The next run of the Tevatron proton-antiproton collider at Fermilab
will see enormous increases in luminosity, initially more than an
order of magnitude larger than those in Run~1.  With the new Main
Injector and Antiproton Recycler rings a total integrated luminosity
of 2 fb$^{-1}$ should be delivered to the CDF and D\O\ collider
experiments by the end of 2002.  Continuous running over multiple years 
and additional improvements to the
collider could result in a total data sample exceeding 10 fb$^{-1}$
prior to the start of the LHC.
Both CDF and D\O\ will have greatly improved
detectors,  with all new charged particle tracking and vertexing, 
improved calorimetry and triggering, and new offline analysis
software.   These improvements
to the accelerator and the detectors enhance the
sensitivity of the experiments for new particle searches.
In particular, given sufficient integrated luminosity, the discovery
of the Higgs boson at the upgraded Tevatron collider may be within reach.

In Run~1, the CDF and D\O\ collaborations began developing the
techniques for searching for the Higgs bosons of the Standard Model
(SM) and Minimal Supersymmetric Standard Model (MSSM).  The Tevatron
Run~1 integrated luminosity of about 100 pb$^{-1}$ was too small to
yield sufficient sensitivity to exclude or discover the SM Higgs.  In
the MSSM, certain Higgs fermion-couplings are enhanced (relative to
their Standard Model values) in some regions of MSSM parameter space.
As a result, one can already deduce some weak restrictions on the MSSM
Higgs parameters based on the Run~1 MSSM Higgs searches for neutral
Higgs production (in association with $b\bar b$ pairs) and charged
Higgs bosons (resulting from top decays).  This Report capitalizes on
the experience gained in Run 1 in estimating the discovery and
exclusion reach for the SM and MSSM Higgs bosons in Run~2, assuming
that CDF and D\O\ combine their results to maximize the sensitivity.

Estimating the discovery and exclusion reach for Higgs bosons requires
accurate knowledge of the search acceptance and expected backgrounds
in the various channels.  No detailed
simulation existed prior to this Workshop, 
and so the participants developed SHW---a simple Monte
Carlo simulation---to represent an ``average'' of the CDF and D\O\
experiments, taking into account the improvements to the detectors.
SHW simulates the detector response to
all the individual particles in the event, including tracking and
calorimeter efficiency, resolution, and geometry, but does not
simulate the effects of multiple interactions, the magnetic field,
lateral shower development, secondary interactions, or details of the
microvertex detectors.  Comparisons of the simulation with the Run 1
full simulation and data are encouraging, and show agreement at the
15-20\% level in acceptance.

Without the real Run~2 data, it is also difficult to get an
accurate estimate of the $b$ quark jet tagging efficiency and mistag
rate, the $\bb$ jet-jet mass resolution, and certain backgrounds that
must be estimated from actual data.  The philosophy in this study is
to make an optimistic yet realistic estimate of the Higgs boson 
discovery and exclusion reach, assuming improvements to 
these performance parameters
of the detectors and analyses.  These estimates are based on Run~1
experience, albeit with less capable detectors, and
detailed simulations of $b$-tagging at the planned Run~2 detectors.
Further work will be necessary to understand some of the relevant 
backgrounds with higher level of accuracy. The completion of the
background analyses will also require direct handling of the actual 
Run 2 data.  A more accurate estimate of the Run 2 Higgs discovery
and exclusion reach can only be achieved after the Tevatron
Run 2 experiments start collecting data.

%  but for such studies 
% handling directly with 
% the actual RUN2 data will be required.

