_{\tilde t_1}-M_{\tilde \chi^0_1}>10$~GeV [17]. 
Our results in Fig.2 show that under the condition
$M_{\tilde t_1} - M_{\tilde \chi^0_1} \ge 6$~GeV, Run 2 can explore the
entire presently allowed parameter space. In order words, if this final
state is not seen at Run 2, only a very small part
of parameter space will be allowed, which satisfies Eq.(\ref{el}) 
or Eq.(\ref{er}) plus $M_{\tilde \chi^0_1} > M_{\tilde t_1} - 6$~GeV.  

We conclude by noting that the more precise $t\bar t$ cross section
measured at Run 2 will further strengthen the upper bound for
$B(t\rightarrow \tilde t_1 \tilde \chi^0_1)$ given in Eq.(\ref{bound3}).
However, as our results show, is it also possible to discover the decay 
$t\rightarrow \tilde t_1 \tilde \chi^0_1$ in Run 2 for values of
$B(t\rightarrow \tilde t_1 \tilde \chi^0_1)$ much smaller than the upper
limits obtained by measuring the $t\bar t$ cross section.
In any event, further constraints on the parameter space can be made
through searching for this final state.

\vspace{.5cm}

\begin{center}{\large 4. Summary } \end{center} 
\vspace{.5cm}

 In  the
framework of the MSSM with the lightest neutralino being the LSP, 
we first determined the allowed range for the 
branching fraction $B(t\rightarrow \tilde t_1 \tilde\chi^0_1)$ in the 
present allowed region 
of parameter space and found a lower bound of 0.07. Then we investigated 
the possibility of observing $t\rightarrow \tilde t_1 \tilde\chi^0_1$
at the Tevatron
by searching for the final state 
$t\bar t \rightarrow Wbc\tilde \chi^0_1 \tilde \chi^0_1$.
 We found that: 
\begin{itemize}
\begin{description}
\item (a) This final state is unobservable at Run 1 ; 
\item (b) Run 2 can either discover this new decay mode or place the
additional constraint $M_{\tilde \chi^0_1} > M_{\tilde t_1} - 5$~GeV
if $ S \ge 3 \sqrt{B+S}$ is required for discovery of the signal, or
$M_{\tilde \chi^0_1} > M_{\tilde t_1} - 6$~GeV if we require
$ S \ge 5 \sqrt{B}$.
\end{description}
\end{itemize}
In our analysis, we neglected the possibility of the enhancement 
of the top pair production cross section in the MSSM. 
In particular, the gluino pair production might be significant,[14]
and would give rise to a new final state $t \bar t\tilde t \tilde t^*$.
This will not affect our conclusion significantly since it will give a
final state with more jets than the signal we are considering.
With such a mechanism of exotic top pair production,
the upper bound on $B( t \rightarrow \tilde t_1 \tilde \chi^0_1 )$
can be relaxed up to 50\%[14], which will enhance the observability of
this new mode at the Tevatron and strengthen our conclusion.
\vspace{.5cm}

\begin{center}{\Large  Acknowledgements}\end{center}

This work was supported in part by the U.S. Department of Energy, Division
of High Energy Physics, under Grant Nos. DE-FG02-91-ER4086
DE-FG02-94-ER40817, and DE-FG02-92-ER40730.
JMY acknowledges partial support provided by the Henan Distinguished
Young Scholars Fund.
XZ was supported in part by National Natural Science Foundation of China.

\vfill
\eject

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\eject

\begin{center} {\bf Figure Captions} \end{center}

Fig. 1 The value of $B(t\rightarrow \tilde t_1 \tilde \chi^0_1)$ versus 
       $M_{\tilde \chi^0_1}$
       for the signal to be observable at Run 2 
       under the criterion $ S \ge 3 \sqrt{B+S}$.
       The region above the curve is the observable region. 

Fig. 2  Same as Fig.~1, but under the criterion $ S \ge 5 \sqrt{B}$.
\eject

\begin{table}
\caption{ }
Typical signal and background cross sections in units of fb after
various cuts at the Tevatron. The basic cuts are  
$p_T^{\rm all}\ge 20 \rm{~GeV} ~, \eta_{\rm all} \le 2.5$ and
$\Delta R \ge 0.5$, and the transverse mass cut is $m_T\ge 90$ GeV.
The signal $t\bar t\rightarrow Wb\bar c \tilde \chi^0_1 \tilde \chi^0_1$
results were calculated by assuming $M_{\tilde t_1}=60$ GeV and 
$M_{\tilde \chi^0_1}=40$ GeV.
We have also everywhere assumed the use of silicon vertex tagging of the
$b$-quark jet with $50 \%$ efficiency and the probability of 0.4\% for a
light quark jet to be mis-identified as a $b$-jet. 
The charge conjugate channels have been included. The numerical results
do not include the branching fractions for the top and anti-top decays;
the actual cross sections are found by multiplying the given cross
sections by the branching fraction factor in the last column, where
$x$ stands for $B(t\rightarrow \tilde t_1 \tilde \chi^0_1)$.

\vspace{0.1in}

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
 & \multicolumn{2}{c|}{Run 1}&\multicolumn{2}{c|}{Run 2}& BF factor  
 							\\ \cline{1-5}
 & basic cuts & basic+$m_T$ cut& basic cuts & basic+$m_T$ cut& \\ \hline
$t\bar t\rightarrow Wb\bar c \tilde \chi^0_1 \tilde \chi^0_1$
                                     &206 & 114 & 287 & 162 & 2x(1-x) \\ \hline
$qb\rightarrow q^\prime t$           &79.5& 2.31& 116 & 4.96 & $1-x$ \\ \hline
$q\bar q^\prime \rightarrow t\bar b$ &32.0& 1.77& 39.0& 2.25 & $1-x$ \\ \hline
$Wb\bar b$                           &113 & 2.04& 132 & 2.50 & 1   \\ \hline
$Wjj$                                &392 & 2.30& 505 & 2.88 & 1   \\ \hline
$t\bar t$                            &5.69& 2.72& 7.9 & 3.82 & $(1-x)^2$\\ \hline
\end{tabular}
\end{center}
\end{table}
\vfill
\end{document}

