\small
\begin{center}
{\it M. Roco,
     A. Belyaev,
     J. Valls}
\end{center}
\normalsize \nopagebreak

This section of the report presents a study to evaluate the
sensitivity reach of the Fermilab Tevatron for the neutral Higgs
bosons of the Minimal Supersymmetric Standard Model produced in
association with bottom quarks, $\pp\to\bb\phi$ with $\phi\to\bb$
($\phi = h,H,A$).  Due to the strongly enhanced $\bb\phi$ couplings at
large $\tan\beta$, this channel becomes potentially important since it
can be the dominant production and decay modes of the neutral Higgs
bosons over a large region of the parameter space.

The events of interest would have four $b$ jets in the final state,
two of which come from a Higgs resonance.  In this Workshop two
analyses have been performed, emphasizing the different strengths of
the two detectors and different aspects of the signature.  Each
analysis is described in the next two sections, and a comparison made
at the end.

\vspace{0.2in}
\large
{\bf D\O\ Analysis} \\ \nopagebreak
\normalsize

This analysis is based on Monte Carlo simulations which have been
tuned to the existing D\O\ detectors in a well-studied environment.
It is assumed that it will be possible to maintain the excellent
performance of the D\O\ calorimeter during Run 2.  The $b$-tagging
algorithm described in Section II.A.3 is used in this analysis.

\vspace{0.2in}
{\bf Monte Carlo Simulation} \\ \nopagebreak

All signal and background event samples used in this analysis were
generated using the CompHEP package~\cite{comphep}.  CompHEP performs
calculations of complete tree-level matrix elements for all parton
processes with up to five partons in the final state.  It has been
interfaced with Pythia V6.023~\cite{spythia} to simulate the parton
fragmentation and hadronization.  Events were generated at a
center-of-mass energy, $\sqrt s = 2$ TeV.  The generation of the
signal and background Monte Carlo samples and the relevant tree-level
cross section calculations are described in more detail in ref.~\cite{sasha}.

\vspace{0.2in}
{\bf Detector Simulation} \\ \nopagebreak

The signal detection efficiencies and accepted background cross
sections are estimated using a fast detector simulation package,
MCFAST~\cite{mcfast}.  MCFAST performs parameterized tracking where
for each generated track, a covariance matrix is assembled, which
represents all the material and detector planes traversed by the ideal
track.  A reconstructed track is produced by smearing the generated
track parameters according to this covariance matrix.

Particle momenta are smeared as prescribed in SHW using
20$\% / \sqrt E$ and 80$\% / \sqrt E$ for the electromagnetic and
hadronic energy resolutions, respectively.  The reconstruction of
calorimeter clusters (jets) is based on the cone algorithm with a
fixed cone radius $\Delta R=\sqrt {\Delta \eta^2 + \Delta \phi^2} =
0.5$.

The beam vertex is centered at the origin with a smearing of 30 $\mu$m in
both $x$ and $y$ and 25 $cm$ in $z$.  In this study only one interaction
per beam crossing is considered.

\vspace{0.2in}
{\bf Signal Event Samples} \\ \nopagebreak

This analysis uses only the leading order cross sections for the
signal production process.  Next-to-leading order
corrections~\cite{DSSW} can be significant at the Tevatron, ranging
from $-40\%$ for $m_\phi =$ 40 GeV to $+40\%$ for $m_\phi =$ 1000 GeV.
It was also shown in ~\cite{DSSW} that the largest uncertainty in the
$\bb H$ production cross section comes from varying the factorization
scale, $\mu$.  In this analysis, the scale $\mu = m_\phi$ is chosen.
Signal cross sections are determined using a running $b$-quark mass,
with $m_b$ varying from 3.4 to 3.1 GeV in the Higgs mass range between
$m_\phi =$ 90 to 300 GeV.  Table~\ref{t:tab1} lists the the production
cross sections for $\pp\to\bb\phi$ for the pseudoscalar Higgs boson
$\phi = A$, in femtobarns for $\tan\beta=$1.  The cross sections after
applying parton-level kinematic cuts on $p_T$ and $\Delta R$ are also
given in Table ~\ref{t:tab1}.  The decay branching ratios for
$\phi\to\bb$ are obtained from HDECAY~\cite{hdecay}.  It is assumed
that the SUSY particles are heavy enough such that the decays of Higgs
bosons into them are kinematically forbidden.

\begin{table*}
\caption{Signal Cross sections for $\tan \beta =$ 1.}
\label{t:tab1}
\begin{tabular}{ccrr}
$m_A$ & $m_b$ &  \ \ \ \ \ \ \ \ \ \ \ $\sigma$ (fb)  &  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ $\sigma$ (fb) \\ 
 & & & \\
 (GeV/c$^2$) & (GeV/c$^2$) & \ \ no cuts & $p_T >$ 15 GeV/c \\
 & & & and $\Delta R >$ 0.5 \\ \hline
 & & & \\
 90   &  3.40  &  13.820  & 0.7492 \\ 
100   &  3.38  &   8.628  & 0.5224 \\ 
110   &  3.36  &   5.831  & 0.3730 \\ 
120   &  3.34  &   3.730  & 0.2556 \\ 
130   &  3.32  &   2.563  & 0.1924 \\ 
140   &  3.30  &   1.733  & 0.1366 \\ 
200   &  3.22  &   0.255  & 0.0271 \\ 
250   &  3.18  &   0.064  & 0.0076 \\ 
300   &  3.14  &   0.018  & 0.0024 \\
\end{tabular}
%\caption{Signal Cross sections for $\tan \beta =$ 1.}
%\label{t:tab1}
\end{table*}

\newpage
\vspace{0.2in}
{\bf Backgrounds} \\ \nopagebreak

The dominant backgrounds come from QCD multi $b$-jet production.
These include the irreducible backgrounds from $\qq,gg\to\bb\bb$ and
$\pp\to Z\bb$, as well as the reducible backgrounds from $\bb jj$ and
$W\bb$ events with the mistagging of a light quark ($u,d,s$), charm or
gluon jet as a $b$-jet.  Table ~\ref{t:tab2} lists the leading order
cross sections in picobarns for the background processes considered in
this study.  The value of $p_T^{min}$ is set to 15 GeV/c for the
$W\bb$ and $Z\bb$ processes.  This value is raised to 25 GeV/c for
$\bb jj$ to obtain statistically significant samples after applying
the selection criteria described below.  From Table ~\ref{t:tab2}, a
serious background arises from QCD $\bb jj$ production which is
several orders of magnitude larger than the signal cross section.
Reducing this overwhelming background requires a $b$-tagging algorithm
with a very high purity.  Other background processes, such as $\ttbar$
production and $Z\cc$, are less important and have negligible
contributions after the analysis cuts are applied.


\begin{table*}
\caption{Background cross sections.}
\label{t:tab2}
\begin{tabular}{cr}
Process & $\sigma (pb)$ \\ & \\ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ $p_T > p_T^{min}$ \\ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ and $\Delta R >$ 0.5 \\ \hline & \\ $Z\bb$ & 3.3 * 0.15 BR($Z\to\bb$) \\
$W\bb$       &   3.1 * 0.68 BR($W \to q \bar q$)  \\  
$\bb\bb$     &     2.4 \\
$\bb jj$     &  1610.8 \\
\end{tabular}
%\caption{Background cross sections.}
%\label{t:tab2}
\end{table*}

\vspace{0.2in}
{\bf Event Selection} \\ \nopagebreak

The $\bb\bb$ final state is characterized by two clear signatures, the
four-jet topology and a high $b$-quark content.  These properties are
the main handles for suppressing the enormous QCD multi-jet
backgrounds.  Events are passed through a filtering algorithm intended
to select hadronic events compatible with the four-jet topology and to
use the $b$-tagging information to reduce the dominant QCD
backgrounds.  The efficient identification of jets arising from $b$
quark production plays an important role in the search for the Higgs
bosons since for sufficiently large $\tan\beta$ values the neutral
Higgs bosons decay predominantly to $\bb$ with a branching ratio of
about 90$\%$.