\vspace{0.2in}
{\bf Search for the Standard Model Higgs Boson} \\

In the mass region of interest to the Tevatron 
(100~GeV$\lsim\mhsm\lsim 200$~GeV),
the SM Higgs boson is produced most copiously via $gg$ fusion, with a cross
section from about 1--0.1~pb.  For $\mhsm\lsim 135$~GeV, the Higgs boson decays
dominantly to $\bb$.  Since the cross section for the QCD
production of $\bb$ dijet events is orders of magnitude larger than
the Higgs production cross section, the  $gg \to h_{SM} \to b \bar b$  
channel is not a promising channel and thus
has not been investigated in this Report.
For $\mhsm\gsim 135$~ GeV, the Higgs boson decays
dominantly to $WW^{(*)}$ (where $W^{*}$ is a virtual $W$),
and the channel $gg\to \hsm\to WW^{(*)}$ is accessible to the
Tevatron Higgs search.

The next largest Higgs cross section is for the production of the SM
Higgs boson in
association with a vector boson.  The combined $W\hsm$ and $Z\hsm$ cross
sections is about 0.2---0.5~pb in the mass region of interest
($100\lsim\mhsm\lsim 135$~GeV), while the dominant Higgs decay is
$\hsm\to b\bar b$.  These processes lead to four main final
states: $\ell\nu\bb$,
$\nn\bb$, $\lpm\bb$, and $\qq\bb$.  Of these channels the first three
have distinct signatures on which the experiments can trigger
(high $p_T$ leptons and/or missing $E_T$) and the backgrounds are
controllable, typically dominated by vector-boson pair production,
$t\bar t$ production and QCD dijet production.  The backgrounds can in
all cases be estimated and/or cross-checked with actual data, allowing
the systematic error to remain roughly a constant fraction of
the total background. 
The signal efficiencies and backgrounds have all been estimated with
both the CDF Run~1 detector simulation and with the simple SHW
simulation.  In addition, the selection was optimized using neural
network techniques, resulting in a demonstrable gain 
in the significance of the Higgs signal for the
$\ell\nu\bb$ and $\nn\bb$ channels.

As noted above, the $b$-tagging efficiencies and the $\bb$ mass
resolution play a key role in determining the ultimate efficiency and
background rejection.  Much work remains, using real data studies, to
optimize the performance in both these areas.  In this regard, we have
been optimistic in this Report, assuming a ``loose'' $b$-tag
efficiency of 75\% at large jet $E_T$, and a ``tight'' $b$-tag
efficiency of 60\% at large jet $E_T$.  We believe that these are
realistic numbers, based on simulation studies.  For the mass
resolution, we have assumed in the final results a 10\% resolution on
the ``core'' of the distribution; inefficiencies due to the low side
tail remain after this rescaling of the simulation output.  This is
aggressive, but simulations suggest that a 10\% $b\bar b$ mass
resolution may be achievable.  Moreover, given CDF's demonstrated 12\%
$\bb$ mass resolution in $Z\to\bb$ events at Run~1, we believe that an
ultimate goal of a 10\% mass resolution is not overly optimistic.

For backgrounds we have used Monte Carlo estimates everywhere except
in the $\nn\bb$ channel, where there is a significant contribution
from QCD $\bb$ dijet production.  This background comes from the
extreme tail of a very large cross section, and is thus very difficult
to model.  In the CDF Run~1 analysis of this channel, QCD $\bb$ dijets
constituted half of the total background.  
D\O\ searches involving the same topologies have considerably lower   
background levels, despite the absence of a $b$ tag requirement,              
due to their better missing $E_T$ resolution.
To be conservative, we have taken the unknown
QCD $b\bar b$ dijet background to the $\nn\bb$ channel to be equal in
size to the sum of all other contributing background processes.

Larger Higgs masses ($\mhsm\gsim 135$~GeV) had not been studied in previous
Tevatron studies.  This Workshop produced several analyses aimed at
exploiting the distinct signatures present when the Higgs 
boson decay branching ratio to $WW^{(*)}$ becomes appreciable.
In this case, there are final states with $WW$ (from the
gluon-fusion production of a single Higgs boson), and
$WWW$ and $ZWW$ arising from associated vector boson--Higgs boson
production. Three
search channels emerged in the Workshop as potentially sensitive at
these high Higgs masses: like-sign dilepton plus jets ($\lsdilep$)
events, high-$p_T$ lepton pairs plus missing $E_T$ ($\lpm\nn$), and
trilepton ($\trilep$) events.  Of these, the first two were found to
be most sensitive.

