
In the next run of the Tevatron collider, with the new Main Injector
and Antiproton Recycler, the machine will deliver more than an order
of magnitude more instantaneous luminosity, and ultimately more than
two orders of magnitude integrated luminosity to the CDF and D\O\
experiments.  This prospect greatly enhances the discovery potential
for new particles, since more integrated luminosity translates into
more sensitivity at higher masses.  As will be seen below, this is
particularly important for the search for the Higgs boson, since the
discovery reach is limited by statistics.

In Run 1 the Tevatron operated with six proton and six antiproton
bunches, colliding every 3.5 $\mu$sec.  Instantaneous luminosities at
the beginning of each store typically reached
1.6$\times$10$^{31}$/cm$^2$/sec, or about 2~pb$^{-1}$ per week
integrated luminosity delivered to the experiments.  The main
limitations were in the proton and antiproton beam currents, and the
antiproton stacking rate.

In Run 2 the new Main Injector will provide emittance much better
matched with that of the Tevatron, greatly improving the antiproton
transfer efficiency to the Tevatron, and also will give a threefold
increase in the antiproton production rate.  At the end of each
Tevatron store, beams will be decelerated and the antiprotons
extracted into the new Antiproton Recycler, and re-used in the
subsequent store.  This will effectively double the antiproton
stacking rate.

In addition the Tevatron will switch to 36-bunch operations, which
will greatly alleviate the problem of multiple interactions, keeping
it at roughly the same level as in Run 1.  The machine energy will
increase from 1.8 TeV to 2.0 TeV in the center of mass; this typically
increases physics cross sections by about 30-40\%.

The initial goal of Run 2 (called Run 2a) is to deliver $>$2 fb$^{-1}$ by then end of
2002, with instantaneous luminosities of up to
2$\times$10$^{32}$/cm$^2$/sec.  With 36$\times$36 bunches the crossing
time will be 396 nsec; however both CDF and D\O\ have reconfigured
their front-end electronics to accommodate 132-nsec crossing times,
since with subsequent improvements the Tevatron will operate with more
bunches, with this collision crossing time.

Further improvements to the luminosity will require successful
research and development in the areas of improved antiproton
availability and controlling the effect of the beam-beam interaction.
If these lead to luminosities in the range of
5$\times$10$^{32}$/cm$^2$/sec, then in Run 2b the Tevatron could
deliver 15~fb$^{-1}$ by then end of 2007 \cite{holmes}.

This report presents results of feasibility studies for Higgs searches
at the Tevatron during the upcoming data taking.  During Run 1,
initial Higgs searches were made by both CDF \cite{juano,cdfrun1higgs} and
D\O \cite{hobbsfit}.  Figure~\ref{f-cdf-runI} shows the Run 1 Standard
Model Higgs cross section limits from CDF in each final state studied
and also the limit obtained by combining all channels.  In addition to
the Run 1 experimental results, initial Run 2 feasibility studies were
performed in refs.~\cite{tev2k,snowmass96,tev33}.  These studies
considered production of the Standard Model Higgs boson with $M_H <
130$~GeV, and concluded that $25\ \mathrm{fb}^{-1}$ was needed to
discover a 120~GeV Higgs boson at the $5\sigma$ level.  The present study
improves upon the existing work in a number of significant ways. 
In this report, a improved background analysis and a
more realistic detector simulation has been employed.  In addition, 
results from all the leading channels were combined, and new channels
relevant for the search for Higgs bosons of higher mass were
examined.  We first discuss in detail the simulation and analysis methods
used in this report.  We then focus on the search for the Standard Model
Higgs boson in a variety of channels.  Finally, we consider  
new search techniques relevant for 
Higgs bosons that arise in theories beyond the Standard Model. 

\begin{figure}
  \begin{center}
    \parbox{5.0in}{\epsfxsize=\hsize\epsffile[70 130  520 670]{tevatron/cdf-run1-higgs.eps}}
  \end{center}
  \caption[0]{CDF Run 1 95\% CL upper limits on the cross section times branching 
           ratio for production of a Standard Model Higgs boson in association 
           with a $W$ or $Z$, with Higgs decaying to $\bb$ \cite{cdfrun1higgs}.  The four dashed 
           curves show the limits from the individual search channels, and the
           solid curve labeled ``$VH$ combined'' shows the limit from combining
           all four channels.  The expectation from Standard Model Higgs production 
           is shown by the solid curve labeled ``Standard Model.''}
  \label{f-cdf-runI}
\end{figure}