The significance of the signal can be further improved by
reconstructing the Higgs mass.  The di-jet mass is reconstructed only
from the $b$-tagged jets resulting in a number of possible pair-wise
combinations, $m_{ij}$.  Using these combinations, it may be possible
to define a smooth combinatoric background distribution with an
overall normalization which can be determined from the data.
Otherwise, it becomes difficult to determine the significance of a
mass peak if, for instance, one takes only the $m_{ij}$ combination
closest to the assumed Higgs mass.


\begin{figure}
  \begin{center}
   \parbox{2.6in}{\epsfxsize=\hsize\epsffile{./bbbb/mass-abb-100.eps}}
   \parbox{2.6in}{\epsfxsize=\hsize\epsffile{./bbbb/mass-abb-200.eps}} \\
   \parbox{3.0in}{\epsfxsize=\hsize\epsffile{./bbbb/pt-bbbb.eps}}
   \caption{Distributions of $p_T$ for the four leadings jets in the 
            signal sample from $\bb A$ production for $m_{\phi} = 100$ GeV/c$^2$ 
            (top left), and $m_{\phi} = 200$ GeV/c$^2$ (top right).  
            Also shown are the $p_T$ spectra from the $gg\to\bb\bb$
            background sample.}
  \label{fig-ptspectra}
  \end{center}
\end{figure}


The first level of event selection is performed to filter and select
events which satisfy Run~1 multi-jet trigger requirements of at least
four reconstructed jets in the event with $p_T >$ 15 GeV and
$|\eta|<2$.  The $p_T$ spectra of the leading jets are determined by
the Higgs mass.  This is illustrated in Figure~\ref{fig-ptspectra} where
the $p_T$ distributions of the four leading jets are shown for two
signal samples, with $m_{\phi}$ = 100 GeV/c$^2$ and $m_{\phi}$ = 200
GeV/c$^2$.  For comparison, the bottom plot shows the jet $p_T$
spectra for the irreducible QCD $\bb\bb$ background (this plot was
generated using a sample with a $p_T^{min}$ cut of 15 GeV/c).  The
following selection criteria on the $p_T$ of the leading jets are
chosen to optimize the significance, $S/\sqrt B$, where $S$ and $B$
are the number of signal and background events, respectively,
remaining after cuts: 
\begin{itemize}
\item[$\bullet$] leading jet $p_T > M_{\phi}/2 -5$ 
\item[$\bullet$] second leading jet $p_T >$ max$(30, M_{\phi}/4 +10)$
\item[$\bullet$] third and fourth leading jets $p_T >$ 30 GeV
\end{itemize}
Figure~\ref{fig-ptlcut} shows the optimal values
for the leading jet $p_T$ cut for four different values of the Higgs
mass.

\begin{figure}
  \begin{center}
   \parbox{4in}{\epsfxsize=\hsize\epsffile{./bbbb/ptlcut.eps}}
   \caption{The selection criteria on the $p_T$ of the leading jets are chosen
            to optimize the statistical significance $S/\sqrt B$.  These plots show
            the significance for different leading jet $p_T$ cuts for four different
            values of the Higgs mass.}
  \label{fig-ptlcut}
  \end{center}
\end{figure}

The $p_T$ requirement on the third and fourth jets is determined by
the value of the $p_T^{min}$ cut used to generate the Monte Carlo
samples.  The selection criteria require that at least three of the
four leading jets are $b$-tagged.  Table~\ref{t:tab3} lists the
signal acceptances for the single channel $\bb A$, where
$\epsilon_{p^j_T}$ is calculated after requiring the multi-jet
triggers.  The $\epsilon_{2b,3b,4b}$ are calculated after the trigger and
jet $p_T$ cuts are applied, and requiring at least two, three or four
$b$-tags, respectively.  The total efficiency $\epsilon_{tot}$ refers
to the remaining events after the nominal selection requiring at least
three $b$-tags.  Table~\ref{t:tab4} lists the number of expected
events passing the selection criteria for the pseudoscalar Higgs
signal and the various background processes, for an integrated
luminosity of ${\cal L}=2~$fb$^{-1}$.  The sensitivities $S/B$ and
$S/\sqrt B$ are given for $\tan\beta$ = 40.


\begin{table*}[ht!]
\caption{Signal acceptances for $p \overline p \to b \overline b A$ in the Higgs mass
range between 90 and 300 GeV/c$^2$.}
\label{t:tab3}
\begin{tabular}{ccccccc}
%\noalign{\vskip-6pt}
$m_A$ & $\epsilon_{trig}$ & $\epsilon_{p^j_T}$ & $\epsilon_{2b}$ & $\epsilon_{3b}$ & $\epsilon_{4b}$ & $\epsilon_{tot}$ \\
 (GeV/c$^2$) & ($\%$) & ($\%$) & ($\%$) & ($\%$) & ($\%$) & ($\%$) \\ \tableline
\noalign{\vskip5pt}%& & & & & & \\
 90 & \ 3.46 $\pm$ 0.03 & 27.46 $\pm$ 0.22 & 68.87 $\pm$ 0.24 & 34.36 $\pm$ 0.41 & 5.23 $\pm$ 0.30 & 0.33 $\pm$ 0.01 \\ 
100 & \ 3.97 $\pm$ 0.03 & 30.95 $\pm$ 0.22 & 69.38 $\pm$ 0.26 & 36.79 $\pm$ 0.37 & 5.62 $\pm$ 0.28 & 0.45 $\pm$ 0.01 \\ 
110 & \ 4.39 $\pm$ 0.04 & 33.32 $\pm$ 0.21 & 70.75 $\pm$ 0.28 & 36.90 $\pm$ 0.35 & 6.64 $\pm$ 0.28 & 0.54 $\pm$ 0.01 \\ 
120 & \ 4.81 $\pm$ 0.04 & 35.63 $\pm$ 0.20 & 70.17 $\pm$ 0.30 & 36.27 $\pm$ 0.34 & 6.50 $\pm$ 0.27 & 0.62 $\pm$ 0.01 \\ 
130 & \ 5.39 $\pm$ 0.04 & 36.43 $\pm$ 0.20 & 71.32 $\pm$ 0.30 & 38.14 $\pm$ 0.33 & 6.46 $\pm$ 0.26 & 0.75 $\pm$ 0.02 \\ 
140 & \ 5.78 $\pm$ 0.05 & 37.69 $\pm$ 0.20 & 70.81 $\pm$ 0.31 & 38.37 $\pm$ 0.32 & 6.60 $\pm$ 0.26 & 0.84 $\pm$ 0.02 \\ 
200 & \ 8.20 $\pm$ 0.06 & 38.72 $\pm$ 0.19 & 72.08 $\pm$ 0.33 & 38.26 $\pm$ 0.30 & 6.33 $\pm$ 0.24 & 1.21 $\pm$ 0.02 \\ 
250 & \ 9.47 $\pm$ 0.07 & 38.63 $\pm$ 0.19 & 70.87 $\pm$ 0.33 & 37.12 $\pm$ 0.30 & 7.23 $\pm$ 0.25 & 1.36 $\pm$ 0.03 \\ 
300 &  10.78 $\pm$ 0.08 & 38.15 $\pm$ 0.19 & 71.07 $\pm$ 0.33 & 36.25 $\pm$ 0.30 & 6.80 $\pm$ 0.24 & 1.49 $\pm$ 0.03 \\
\end{tabular}
%\caption{Signal acceptances for $p \overline p \to b \overline b A$ in the Higgs mass
%range between 90 and 300 GeV/c$^2$.}
%\label{t:tab3}
\vspace*{1pc}
\end{table*}


\begin{table*}[h]
\caption{The expected number of events and sensitivities, with an
integrated luminosity of ${\cal L} = 2$~fb$^{-1}$, for the signal
$p \overline p \to b \overline b A$ and the various background processes.
The sensitivities $S/B$ and $S/\sqrt B$ are given for $\tan \beta =$ 40.}
\label{t:tab4}
\begin{tabular}{ccccccccccc}
Higgs Mass    &    90  &   100  &  110  &  120  &  130  &  140  &  200  &  250 & 300 \\
(GeV/c$^2$)   &        &        &       &       &       &       &       &      & \\ 	\hline
\noalign{\vskip5pt}%  & & & & & & & & & \\
$S \ (\tan\beta = 1)$  &  0.090 & 0.078  & 0.063 & 0.046 & 0.038 & 0.029 & 0.006 & 0.002 & 0.000\\
$\times BR$   &  0.83  & 0.81   & 0.77  & 0.68  & 0.53  & 0.34  & 0.003 & 0.001  & 0.001 \\ \hline
\noalign{\vskip5pt}%  & & & & & & & & \\
$S \ (\tan \beta = 40)$&\  144  &\  125  &\  101 &\ \ 74&\ \ 61 &\ \ 46 &\ \ 10 &\ \ \ 3 &\ \ \ 1 \\
$\times BR$   &  0.91  & 0.91   & 0.91  & 0.91  & 0.90  & 0.90  & 0.90  & 0.90 &  0.89 \\ [5pt]
 \noalign{\vskip3pt}% & & & & & & & & & \\
$\bb jj$      &  2384  &  2225  &  2149 &  1999 &  1873 &  1571 &\  598 &\   297 &\  127 \\
$\bb\bb$      & \ 373  &\  349  &\  312 &\  280 &\  243 &\  207 &\ \ 72 &\ \  32 &\ \ 14 \\
$Z\bb$        & \ 111  &\  108  &\  102 &\ \ 95 &\ \ 85 &\ \ 76 &\ \ 36 &\ \  19 &\ \ 10 \\
$W\bb$        &\ \ 27  &\ \ 27  &\ \ 26 &\ \ 24 &\ \ 22 &\ \ 21 &\ \ 13 &\ \ \ 8 &\ \ \ 5\\ [5pt]
%  & & & & & & & & & \\
Total Background & 2895  & 2709 &  2589 &  2398 &  2223 &  1875 &\  719 &\  356  &\  156 \\ \hline
\noalign{\vskip3pt}  %  & & & & & & & & & \\
$S/B$         &  0.050 &  0.046 & 0.039 & 0.031 & 0.028 & 0.025 & 0.014 & 0.008  & 0.005 \\
$S/\sqrt B$   &  2.68  &  2.39  &  1.98 &  1.52 &  1.30 &  1.07 &  0.37 & 0.15   & 0.07 
\end{tabular}
%\caption{The expected number of events and sensitivities, with an
%integrated luminosity of ${\cal L} = 2$~fb$^{-1}$, for the signal
%$p \overline p \to b \overline b A$ and the various background processes.
%The sensitivities $S/B$ and $S/\sqrt B$ are given for $\tan \beta =$ 40.}
%\label{t:tab4}
\vspace*{1pc}
\end{table*}