Note that in this study, the same analysis selection has been assumed
for integrated luminosities ranging over an order of magnitude.  This
is not the typical pattern in new particle searches in high energy
physics: as the integrated luminosity increases, better understanding of
signal and background separation typically leads to the tightening of
selection cuts in order to keep background low while maintaining the signal
efficiency.  Of course, some backgrounds will remain irreducible, but it
is possible that the integrated luminosity thresholds could be
lowered with respect to those reported here, as experience is gained with
real data.


The final combined result of the integrated luminosity required to
exclude or discover the SM Higgs boson, as a function of the Higgs
mass, depicted in \fig{f:combined-final}, is obtained by combining the
sensitivity of all the channels described above, and assuming that the
data from the CDF and D\O\ experiments can be combined.  This result
is achieved by forming a joint likelihood from the product of the
Poisson probabilities of single-channel counting of signal and
background in each channel.  A nominal systematic error on the
expected background was taken into account by Bayesian integration.

The final result shows that for an integrated luminosity of
10~fb$^{-1}$, if the SM Higgs boson does not exist in the energy range
explorable at the Tevatron, then one can attain a 95\% CL exclusion
for masses up to about 180~GeV.  Moreover, if the SM Higgs happens to
be sufficiently light ($\mhsm\lsim 125$~GeV), then a tantalizing
$3\sigma$ effect will be visible with the same integrated luminosity.
With about 25~fb$^{-1}$ of data, $3\sigma$ evidence for the Higgs
boson can be obtained for the entire Higgs mass range up to 180~GeV.
However, the discovery reach is considerably more limited for a
5$\sigma$ Higgs boson signal.  Even with 30~fb$^{-1}$ of integrated
luminosity, only Higgs bosons with masses up to about 130~GeV can be
detected with 5$\sigma$ significance.  

Suppose that the Higgs boson mass is 115~GeV, which lies just above
the 95\% CL exclusion limit achieved by LEP \cite{tomjunk}.  At the
Tevatron, with 5~fb$^{-1}$ of integrated luminosity per experiment,
there would be sufficient data to see a 3$\sigma$ excess above
background, providing evidence for a Higgs boson.  With 15~fb$^{-1}$
of integrated luminosity per experiment, a $5\sigma$ discovery of the
Higgs boson would be possible.

The above integrated luminosity requirement crucially depend on the
success of a greatly improved $\bb$ mass resolution and $b$-tagging
rates (as compared to Run~1).  Nevertheless, these results clearly
provide strong motivation to the accelerator division to deliver the
largest possible integrated luminosity, and to the experimental
collaborations to optimize the data analyses and reconstruction
techniques, and continue to study new methods and ideas for enhancing
the sensitivity in this search.

Other Higgs signatures could help improve the sensitivity of the Higgs
search at the Tevatron.  In this Report, 
none of the channels corresponding to the $\tau^+\tau^-$ decay mode of
the Higgs have been investigated, as the small branching ratio 
(less than $8\%$) makes the corresponding signal rates small.  
Still, a significant improvement of $\tau$-lepton identification 
could lead to a viable Higgs signal in the low Higgs-mass 
($\mhsm\lsim 130$~GeV) regime.  This possibility deserves further
study.  Perhaps more promising is the detection of the Higgs boson via
$t\bar t\hsm$ production (the Higgs boson is radiated off the
top-quark), followed by $\hsm\to b\bar b$.  Initial studies
\cite{rainwater} suggest that this channel could be observable at the
upgraded Tevatron, with a statistical significance  
comparable to the Higgs signals in the $W\hsm$ and
$Z\hsm$ channels.  Clearly, if this is confirmed by a more detailed
analysis, it would improve the prospects for a Higgs signal at the
Tevatron, perhaps even lowering significantly the total integrated
luminosity required for evidence of a Higgs signal or a discovery.