\vspace{0.2in}\break
{\bf Tagging Issues} \\ \nopagebreak

For comparison, the total number of events passing the selection
criteria which require two instead of three $b$-tags are 235 and
1.46$\times 10^5$ events for the signal (assuming $\tan \beta = 40$)
and background, respectively, with $m_A =$ 100 GeV/c$^2$.  Due to the
very small signal-to-background ratio, using only two $b$-tags is not
reliable for this production mode.  Requiring that all four leading
jets to be tagged would have the advantage of eliminating the $W\bb$
and $\bb jj$ backgrounds.  However, the signal event rate becomes
substantially degraded.  This study indicates that the signal to
background ratio $S/B$, at $m_A =$ 100 GeV/c$^2$, increases from 0.046
to 0.113 while the statistical significance of the signal $S/\sqrt B$
decreases from 2.39 to 1.47.  This decrease is due to the fourth jet
being typically considerably softer than the third jet in the signal
events as shown in Figure~\ref{fig-ptspectra}.

Let us examine the case where the $b$-tag requirement is relaxed such
that the three $b$-tags do not necessarily have to be from the four
leading jets.  In this case, for $m_A =$ 100 GeV/c$^2$ and three
$b$-tags, there are 168 signal events with an estimated background of
2898 giving a significance of $S/\sqrt B = 3.12$.  Requiring four
$b$-tags improves the sensitivities with $S/B =$ 0.244 and $S/\sqrt B
=$ 3.52.

To simplify the algorithm for reconstructing the Higgs mass for
candidate events, the selection requires that only $b$-tags from the
four leading jets are considered.  This analysis is performed by
requiring only three $b$-tagged jets on account of the substantial
loss of statistical significance in requiring four $b$-tags.  Tagging
efficiencies are based only on displaced tracks coming from secondary
vertices, not including soft lepton tags.  Soft lepton tagging of $b$
jets will increase the overall $b$-tagging efficiency, however, this
has not been considered in this study.  The analysis performs full
vertex reconstruction and $b$-tagging on an event-by-event basis,
i.e., tagging efficiencies are not based on any rate parameterization.

\vspace{0.2in}
{\bf Higgs Mass Reconstruction} \\ \nopagebreak

One does not know {\em a priori} which $b$-jets resulted from the
Higgs decay.  For each combination of tagged jets $\{i,j\}$, the
di-jet invariant mass $m_{ij}$ is reconstructed.  There are either
four or six possible di-jet combinations for each event.  To reduce
the combinatoric background from incorrect di-jet combinations,
further cuts are applied.  The jets $\{i,j\}$ are required to be well
separated azimuthally: $\phi_1 < \Delta \phi_{ij} < \phi_2$, where the
values of $(\phi_1,\phi_2)$ range from (70$^o$,290$^o$) for $m_{\phi}
=$ 90 GeV to (120$^o$,240$^o$) for $m_{\phi} =$ 300 GeV.
Alternatively, one can also use the variable $\Delta R =
\sqrt{(\phi_i-\phi_j)^2 + (\eta_i-\eta_j)^2}$ to impose jet isolation.

Finally, a cut on the invariant mass $m_{ij}$ of the di-jet candidate
is necessary to further suppress the remaining QCD backgrounds.  The
di-jet mass resolution of the $\bb$ system coming from the Higgs decay
is $\sigma(m_{b \overline b}) = 15\%$.  For the signal event sample,
all di-jet $m_{ij}$ combinations which are reconstructed within $\pm
2.5 \sigma$ of the Higgs mass constitute the {\em signal S}.
Similarly, for the background samples, all di-jet $m_{ij}$
combinations which are reconstructed within $\pm 2.5 \sigma$ of the
assumed Higgs mass constitute the {\em background B}.

\vspace{0.2in}
{\bf Combining $\bb A$, $\bb H$, $\bb h$} \\ \nopagebreak

At sufficiently large $\tan \beta$ values, one of the CP-even Higgs
bosons and the pseudoscalar $A$ have similar couplings and are
degenerate in mass as illustrated in the following plots.  The program
{\tt hmsusytev.f}~\cite{hehprog} is used to derive the couplings and
masses.  In Figure ~\ref{fig-couplings} the ratios of the CP-even
Higgs couplings $g^2$ to $\tan^2 \beta$ as a function of pseudoscalar
mass are shown for the case of maximal and minimal mixing.
Figure~\ref{fig-massdiff} shows the mass differences ($m_A - m_h$) and
($m_H - m_A$) versus the pseudoscalar mass for different $\tan \beta$
values in the maximal (top plots) or minimal (bottom plots) mixing
scenarios.


\begin{figure}
  \begin{center}
   \parbox{4in}{\epsfxsize=\hsize\epsffile{./bbbb/coupling.eps}}
   \caption{The ratio of the CP-even Higgs bosons coupling $g^2$ to
            $\tan^2 \beta$ as a function of the pseudoscalar mass $m_A$.}
   \label{fig-couplings}
  \end{center}
\end{figure}

\begin{figure}
  \begin{center}
   \parbox{5in}{\epsfxsize=\hsize\epsffile{./bbbb/massdiff.eps}}
   \caption{Contours of $(m_A - m_h$) and $(m_H - m_A$) as a function of the
            pseudoscalar mass $m_A$ for various $\tan \beta$ values in the maximal (top
            plots) or minimal mixing (bottom plots) scenario.}
   \label{fig-massdiff}
  \end{center}
\end{figure}

The $g^2$ couplings and the degree of mass degeneracy determine the
additional contribution from the CP-even Higgs bosons which should be
added to the pseudoscalar Higgs signal.  In the case of maximal
mixing, the light Higgs coupling for $m_A\lsim 115$~GeV is roughly
equal to $\tan^2 \beta$.  This is also the case for the heavy Higgs
coupling for $m_A\gsim 125$~GeV.  However, it is not correct to
simply double the signal from $\bb A$ production since the additional
contribution from $h, H$ may not be within the 2.5$\sigma$ mass
window.  Figure~\ref{fig-massdiff} shows that the mass differences between
the scalar Higgs bosons and pseudoscalar are large for small $\tan
\beta$ values.  Doubling the $\bb A$ production rate would lead to an
overestimate of the signal at low $\tan \beta$.  This analysis assumes
that the shapes of the di-jet mass distributions for the CP-even and
the pseudoscalar Higgs bosons are identical, except for a shift in the
mass peaks due to the mass differences ($m_A - m_h$) and ($m_H -
m_A$).  It is also assumed that the relative normalization of the mass
distributions is given by the ratio $g^2/\tan^2 \beta$.  The
additional contribution from the Higgs scalars is determined by the
fraction of the mass distributions within the 2.5$\sigma$ mass window
around the assumed pseudoscalar mass $m_A$.

\vspace{0.2in}
{\bf Results} \\ \nopagebreak

The signal and background estimates described above are used to
estimate the discovery potential and exclusion reach for the Higgs
bosons of the MSSM.  For a given luminosity and an assumed Higgs mass,
one can determine the minimum value of $\tan \beta$ leading to a
5$\sigma$ discovery ($\sigma = S/\sqrt B$) or exclusion at 95$\%$ CL
(1.96$\sigma$).  The results are shown in Figure~\ref{fig-limits}.  The
sensitivity reach in the $\tan \beta$ and $m_A$ parameter space is
shown for different values of the delivered luminosity per experiment.
These results were obtained assuming maximal mixing, where SUSY
parameters are chosen to give the largest predicted value for the
Higgs mass.  For comparison the LEP excluded region ($m_A < 90$
GeV/c$^2$) is also shown.

In the intermediate Higgs mass range, these results indicate that the
Run 2 sensitivity reach, assuming $\tan \beta = 40$, is about 160
GeV/c$^2$ at 95$\%$ CL exclusion with a delivered luminosity of
2~fb$^{-1}$, extending up to 190 GeV/c$^2$ with 5~fb$^{-1}$.  The
5$\sigma$ discovery reach is up to 115 GeV/c$^2$ at 2~fb$^{-1}$ and 
150~GeV/c$^2$ at 5 fb$^{-1}$.  For larger Higgs masses, the sensitivity
reach degrades significantly due to the decreasing production rates.

\begin{figure}
  \begin{center}
   \parbox{3in}{\epsfxsize=\hsize\epsffile{./bbbb/mssm_discovery.eps}}
   \parbox{3in}{\epsfxsize=\hsize\epsffile{./bbbb/exclusion.eps}}
   \caption{95$\%$ CL exclusion curves and 5$\sigma$ discovery contours
            for $\pp\to\bb\phi$ with $\phi = h,H,A$.  The curves show the sensitivity 
            reach for the MSSM neutral Higgs bosons in the $\tan \beta$ and 
            $m_A$ parameter space.  The LEP excluded region ($m_A < 90$ GeV/c$^2$) 
            is also shown for comparison.  The results are shown for the case of 
            maximal mixing where SUSY parameters are chosen to give the largest 
            predicted value for the Higgs mass.}
   \label{fig-limits}
  \end{center}
\end{figure}

The estimates for signal efficiencies and backgrounds are affected by
various systematic effects, such as the imperfect modeling of the
physics processes and the detector response.  Uncertainties arising
from the inaccurate description and reconstruction of the energy flow,
as well as the initial and final state radiation have not been
studied.  The main source of uncertainty in this analysis arises from
the evaluation of the QCD multi $b$-jet backgrounds.  Additional
factors which strongly influence the background estimates presented
here include the predictions for QCD multi-jet production, the parton
density distributions, the choice of scale for $\alpha_s$ and
higher-order corrections.  Another critical issue which have not been
evaluated is the effect of high luminosity conditions where the impact
of overlapping interactions may become important.

\vspace{0.2in}
{\bf Summary} \\ \nopagebreak

This report has presented a strategy to search for the neutral Higgs
bosons of the Minimal Supersymmetric Standard Model, where the Higgs
bosons are produced in association with bottom quarks.  Prospects for
5$\sigma$ discovery and 95$\%$ CL exclusion in the process
$\pp\to\bb\phi$, with $\phi = h,H,A$, have been presented.  Results
indicate that the Tevatron Run 2 sensitivity reach, assuming $\tan
\beta = 40$, is about 160 GeV/c$^2$ at 95$\%$ CL exclusion with a
delivered luminosity of 2~fb$^{-1}$, extending up to 190 GeV/c$^2$ with
5~fb$^{-1}$.  The 5$\sigma$ discovery reach is up to 115 GeV/c$^2$ at
2~fb$^{-1}$ and 150 GeV/c$^2$ at 5~fb$^{-1}$.  These results demonstrate
that the Tevatron can significantly constrain a large fraction of the
MSSM parameter space by studying the production of the neutral Higgs
bosons produced in conjunction with $b$ quark pairs.

\vspace{0.2in}
\large
{\bf CDF analysis}\\ \nopagebreak
\normalsize

The CDF-based analysis represents an extrapolation of the technique
used in the analysis of CDF Run~1 data to the new detector geometry
and improved $b$-tagging efficiency anticipated in Run~2.  The
estimates of background are made from Run~1 data, with appropriate
scaling for improved acceptance and efficiency\footnote{No correction
for the increased center-of-mass energy is made to either the Higgs
signal or the background.  This should be conservative in that, all
else being equal, the sensitivity should increase with center-of-mass 
energy.}


Figure~\ref{bbxxs1} show the expected rates for $\bb\phi\to \bb\bb$
production at large $\tan\beta$ as a function of the Higgs mass. In
this regime ($\tan\beta \gtrsim 20$) $\phi$ is either $h$ or $A$ for
masses below the light Higgs upper bound, or either the $H$ or $A$ for
masses above the light Higgs upper limit.  All rates are shown for the
case of vanishing mixing parameters or non-mixing case defined by
$\mu=A_t=A_b=0$ with $\mu$ the Higgs mass parameter and $A_t$ and
$A_b$ the soft SUSY Yukawa breaking parameters.  In all cases, a top
quark mass of $M_t=175$ GeV/c$^2$ and a SUSY mass scale of $M_S=1$ TeV
are assumed. To calculate the Yukawa coupling we use a running bottom
quark mass evaluated at the Higgs mass scale ($M_b\simeq 3$
GeV/c$^2$). All cross sections are evaluated at leading order (LO)
with the CTEQ3 parton distributions functions and the renormalization
scale equal to the Higgs mass.

\begin{figure}[tb]
  \centerline{\parbox{4.0in}{\epsfxsize=\hsize\epsffile{./bbbb/xs_signal.eps}} }
  \caption{Production cross sections for 
           $(b\bar{b}h + b\bar{b}A)\rightarrow b\bar{b} b\bar{b}$ (upper plot) and
           $(b\bar{b}H + b\bar{b}A)\rightarrow b\bar{b} b\bar{b}$ (lower plot) 
           as a function of the Higgs mass.
           The two plots correspond to the different degenerate states,
           $M_h=M_A$ for Higgs masses below the light Higgs upper
           bound, and $M_H=M_A$ for Higgs masses above the light Higgs
           upper bound. Results are shown for $\tan\beta \ge 20$ and the non-mixing
           scenario.}
  \label{bbxxs1}
\end{figure}

\vspace{0.2in}
{\bf Signal Monte Carlo Simulation} \\ \nopagebreak

For signal modelling we used a modified version of the parton level
Monte Carlo program PAPAGENO~\cite{papageno} together with the Lund
PYTHIA V5.6 string fragmentation and hadronization
program~\cite{PYTHIA}.  Fixed weight $\pp\to\bb\phi$ events with
$\phi\to\bb$ are generated at leading order (LO) and fragmented inside
PYTHIA.  The mass of the Higgs has been set to values between
$M_{\phi}$=70 GeV/c$^2$ to 300 GeV/c$^2$. In order to setup parton
showers and fragmentation using PYTHIA, the color-flow information
for colored particles is treated properly.  Both initial and final
state showering are allowed at energy scales corresponding to the
Higgs mass. After fragmentation, events are then passed through the
CDF Run~1 simulation and reconstruction code.

\vspace{0.2in}
{\bf Event Selection} \\ \nopagebreak

The CDF Run~1 multijet trigger requirements are used as the first
step in the data selection. This sample is defined by events that satisfy:
\begin{itemize}
\item[a)] total trigger cluster $\sum E_T^{L2} > 125$ GeV, and
\item[b)] 4 trigger clusters with $E_T^{L2}> 15$ GeV
\end{itemize}
where a level 2 (L2) trigger cluster is defined by a nearest-neighbor
reconstruction algorithm, seeded by a tower of $E_T > 3$ GeV and
including only towers of $E_T > 1$ GeV.  The event selection follows
by requiring events with at least four offline reconstructed jets with
$\et >15$ GeV and $|\eta|\le 2.1$. Jets are defined as localized
energy depositions in the calorimeters and are reconstructed using an
iterative clustering algorithm with a fixed cone of radius $\Delta R =
\sqrt{\Delta\eta^2 + \Delta\phi^2} = 0.4$ in $\eta-\phi$ space. Jet
e\-ner\-gies are then corrected for energy losses in uninstrumented
detector regions, energy falling out\-side the clustering cone,
contributions from underlying event and multiple interactions, and
calorimeter nonlinearities.

\begin{table*}[t!]
\caption{Optimized $\et$ thresholds for the three highest $\et$ jets in
the event as a function of the signal mass.}
\label{eth}
\begin{tabular}{ccccccccccccc} 
 & \multicolumn{12}{c}{$M$ (GeV/c$^2$)} \\ [0.1cm] \hline
 \multicolumn{13}{c}{} \\ [-0.2cm]
 & 70 & 80 & 90 & 100 & 110 & 120 & 130 & 140 &
 150 & 200 & 250 & 300 \\ [0.1cm] \hline
 \multicolumn{13}{c}{} \\ [-0.2cm]
$\et(jet 1)$ (GeV) & $40$ & $40$ & $42$ & $42$ & $46$ & $48$ & $50$ & $54$ & $58$ 
& $75$ & $95$ & $120$ \\ [0.05cm]
$\et(jet 2)$ (GeV) & $32$ & $32$ & $32$ & $34$ & $34$ & $34$ & $38$ & $38$ & $42$ 
& $55$ & $72$ & $85$ \\ [0.05cm]
$\et(jet 3)$ (GeV) & $14$ & $14$ & $14$ & $14$ & $14$ & $14$ & $14$ & $14$ & $14$ 
& $40$ & $55$ & $70$ \\ [0.1cm]
\end{tabular}
%\caption{Optimized $\et$ thresholds for the three highest $\et$ jets in
%the event as a function of the signal mass.}
%\label{eth}
\end{table*} 

The typical topology of the signal events consist of two primary $b$
quarks and a Higgs $\phi$, which is radiated from one of the primary
$b$ quarks. There is, thus, a very high energetic primary $b$ quark
with momentum of the order of the mass of the Higgs boson, $M_{\phi}$,
balanced by the Higgs and the other primary $b$ quark, which is
generally much softer.  The Higgs decays into a $\bb$ pair with
typical transverse momentum of the order of $M_{\phi}/2$. The four
highest-$E_T$ (uncorrected) jets in the event are then ordered
in $E_T$:
\begin{equation}
E_T^{1} \ge E_T^{2} \ge E_T^{3} \ge E_T^{4}
\end{equation}
and a mass dependent requirement made for $E_T^{1}$,
$E_T^{2}$, and $E_T^{3}$. The $E_T$ thresholds for these cuts are 
shown in Table~\ref{eth} as a function of the Higgs mass. They have been 
optimized by maximizing the significance of the signal.