\vspace{0.2in}
{\bf Search for Higgs Bosons of Low-Energy Supersymmetry} \\

The possibility that nature is supersymmetric 
at the TeV scale opens up several new
experimental alternatives in the search for Higgs bosons.  The Minimal
Supersymmetric Standard Model (MSSM) requires two Higgs doublets, 
which yields five physical scalars: two CP-even neutral scalars
($\hl$ and $\hh$), a CP-odd scalar ($\ha$) and a
charged Higgs pair ($ \hpm$).  At tree level, 
the masses and couplings of these particles are
governed by two parameters, $\tan\beta\equiv v_2/v_1$ (the ratio
of the two neutral Higgs field vacuum expectation values)
and one of the Higgs masses (usually chosen to be $\mha$).
When loop effects are taken into account, one finds that 
Higgs masses and couplings depend additionally on various
supersymmetric mass parameters.  Such effects can be significant in
certain regions of the MSSM parameter space.   These include
an increase in the upper bound of the mass of the lightest
CP-even Higgs boson ($\mhl\lsim 130$~GeV, assuming an average top
squark mass no larger than 1~TeV), a possible suppression or
enhancement of the dominant decay
rate $\phi\to b\bar b$ (where $\phi=\hl$, $\hh$, and/or $\ha$),
and CP-violating effects that can mix the CP-even and CP-odd eigenstates.
 
In various regimes of the $\mha$---$\tan\beta$ parameter space, the
phenomenology of the Higgs bosons can be very different.  For example,
in the regime where $\mha\gg m_Z$, known as the decoupling limit, the
light scalar $\hl$ possesses the same production cross-sections and
decay rates as $\hsm$, and is thus indistinguishable from the SM Higgs
boson.  In this case, the SM Higgs search analyses apply, while all
other Higgs bosons are too heavy and not observable at the Tevatron.
In contrast, if $\mha\sim {\cal O}(m_Z)$, then the $\hl$ properties
differ significantly from those of $\hsm$.  In this parameter range,
it may be possible to detect more than one Higgs state at the
Tevatron, or demonstrate that an observed Higgs signal does not
correspond to the one expected from the SM Higgs boson.

In the latter case, we can still make use of the Standard Model Higgs
analyses as follows.  For each Higgs production/decay channel,
we first define theoretical ratios (denoted
collectively by $R$) of $\sigma\times {\rm BR}$ for Higgs production
and decay in the MSSM relative to its Standard Model value.   
Then, we can derive a lower limit for the required luminosity $L$ in order
to obtain a Higgs signal of fixed significance ({\it e.g.} 95\% CL
limit or a $5\sigma$ discovery).  If $R=1$, the result for $L$ is
simply the one obtained in the Standard Model Higgs search analysis.
If $R\neq 1$, then we expect $R\sqrt{L}$ to be constant in the
Gaussian limit, which yields a lower limit for $L$ as a function of
$R$ (say, at fixed Higgs mass).  In the regime where Poisson
statistics is required, this scaling is somewhat modified; the
corresponding $R$-plots were given in Section III.B.1.

The MSSM analysis proceeds as follows.  The Higgs signatures arising from 
associated vector boson--Higgs boson production followed by Higgs decay
to $b\bar b$, treated in the SM analysis,
also apply to the case of the CP-even Higgs bosons of the MSSM.  For a
given point in supersymmetric parameter space (which depends on
$\tan\beta$, $\mha$, and other supersymmetric mass parameters, such as
the third generation squark masses, the gaugino masses, the 
trilinear couplings $A_t$, $A_b$ and higgsino mass parameter $\mu$,
which govern the size of the
radiative corrections), one can compute the corresponding $R$ values
for the associated vector boson--Higgs boson production and subsequence
Higgs decay to $b\bar b$.  Comparing with the $R$-plots previously
obtained, one can then either exclude or discover a CP-even Higgs
boson of a given mass for a fixed integrated luminosity.  In this way, one can
map out the MSSM Higgs parameter space in the $\mha$---$\tan\beta$
plane (under various assumptions for the values of the other supersymmetric
parameters that govern the impact of the loop-effects) and determine
which parameter regimes are accessible to the Tevatron Higgs search at
a given luminosity.