Figure~\ref{etj} shows the the $E_T^{j}$, $j=1,2,3,4$ distributions
for two different signal Higgs masses ($M = 120, 250$ GeV/c$^2$)
compared with the QCD background shapes.

\begin{figure}
  \centerline{\parbox{5.8in}{\epsfxsize=\hsize\epsffile[0 0 560 220]{./bbbb/etj.eps}}}
  \caption{Transverse energy distributions for the four leading jets
           in the event. The solid histograms correspond to QCD background. 
           The dashed and dotted histograms correspond to signal masses of 
           $M=250$ and $120$ GeV/c$^2$ respectively.}
  \label{etj}
\end{figure}

We then require that at least three among the four highest-$E_T$ jets
in the event are identified (tagged) as $b$ quark candidates.  We use
the CDF secondary vertex algorithm~\cite{secvtx} with the intrinsic
Run~1 efficiencies and mistag rates per jet inside the SVX fiducial
region. The results are then applied to $b$ jets at generator level
within the increased geometrical acceptance of the Run 2 CDF silicon
vertex detector (SVX-II). The SVX-II extends the $b$-tagging
capabilities up to the range $|\eta|<2$.  The $b$-tagging algorithm
begins by searching for secondary vertices that contain three or more
displaced tracks. If none are found, the algorithm searches for
two-track vertices using more stringent track criteria. A jet is
tagged if the secondary vertex transverse displacement from the
primary one exceeds three times its uncertainty.

Table~\ref{seff} shows the trigger efficiency ($\epsilon_{trig}$),
$E_T^j$ efficiencies ($\epsilon_{E_T^j}$), double $b$-tag
($\epsilon_{\ge 2b}$) and triple $b$-tag ($\epsilon_{\ge 3b}$)
efficiencies, and total efficiencies ($\epsilon_{tot}$) as a function
of the Higgs mass. The double and triple $b$-tag efficiencies are
calculated after the trigger and $E_T^j$ cuts are applied.  The total
efficiency applies to the triple $b$-tag selection.  All errors shown
are statistical only.

Figure~\ref{invm} shows the reconstructed dijet invariant mass 
distribution for different signal masses.
The invariant mass of the dijet system is defined as $M_{ij} = 
\sqrt{2 E_T^i E_T^{j} [\cosh(\Delta\eta)_{ij} - 
\cos(\Delta\phi)_{ij}]}$.
The distributions contain a Gaussian core with a resolution of
$10$--$20$\% depending slightly on the Higgs mass.  To maximize the
signal dijet mass resolutions we use the reconstructed invariant mass
of the highest-$\et$ jets in the event for masses $M\ge 120$
GeV/c$^2$. For masses $M<120$ GeV/c$^2$ we use the invariant mass of
the second and third highest-$\et$ jets in the event. In all cases,
the two highest-$\et$ jets in the event are always required to be
tagged.  The tails of the distributions are dominated by the cases
where the jet assignment in the mass reconstruction is incorrect. In
most of these cases, one of the jets assigned to the Higgs is a
primary $b$ quark jet.

\begin{figure}
  \centerline{\parbox{5.2in}{\epsfxsize=\hsize\epsffile{./bbbb/sigres.eps}}}
  \caption{Signal dijet invariant mass distributions. From top left the 
           distributions correspond to Higgs masses of 
           $M=70, 80, 90, 100, 110, 120, 130, 140, 150, 200, 250$ 
           and $300$ GeV/c$^2$, respectively.}
  \label{invm}
\end{figure}

\begin{table*}[t!]
\caption{Signal acceptances as a function of the Higgs mass.}
\label{seff}
\begin{tabular}{cccccc}
$M$ & $\epsilon_{trig}$  & $\epsilon_{E_T^j}$ & $\epsilon_{\ge 2b}$ &
$\epsilon_{\ge 3b}$ & $\epsilon_{tot}$   \\ [0.1cm]
(GeV/c$^2$) &  (\%) & (\%) & (\%)& (\%) & (\%) \\ [0.15cm] \hline
& & & & &  \\ [-0.2cm]
70 & $1.25\pm0.02$ &  $92.7\pm0.3$ & $78.9\pm0.7$ &
$28.6\pm0.7$ & $0.33\pm0.01$
 \\ [0.05cm]
80 & $1.48\pm0.02$ &  $93.0\pm0.2$ &  $78.2\pm0.6$ &
$27.7\pm0.6$ & $0.38\pm0.01$ 
 \\ [0.05cm]
90 & $1.70\pm0.02$ &  $89.7\pm0.3$ &  $79.0\pm0.8$ &
$27.6\pm0.8$ & $0.42\pm0.01$ 
 \\ [0.05cm]
100 & $1.90\pm0.03$ & $85.8\pm0.3$ &  $78.8\pm0.6$ &
$27.2\pm0.6$ & $0.44\pm0.01$ 
 \\ [0.05cm]
110 & $2.23\pm0.03$ & $80.7\pm0.3$ &  $76.6\pm0.6$ &
$25.5\pm0.6$ & $0.46\pm0.01$ 
 \\ [0.05cm]
120 & $2.42\pm0.04$ & $79.6\pm0.3$ &  $77.1\pm0.8$ &
$27.0\pm0.7$ & $0.52\pm0.01$ 
 \\ [0.05cm]
130 & $2.65\pm0.04$ & $72.8\pm0.3$ &  $77.5\pm0.7$ &
$26.3\pm0.6$ & $0.51\pm0.02$ 
 \\ [0.05cm]
140 & $2.75\pm0.04$ & $69.5\pm0.3$ &  $77.1\pm0.8$ &
$28.1\pm0.8$ & $0.54\pm0.01$ 
 \\ [0.05cm]
150 & $3.15\pm0.05$ & $61.6\pm0.3$ &  $79.4\pm1.0$ &
$27.3\pm1.1$ & $0.53\pm0.02$ 
 \\ [0.05cm]
200 & $4.35\pm0.07$ & $31.3\pm0.3$ &  $82.6\pm1.3$ &
$31.0\pm1.3$ & $0.42\pm0.02$
 \\ [0.05cm]
250 & $4.95\pm0.07$ & $18.5\pm0.3$ &  $78.7\pm1.5$ &
$25.9\pm1.5$ & $0.24\pm0.01$ 
 \\ [0.05cm]
300 & $6.71\pm0.10$ & $11.5\pm0.2$ &  $79.0\pm1.5$ &
$23.3\pm1.5$ & $0.18\pm0.01$ 
 \\ [0.1cm]
\end{tabular}
%\caption{Signal acceptances as a function of the Higgs mass.}
%\label{seff}
\end{table*} 

\vspace{0.2in}
{\bf Backgrounds} \\ \nopagebreak

Backgrounds for the process 
$p\bar{p}\to bb\phi\to \bb\bb$ include all
sources of standard model heavy flavor multijet events. These include
QCD heavy flavor production, fake multitags, $\ttbar$ ($t\to Wb$, 
$W\to q\bar{q}'$), $Z$ + jets ($Z\to \bb/\cc$), 
$W\bb/\cc$ and $Z\bb/\cc$.

\vspace{0.2in}
\underline{QCD} \\ \nopagebreak

The dominant source of background is QCD heavy flavor production.
This is also the most difficult to estimate due to uncertainties in
the predicted total rates as well as heavy flavor jet rates.  Rather
than attempting to estimate the QCD background rates directly from
Monte Carlo, instead we follow the approach used in~\cite{juano} in
the search for standard model Higgs bosons via $VH\to jj\bb$
($V=W,Z$). In~\cite{juano}, the CDF Run~1 multijet data sample was
used to calculate first the double $b$ tagged dijet invariant mass
distribution.  The shape of this distribution is then fit, using a
binned maximum-likelihood method, to a combination of signal, QCD
heavy flavors, fake double tags and other standard model
backgrounds. The QCD heavy flavor and signal normalizations are left
free in the fit while the rest of backgrounds are constrained by
Gaussian functions to their expected values and uncertainties.  Fake
double tags are estimated from data while the other physics
backgrounds are calculated from Monte Carlo.  The double $b$-tag data
selection as well as details of the fit can be found in~\cite{juano}.

The fit yields zero signal contribution for the $\bb\phi\to\bb\bb$
process for all signal masses. The results of the fit are shown in
Table~\ref{fit}. The QCD heavy flavor background expectations are now
corrected for the $E_T^j$ ($j=1,2,3$) and triple $b$-tag acceptances
corresponding to the present analysis.  QCD heavy flavor acceptances
have been calculated with the PYTHIA Monte Carlo program with its QCD
leading order $2\to 2$ hard scattering processes and parton shower
modelling.  A sufficiently large number of events were generated with
a hard scattering $p_T > 40$ GeV/c in order to obtain unbiased and
statistically significant samples. Below this $p_T$ bin no events
satisfy the trigger requirements.  Fake triple $b$ tag rates are
calculated directly from Run~1 data using fake tagging rate
parametrizations.  Table~\ref{extr} shows the expected QCD heavy
flavor and QCD fake rates as obtained from data for the selection
described in this analysis and after extrapolated to a Run 2 total
integrated luminosity of 1~fb$^{-1}$.