We have studied three examples: 
(i)~the top-squark (stop) mixing parameters is set to zero, which
minimizes the maximal value of the radiatively-corrected light CP-even
Higgs mass (the so-called ``minimal-mixing'' or ``no-mixing'' scenario);
(ii)~the stop mixing parameters are chosen to maximize 
the value of the lightest CP-even Higgs mass
(the ``maximal-mixing'' scenario); and (iii)~the stop mixing 
parameters and the gluino mass are chosen in order to suppress 
the $b\bar b$ coupling of the Higgs state that is primarily
produced in association with the gauge bosons
(the ``suppressed $V\phi\to Vb\bar b$ production'' scenario).
Case~(iii) exemplifies a possible worst case scenario for the MSSM Higgs
search at the upgraded Tevatron.
%in certain regions of the $m_A$---$\tan\beta$ plane.
In the case of minimal mixing, a Higgs boson produced in association
with the gauge bosons may be excluded at the 95$\%$ CL with as little as
5~fb$^{-1}$ of data per experiment, 
and can be discovered at the $5\sigma$ level
over nearly the entire region of the $m_A$---$\tan\beta$
plane with less than 20~fb$^{-1}$ per experiment.  However, in the other 
two cases mentioned above, our results
show that an integrated luminosity
of order 20---30~fb$^{-1}$ is required to obtain 
a 5$\sigma$ discovery over a significant portion of the parameter
space.   Yet, even in these cases, 
10~fb$^{-1}$ is sufficient to exclude the Higgs sector of the MSSM at 
the 95$\%$ CL, for most values of $m_A$ and $\tan\beta$
(independent of the values of the stop mixing parameters, assuming
that the average top squark mass is not much larger than 1~TeV), if no
Higgs signal is detected.  However, in the suppressed 
$V\phi\to Vb\bar b$ production scenario, there is a non-negligible
region of the MSSM parameter space in which even a 95$\%$ CL Higgs 
exclusion limit is not achievable at 30~fb$^{-1}$.
Note that if the Higgs signature due to $t\bar t\hsm$ (with $\hsm\to
b\bar b$), examined in \Ref{rainwater}, proves to be a viable
discovery mode, then the analogous MSSM Higgs signatures could improve the
upgraded Tevatron coverage of the MSSM Higgs parameter space described above.


In the large $\tan\beta$ regime of the MSSM, some of the
neutral Higgs boson couplings to down-type fermions (such as
$b\bar b$) are enhanced, and lead to production cross
sections for Higgs bosons that are significantly larger than those of the
Standard Model Higgs boson.
As a result, in general two of the neutral Higgs
bosons of the MSSM can also be discovered in an additional channel:
$b\bar b\phi$ production, followed by $\phi\to b\bar b$ (where
$\phi$ is either the CP-odd Higgs boson or the neutral CP-even
Higgs boson with enhanced coupling to $b\bar b$,
at large $\tan\beta$).  The corresponding channel cannot be observed
in the case of the SM Higgs boson, since the $\hsm b\bar b$ coupling
is suppressed by a factor of $m_b/m_W$ and has no additional
enhancement.  The production of a neutral MSSM Higgs boson in association
with a $\bb$ pair followed by Higgs decay to $b\bar b$ leads to a
distinctive final state with four high-$E_T$ $b$ jets.  These events
can be observed by positively tagging at least three of these
$b$-jets, which dramatically reduces the QCD multijet background.  The
cross section for this process is proportional to $\tan^2\beta$, and
is thus greatly enhanced at large $\tan\beta$.  The studies presented
in this Workshop show that an interesting region of the MSSM parameter
space at high $\tan\beta$ is accessible in Run~2.  In particular, some
limits already emerge with 2~fb$^{-1}$ of data in the region
of high $\tan\beta$ and low $\mha$.  The region of sensitivity grows
to slightly lower values of $\tan\beta$ and larger values of $\mha$ as
the luminosity is increased further.  However, one finds that
there are large supersymmetric and QCD corrections that must be taken
into account, which will require detailed theoretical analysis in the
coming years.  Nevertheless, the enhanced $b\bar b\phi$ production
process increases the overall sensitivity of the Tevatron MSSM Higgs
search, and provides some complementary coverage in the
$\mha$---$\tan\beta$ plane with respect to the associated vector
boson--Higgs boson production discussed above.