As a comparison, Table~\ref{tabqcd} shows the expected initial rates
for the individual and total QCD processes leading to heavy flavors in
the final state as obtained from PYTHIA.  Also shown are the QCD
acceptances and expected events for 1~fb$^{-1}$ integrated luminosity
for the present analysis.  The heavy flavor content in QCD events are
conventionally classified in three groups: direct production
($q\bar{q},gg \to Q\bar{Q}$), flavor excitation ($Qg\to Qg$), and
gluon splitting ($g\to Q\bar{Q}$) in initial or final state shower
evolution. The relative contributions to the total cross sections are
very uncertain and depend on the center of mass energy, the modelling
of initial and final state radiation, shower evolution and
fragmentation.

\begin{table*}[t!]
\caption{Observed and expected double $b$-tag events in 91 pb$^{-1}$ of 
CDF Run~1 data as obtained from the fit.}
\label{fit}
\begin{tabular}{cccccc}
 & data & QCD heavy flavors & Fakes & $\ttbar$ & $Z$ + jets 
\\ [0.1cm] \hline
 & & & & &  \\ [-0.2cm]
events & $589$ & $470 \pm 27$ & $85 \pm 11$ & $23 \pm 6$ & $16 \pm 4$ 
\\ [0.12cm]
\end{tabular}
%\caption{Observed and expected double $b$-tag events in 91 pb$^{-1}$ of 
%CDF Run~1 data as obtained from the fit.}
%\label{fit}
\end{table*} 

\begin{table*}[t!]
\caption{Expected QCD heavy flavor, QCD fake triple tags and total QCD
events in 1~fb$^{-1}$ total integrated luminosity.}
\label{extr}
\begin{tabular}{c|ccc}
$M$  & QCD heavy flavors & QCD fakes & Total QCD \\ [0.06cm]
(GeV/c$^2$) & \multicolumn{3}{c}{(events per fb$^{-1}$)} \\ [0.1cm]\hline 
     &     &    &    \\ [-0.25cm]
70  & $58.6\pm 12.3$ & $12.1 \pm 10.5$ & $ 70.7 \pm 16.2$ \\ [0.1cm]
80  & $58.6\pm 12.3$ & $12.1 \pm 10.5$ & $ 70.7 \pm 16.2$ \\ [0.1cm]
90  & $56.0\pm 11.9$ & $12.1 \pm 10.5$ & $ 68.1 \pm 15.9$ \\ [0.1cm]
100 & $50.6\pm 11.0$ & $12.1 \pm 10.5$ & $ 62.7 \pm 15.2$ \\ [0.1cm]
110 & $48.0\pm 11.0$ & $ 9.7 \pm  7.8$ & $ 57.7 \pm 13.5$ \\ [0.1cm]
120 & $48.0\pm 11.0$ & $ 7.3 \pm  5.5$ & $ 55.3 \pm 12.3$ \\ [0.1cm]
130 & $45.3\pm 11.1$ & $ 7.3 \pm  5.5$ & $ 52.6 \pm 12.4$ \\ [0.1cm]
140 & $29.3\pm  8.0$ & $ 4.8 \pm  3.4$ & $ 34.1 \pm  8.7$ \\ [0.1cm]
150 & $24.0\pm  7.0$ & $ 2.4 \pm  1.8$ & $ 26.4 \pm  7.2$ \\ [0.1cm]
200 & $ 8.0\pm  3.3$ & $ 1.3 \pm  0.8$ & $  9.3 \pm  3.4$ \\ [0.1cm]
250 & $ 0.0\pm  0.0$ & $ 1.3 \pm  0.8$ & $  1.3 \pm  0.8$ \\ [0.1cm]
300 & $ 0.0\pm  0.0$ & $ 1.3 \pm  0.8$ & $  1.3 \pm  0.8$ \\ [0.13cm]
\end{tabular}
%\caption{Expected QCD heavy flavor, QCD fake triple tags and total QCD
%events in 1~fb$^{-1}$ total integrated luminosity.}
%\label{extr}
\end{table*} 

\break
\vspace{0.2in}
\underline{$\ttbar\to WbW\bar{b}\to \bb$ + jets} \\ \nopagebreak

Background $\ttbar$ events have been simulated using the
HERWIG~\cite{herwig} v5.6 Monte Carlo generator with $M_t=175$
GeV/c$^2$.  The trigger efficiency has been estimated to be $92.0 \pm
0.8\%$ from simulation.  The measured CDF cross section of $7.6^{+
1.8}_{-1.5}$~\cite{xs} is used to estimate the expected number of
events.  Total $\ttbar$ initial rates and acceptances are summarized
in Table~\ref{tabothers}.  The errors shown include both statistical
and systematic uncertainties.  Systematics are dominated by the effect
of the absolute energy scale, modelling of initial state radiation in
HERWIG, and $b$-tag efficiencies.

\begin{table*}[t!]
\caption{Individual and total cross sections and acceptances for the
different QCD hard scattering dijet subprocesses modelled with
PYTHIA. Events are generated with a hard scattering $p_T > 40$ GeV/c.
The $\et$ thresholds used to calculate $\epsilon_{E_T}$ correspond to the 
selection for $M=100$ GeV/c$^2$. Last column shows the expected
rates for 1~fb$^{-1}$.}
\label{tabqcd}
\setlength{\tabcolsep}{3.6pt}
\begin{tabular}{lccccccc}
 & $\sigma$ (pb) & \multicolumn{5}{c}{} & N\\ [0.1cm]
 & $(p_T\!>\!40$ GeV/c) & $\epsilon_{trig}$ (\%) & $\epsilon_{\et}$ (\%)
& $\epsilon_{\ge 2b}$ (\%) & $\epsilon_{\ge 3b}$ (\%)
& $\epsilon_{tot}$ (\%) & (events/fb$^{-1}$)\\ [0.1cm] \hline
 &  \multicolumn{7}{c}{} \\ [-0.2cm]
$q\bar{q},gg\to q\bar{q}$ & $1.2\times 10^4$ & $1.23 \pm 0.01$ 
& $63.9 \pm 0.3$ & $0.15 \pm 0.04$ & $0.0 \pm 0.0$ & $0.0 \pm 0.0$ 
& $0.0 \pm 0.0$ \\
$qq,gg\to qq,gg$ & $4.9\times 10^5$ & $0.98 \pm 0.01$ 
& $60.6 \pm 0.3$ & $0.45 \pm 0.07$ & $0.04 \pm 0.02$ & $0.0002 \pm 0.0001$ 
& $972.6 \pm 561.5$ \\
$gq\to gq$ & $4.4\times 10^5$ & $1.01 \pm 0.01$ 
& $62.6 \pm 0.3$ & $0.45 \pm 0.07$ & $0.02 \pm 0.02$ & $0.0001 \pm 0.0001$ 
& $593.3 \pm 419.5$ \\
$gb(c)\to gb(c)$ & $3.1\times 10^4$ & $0.76 \pm 0.01$ 
& $60.3 \pm 0.3$ & $3.89 \pm 0.20$ & $0.14 \pm 0.04$ & $0.0006 \pm 0.0002$ 
& $198.3 \pm 57.3$ \\
$q\bar{q},gg\to \bb/\cc$ & $8.2\times 10^3$ & $0.94 \pm 
0.01$ & $62.7 \pm 0.2$ & $7.91 \pm 0.21$ & $0.19 \pm 0.04$ 
& $0.0011 \pm 0.0004$ 
& $91.9 \pm 17.7$ \\ [0.15cm] 
Total & $9.8\times 10^5$ & $0.99 \pm 0.01$ 
& $61.6 \pm 0.6$ & $0.59 \pm 0.05$ & $0.03 \pm 0.01$ 
& $0.0002 \pm 0.0001$ 
& $1856.2 \pm 703.5$ \\ [0.15cm] 
\end{tabular}
%\caption{Individual and total cross sections and acceptances for the
%different QCD hard scattering dijet subprocesses modelled with
%PYTHIA. Events are generated with a hard scattering $p_T > 40$ GeV/c.
%The $\et$ thresholds used to calculate $\epsilon_{E_T}$ correspond to the 
%selection for $M=100$ GeV/c$^2$. Last column shows the expected
%rates for 1~fb$^{-1}$.}
%\label{tabqcd}
\end{table*} 