Finally, if the charged Higgs boson is light enough so that the decay
$t\to H^+b$ is allowed, then the Tevatron Higgs boson search at Run~2 
can discover the charged Higgs boson if $\tan\beta$ is sufficiently
larger than 1 (or smaller than 1, although the latter is disfavored by
theoretical considerations).  Again, it is possible to see a signal at
Run~2 at large values of $\tan\beta$ and small values of $\mha$ (the
latter is required in order that $\mhpm<m_t-m_b$).  With additional
luminosity, the region of sensitivity in $\tan\beta$ also grows,
although the ultimate region of MSSM parameter space
at $\tan\beta$ accessible by the charged Higgs search is not as great
as the corresponding region accessible by the search for enhanced
$b\bar b\phi$ production.

\vspace{0.2in}
{\bf Conclusions} \\

The search for the Higgs boson and the dynamics responsible for
electroweak symmetry breaking is the central goal of high
energy physics today.  The Tevatron experiments, if given sufficient
data, are poised to make major advances in meeting this goal.  A
great deal of effort remains in order to 
raise the performance of the accelerator to the level 
demanded by the Higgs search.  The nominal yearly integrated
luminosity for Run~2 is 2~fb$^{-1}$ per year.  However,
10---30~fb$^{-1}$ of data (per experiment) is needed to significantly
improve the Higgs search beyond the current LEP2 limits, with the
higher luminosity crucial for maximizing the coverage both in the
Standard Model and its supersymmetric extension.

Further challenges must be met in bringing the detectors on line and
fully operational, and in developing the techniques and understanding,
particularly in $\bb$ jet-jet mass reconstruction and $b$ jet tagging,
necessary to extract the faint signal of the Higgs boson from the
larger Standard Model background.  In some cases, we were perhaps
optimistic with regard to the expected capabilities of the detector.
However, this Report clearly points to some important goals that the
experimental detectors and analysis methods must achieve if the Higgs
search at the Tevatron is to be successful.  In some cases, the
magnitude of the Standard Model backgrounds are not known at the
required level of accuracy.  Additional theoretical work along with
background studies once higher luminosity data become available will
be crucial for improving the Higgs search strategies and maximizing
the chances for uncovering the Higgs signal.  We believe
that the results obtained in this Report provide a useful attempt to
devise a realistic search strategy for Higgs bosons, 
and provide a benchmark for future improvements.
 
The LHC is expected to begin its physics run in 2006.  The search for
the Higgs boson is one of the primary missions of the ATLAS and CMS
detector collaborations.  With much larger annual luminosities and
energies, they will discover the Higgs boson (in most
theoretical scenarios) if it has not yet been observed.  There is a window of
opportunity for the Tevatron that will be open for the next six to
seven years.  With a little luck and a great deal of determination,
the Higgs boson can be discovered at a sufficiently upgraded Tevatron.
The potential physics payoff is great, and provides a strong motivation to
do the work necessary to meet this challenge in the pre-LHC era.