\begin{table*}[t!]
\caption{Cross sections and acceptances for the $\ttbar$ and different 
$W/Z$ + jets backgrounds. The $\et$ thresholds correspond to the 
selection $M=100$ GeV/c$^2$.}
\label{tabothers}
\begin{tabular}{ccccccc}
 & $\sigma\times BR$ (pb) & $\epsilon_{trig}$ (\%) & $\epsilon_{\et}$ (\%)
& $\epsilon_{\ge 2b}$ (\%) & $\epsilon_{\ge 3b}$ (\%)
& $\epsilon_{tot}$ (\%) \\ [0.1cm] \hline
 &  \multicolumn{6}{c}{} \\ [-0.2cm]
$\ttbar$ & $3.49 \pm 0.83$ & $92.0 \pm 0.8$ 
& $91.0 \pm 0.2$ & $12.3 \pm 0.2$ & $0.17 \pm 0.03$ & $0.14 \pm 0.02$ 
\\ [-0.1cm]
($t\to Wb\to jjb$) & & & & & & \\ [0.1cm]
$Z$+jets & $11.8 \pm 1.4$ & $30.7 \pm 1.2$ & $69.8 \pm 0.5$ 
& $7.5 \pm 0.6$ & $0.27 \pm 0.10$ & $0.06 \pm 0.02$ \\ [-0.01cm]
($Z\to \bb/\cc$) & & & & & & \\ [0.1cm]
$W\bb/\cc$ & $237.2 \pm 13.6$ & $28.5 \pm 1.1$ & $69.8 \pm 0.5$ 
& $0.06 \pm 0.03$ & $0.004 \pm 0.003$ & $0.001 \pm 0.001$ \\ [-0.01cm]
($W\to q\bar{q}',c\bar{s}$) & & & & & & \\ [0.1cm]
$Z\bb/\cc$ & $74.6 \pm 6.4$ & $30.5 \pm 1.2$ & $69.8 \pm 0.5$ 
& $0.07 \pm 0.03$ & $0.004 \pm 0.003$ & $0.001 \pm 0.001$ \\ [-0.01cm]
($Z\to q\bar{q}$) & & & & & & \\ [0.12cm]
\end{tabular}
%\caption{Cross sections and acceptances for the $\ttbar$ and different 
%$W/Z$ + jets backgrounds. The $\et$ thresholds correspond to the 
%selection $M=100$ GeV/c$^2$.}
%\label{tabothers}
\end{table*} 

\vspace{0.2in}
\underline{$W/Z$ + jets} \\ \nopagebreak

The $W/Z\, + \ge n$ jets background has been studied with a
combination of data and Monte Carlo. The CDF measured cross sections
for $W$ + jets, $W\to e\nu$~\cite{vj1} and $Z$ + jets, $Z\to
ee$~\cite{vj2} are used to normalize Monte Carlo production cross
sections for $W/Z\, + \ge n$ jet events.  Generic $W$ + jets and $Z$ +
jets samples generated with the HERWIG Monte Carlo program~\cite{vj3}
and processed through the CDF simulation package were used to estimate
the expected contributions after our selection cuts.  The predominant
source of heavy flavor production in $W/Z\, + \ge n$ jets events is
$Z\, + \ge n$ jets ($Z\to \bb/\cc$) as well as some contribution of
initial and final state gluon splitting and higher order diagrams
leading to $W\bb/\cc$ and $Z\bb/\cc$ events.

Table~\ref{tabothers} shows the initial cross sections and estimated
acceptances for all the $W/Z$ + jets backgrounds leading to heavy
flavor final states. The errors shown include both statistical and
systematic uncertainties. The systematic uncertainties are dominated
by the normalization of the measured cross sections to the predicted
Monte Carlo cross sections.

Figure~\ref{figeff} shows the individual and total efficiencies as a
function of the Higgs mass for the signal and the different standard
model background contributions.

\begin{figure}[hb!]
  \centerline{\parbox{4.8in}{\epsfxsize=\hsize\epsffile{./bbbb/run2eff.eps}} }
  \caption{Individual and total efficiencies (in \%) as a function
           of the signal mass for (a) signal, (b) QCD, (c) $t\bar{t}$, and 
           (d) $Z$ + jets ($Z\rightarrow b\bar{b}/c\bar{c}$).}
  \label{figeff}
\end{figure}

\begin{table*}[t!]
\caption{Expected number of background events as a function of 
the Higgs mass for 1 fb$^{-1}$.}
\label{backs}
\begin{tabular}{c|cccccc}
$M$  & $N_{QCD}$ & $N_{Zjj}$ & $N_{\ttbar}$
 & $N_{W\bb/\cc}$ & $N_{Z\bb/\cc}$ &
$N_{tot}=B$\\ [0.06cm]
(GeV/c$^2$) & \multicolumn{6}{c}{(events per fb$^{-1}$)} \\ [0.1cm]\hline 
     &     &    &    &  & &\\ [-0.25cm]
70 & $70.7 \pm 16.2$ & $4.4 \pm 1.6$ & $13.2 \pm 3.5$ & $1.5 \pm 0.6$ & 
$0.5 \pm 0.2$ & $90.4 \pm 16.7$ \\ [0.1cm]
80 & $70.7 \pm 16.2$ & $4.4 \pm 1.6$ & $13.5 \pm 3.4$ & $1.5 \pm 0.6$ & 
$0.5 \pm 0.2$ & $90.7 \pm 16.6$  \\ [0.1cm]
90 & $68.1 \pm 15.9$ & $4.6 \pm 1.6$  & $13.4 \pm 3.4$ & $1.5 \pm 0.6$ & 
$0.5 \pm 0.2$ & $88.1 \pm 16.3$  \\ [0.1cm]
100 & $62.7 \pm 15.2$ & $4.5 \pm 1.5$ & $13.2 \pm 3.2$ & $1.4 \pm 0.5$ & 
$0.5 \pm 0.2$ & $82.3 \pm 15.6$  \\ [0.1cm]
110 & $57.7 \pm 13.5$ & $4.1 \pm 1.5$ & $12.8 \pm 3.4$ & $1.3 \pm 0.5$ & 
$0.4 \pm 0.2$ & $76.3 \pm 14.0$  \\ [0.1cm]
120 & $55.3 \pm 12.3$ & $3.4 \pm 1.3$ & $12.6 \pm 3.4$ & $1.2 \pm 0.5$ & 
$0.4 \pm 0.2$ & $72.9 \pm 12.8$  \\ [0.1cm]
130 & $52.6 \pm 12.4$ & $2.1 \pm 1.1$ & $12.2 \pm 3.2$ & $1.0 \pm 0.4$ & 
$0.3 \pm 0.1$ & $68.2 \pm 12.9$  \\ [0.1cm]
140 & $34.1 \pm  8.7$ & $1.7 \pm 0.6$ & $11.3 \pm 3.1$ & $0.8 \pm 0.3$ & 
$0.3 \pm 0.1$ & $48.2 \pm  9.3$  \\ [0.1cm]
150 & $26.4 \pm  7.2$ & $1.3 \pm 0.5$ & $10.8 \pm 2.9$ & $0.6 \pm 0.2$ & 
$0.2 \pm 0.1$ & $39.3 \pm  7.8$  \\ [0.1cm]
200 & $ 9.3 \pm 3.4$ & $0.0 \pm 0.0$ & $4.4 \pm 1.2$ & $0.0 \pm 0.0$ & 
$0.0 \pm 0.0$ & $13.7 \pm  3.6$   \\ [0.1cm]
250 & $ 1.3 \pm 0.8$ & $0.0 \pm 0.0$ & $0.9 \pm 0.3$ & $0.0 \pm 0.0$ & 
$0.0 \pm 0.0$ & $ 2.2 \pm  0.9$   \\ [0.1cm]
300 & $1.3 \pm 0.8$ & $0.0 \pm 0.0$ & $0.3 \pm 0.1$ & $0.0 \pm 0.0$ & 
$0.0 \pm 0.0$ & $ 1.6 \pm  0.8$  \\ [0.13cm]
\end{tabular}
%\caption{Expected number of background events as a function of 
%the Higgs mass for 1 fb$^{-1}$.}
%\label{backs}
\end{table*} 



\begin{table*}[t!]
\caption{Expected number of SM signal events ($\tan\beta = 1$),
MSSM signal events for $\tan\beta = 40$ and significances as a function of 
the Higgs mass for 1 fb$^{-1}$.}
\label{final}
\begin{tabular}{c|cc|cc}
$M$  & $S$ & $S/\sqrt{B}$ & $S$ & $S/\sqrt{B}$ \\ [0.06cm]
(GeV/c$^2$) & \multicolumn{2}{c}{($\tan\beta =1$)} &
\multicolumn{2}{|c}{($\tan\beta = 40$)} \\ [0.1cm]\hline 
     &          &   &          &    \\ [-0.25cm]
70   & $0.039$     & $0.0041$  & $133.2$ &  $14.0$  \\ [0.1cm]
80   & $0.027$     & $0.0028$  & $ 91.9$ &  $ 9.7$  \\ [0.1cm]
90   & $0.018$     & $0.0019$  & $62.4$  &  $6.6$   \\ [0.1cm]
100  & $0.012$     & $0.0013$  & $41.0$  &  $4.5$   \\ [0.1cm]
110  & $0.007$     & $0.0008$  & $26.3$  &  $3.0$   \\ [0.1cm]
120  & $0.005$     & $0.0006$  & $19.1$  &  $2.2$   \\ [0.1cm]
130  & $0.002$     & $0.0002$  & $13.7$  &  $1.7$   \\ [0.1cm]
140  & $0.001$     & $0.0001$  & $10.0$  &  $1.4$   \\ [0.1cm]
150  & $0.0004$    & $0.00006$ & $7.0$   &  $1.1$   \\ [0.1cm]
200  & $0.0   $    & $0.0$     & $1.1$   &  $0.3$   \\ [0.1cm]
250  & $0.0   $    & $0.0$     & $0.15$  &  $0.1$   \\ [0.1cm]
300  & $0.0   $    & $0.0$     & $0.03$  &  $0.02$  \\ [0.13cm]
\end{tabular}
%\caption{Expected number of SM signal events ($\tan\beta = 1$),
%MSSM signal events for $\tan\beta = 40$ and significances as a function of 
%the Higgs mass for 1 fb$^{-1}$.}
%\label{final}
\end{table*} 

\break
\vspace{0.2in}
{\bf Results} \\ \nopagebreak

Table~\ref{backs} shows the expected number of events from each
individual background contribution as well as the total backgrounds
for 1~fb$^{-1}$.  Table~\ref{final} shows the expected number of
signal events for $\tan\beta = 1$ (Standard Model case) and for
$\tan\beta = 40$ as well as the signal significances as a function of
the Higgs mass for 1~fb$^{-1}$.

The reconstructed dijet invariant mass for the highest-$\et$ jets in
the event (with both jets required to be $b$-tagged) and with present
CDF Run~1 dijet resolutions is shown in Figure~\ref{sandb} for both
signal and background.  All rates are normalized to 1~fb$^{-1}$.

\newpage


Figure~\ref{figtb} shows the 95\% CL exclusion limits, $3\sigma$
discovery thresholds and $5\sigma$ discovery thresholds in the 
$\tan\beta$--$M_{\phi}$ plane of the MSSM for four different total integrated
luminosity scenarios, ${\cal L}=91$ pb$^{-1}$, 2 fb$^{-1}$, 
10~fb$^{-1}$ and 30 fb$^{-1}$.
Figure~\ref{figlum} shows the required luminosity for 95\% CL
exclusion limits, $3\sigma$ and $5\sigma$ discovery thresholds as a
function of the Higgs mass for the MSSM scenario with $\tan\beta$ = 10 and 40.

In a theory with a non-minimal Higgs sector (beyond the SM), the $\phi\bb$ 
coupling differs from the corresponding $\hsm\bb$ coupling of the Standard
Model Higgs boson.  As a result, the production cross-section for
$gg$, $q\bar q\to\bb\phi\to\bb\bb$ is given by
\begin{equation}
\sigma_{\bb\bb} = \left( \frac{y_b}{y_b^{\rm SM}} \right)^2
\frac{{\rm BR}(\phi\to \bb)}{{\rm BR}(\hsm\to \bb)} \;
\sigma_{\bb\bb}^{\rm SM}\,,
\end{equation}
where $y_b$ [$y_b^{\rm SM}$] is the $\phi\bb$ [$\hsm\bb$] coupling.  
It is convenient
to define a ratio ${\cal R}$ of the Higgs production amplitude in the
general model divided by the corresponding SM amplitude.  In terms of the
cross-sections, $\sigma_{\bb\bb}\equiv {\cal R}^2 \sigma_{\bb\bb}^{\rm SM}$, 
where
\begin{equation}
{\cal R} = \left( \frac{y_b}{y_b^{\rm SM}} \right)\; 
\left[\frac{{\rm BR}(\phi\to \bb)}{{\rm BR}(\hsm\to \bb)}
\right]^{1/2}\,.
\label{calrdef}
\end{equation}
Figure~\ref{kf} shows the enhancement factor ${\cal R}$
as a function of the Higgs mass, the integrated total luminosity, and
for 95\% CL, $3\sigma$ and $5\sigma$ discovery thresholds.
The ${\cal R}$ factor contains the entire model dependence of the 
cross-section and allows one to present the results in a model-independent way.

\begin{figure}
  \centerline{\parbox{4.0in}{\epsfxsize=\hsize\epsffile{./bbbb/sandb.eps}} }
  \caption{Reconstructed dijet invariant mass for the highest-$\et$
           jets in the event for (a) signal ($M=130$ GeV/c$^2$ and $\tan\beta$ = 40), 
           (b) background (QCD, $Z$ + jets with $Z\rightarrow b\bar{b}/c\bar{c}$
           and $t\bar{t}$), and (c) background only (solid histogram)
           and signal + background (dashed histogram). All distributions are 
           normalized to 1 fb$^{-1}$ of total integrated luminosity.}
  \label{sandb}
\end{figure}

\begin{figure}
  \centerline{\parbox{4.8in}{\epsfxsize=\hsize\epsffile{./bbbb/run2tanb.eps}} }
  \caption{Discovery and exclusion contours in the $\tan\beta$--$M_{\phi}$
           plane of the MSSM for total integrated luminosities of 91 pb$^{-1}$,
           2 fb$^{-1}$, 10 fb$^{-1}$ and 30 fb$^{-1}$.}
  \label{figtb}
\end{figure}

\begin{figure}
  \centerline{\parbox{4.8in}{\epsfxsize=\hsize\epsffile[0 0 560 280]{./bbbb/run2lumtb.eps}} }
  \caption{Neccesary integrated luminosity for 95\% CL exclusion limits
           and $5\sigma$ and $3\sigma$ discovery thresholds as a 
           function of the Higgs mass for the MSSM scenario with $\tan\beta$ = 10 and 40.}
  \label{figlum}
\end{figure}

\begin{figure}[ht!]
  \centerline{\parbox{4.5in}{\epsfxsize=\hsize\epsffile{./bbbb/kf.eps}} }
  \caption{Enhancement factor ${\cal R}$ [eq.~(\ref{calrdef})] 
           as a function of the Higgs mass
           for 95\% CL exclusion limits, $5\sigma$ and $3\sigma$ discovery 
           thresholds and different total integrated luminosities.}
  \label{kf}
\end{figure}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\vspace{0.2in}
%\newpage
\break
\large
{\bf Comparison of analyses} \\
\normalsize \nopagebreak

% comparison of CDF and D0 bbbb analyses

Starting from quite different input assumptions and methods,
the two $\bb\bb$ analyses discussed above arrive at quite
similar estimates for the exclusion and discovery reach for the 
MSSM scalar and pseudoscalar Higgses at large $\tan\beta$.  

The first main difference is that the analyses use different Monte
Carlo generators; the D\O\ analysis uses {\sc COMPHEP}, whereas the
CDF analysis uses a generator developed during the Workshop from a
modified version of {\sc PAPAGENO} with {\sc PYTHIA} fragmentation.
The cross sections and kinematic distributions from the two generators
agree reasonably well.  %% check this more carefully %%

% trigger and kinematics

The two kinematic selections proceed along similar lines, both
demanding four jets.  The D\O\ analysis demands a minimum jet
transverse momentum of 30 GeV$/c$ and leading and next-to-leading
jet $p_T$'s which increase with Higgs mass.  The CDF analysis
demands $\sum(E_T) > 125$ GeV and four jets with a minimum of
15 GeV transverse energy.\footnote{This is motivated by the Run 1 trigger
requirements, which may loosen for Run 2 if the experiment uses
the SVT to tag secondary vertices in three-jet events.}

% b tagging

Though there are potentially four taggable $b$ jets in the signal,
both analyses require three tags for optimal sensitivity.  The 
D\O\ analysis assumes a $b$ tagging efficiency based on the Monte
Carlo study of Section II.A.3, which has a maximum efficiency of
55\%.   The CDF analysis uses, conservatively, the Run 1 tagging
efficiencies per taggable jet, but the much larger Run 2 detector 
geometry to determine taggability.  This is perhaps the largest
source of difference between the two analyses, since the cube of the
tagging efficiency determines the signal rate.

% backgrounds

By far the largest background comes from QCD $\bb jj$ production, and
the CDF simulations of its total rate did not agree with the observed
rate in analyses of Run~1 data.  The only weapons against it are the
requirement of the third $b$ tag and reconstructing the Higgs mass.
The D\O\ analysis relies on Monte Carlo simulations of the background,
and the CDF analysis uses Monte Carlo scaled by a factor determined
with Run 1 data, and taking into account the increased center of mass
energy in Run 2.  Given the different signal selections, it is
difficult to say how well the two methods agree.

% mass fitting

The two analyses also take different approaches to Higgs mass 
reconstruction.  The D\O\ analysis uses all possible $\bb$ combinations
in an event, and a 15\% resolution (for the correct combination) based 
on the MC studies.  The CDF analysis uses jets 1 and 2 at high Higgs 
masses, and jets 2 and 3 at lower Higgs masses.  The assumed resolution 
is that of Run 1, typically 15\% for the correct combination for a 
150 GeV/$c^2$ Higgs mass.  

% results

All these differences nevertheless lead to quite similar estimates for
exclusion and discovery.  Since the reach in $\tan\beta$ goes as the 
square of the cross section limit, the 30-40\% lower reach of the D\O\
analysis implies that the two analyses differ by perhaps 15-20\% in the
end.  Such differences are easily understood in the context of the 
foregoing paragraphs.

% prospects for improvement

Both analyses assume rather conservative $b$ tagging efficiency
and mass resolution; these are quite likely to be better in the 
actual run.  Furthermore, the role of an improved trigger should 
be studied further; the fact that in many events one of the $b$ jets
is very far forward could perhaps mean that it is optimal to require
only three jets in the central region.  

In any case, this search represents the main mode for discovering
or ruling out the MSSM Higgs at large $\tan\beta$, and demonstrates
one of the unique advantages of hadron colliders.

