
We consider the weak gauge boson fusion process, $\qq\to \qq\hsm$,
where the quark and anti-quark both radiate vector bosons which then
annihilate to produce the Higgs boson.  This includes $WW$ and $ZZ$
fusion originating from all allowed combinations of initial quarks
and/or antiquarks.  The two scattered (anti)quarks are observed in the
detector as forward jets, of $E_T\approx 20$ to 80~GeV and provide a
telltale signature for the process. Tagging these forward jets is a
very powerful tool to suppress backgrounds, and has already been shown
to be a highly promising tool for intermediate mass Higgs boson
studies at the LHC~\cite{wbfLHC}.
 
\vspace{0.2in}
{\bf Selection Criteria} \\ \nopagebreak

Here, we concentrate on the dominant decay mode for the Higgs mass
region of interest, $H\to \bb$. The Higgs boson would appear as a
$\bb$ invariant mass peak in 4-jet events in which two of the jets
are identified as $b$ quarks. Let us consider the case of
$m_H=120$~GeV as an example. The signal rate is given by
\begin{equation}
   \sigma(qq\to qqH)\;B(H\to\bb) = 58\;{\rm fb}\;,
\end{equation}
which is reduced to about 40~fb after minimal acceptance cuts of
\begin{eqnarray}
   E_T(b) &>& 20\;{\rm GeV}\;, \qquad |\eta(b)|<2 \;, \\
   E_T(j) &>& 10\;{\rm GeV}\;, \qquad |\eta(j)|<4 \;, \\
   \Delta R_{jj} &=& \sqrt{(\eta_{j_1}-\eta_{j_2})^2+
  (\phi_{j_1}-\phi_{j_2})^2} > 0.7\,,
\end{eqnarray}
where $\eta$ and $\phi$ is the corresponding pseudorapidity and
azimuthal angle. Here the jet separation cut is applied to all four
jets, including the two $b$-quark jets.
 

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

An irreducible background to these signal events arises from real
emission QCD corrections to $\bb$ production. We have calculated
the SM $\bb jj$ cross section with full ${\cal O}(\alpha_s^4)$
matrix elements, i.e. with a tree level parton Monte Carlo program. We
find a cross section of 2.4~nb for this irreducible background within
the minimal cuts given above and for $b$-quark pair invariant masses
above 100~GeV.
 
A significant reduction of the background is possible by exploiting
the characteristic features of the weak boson fusion signal. The two
tagging jets of the signal typically have $E_T(j)>20$~GeV, and they
are widely separated, $\eta_{jj} = | \eta_{j_1}-\eta_{j_2}|>3$, with
the two $b$-quark jets located between these two tagging jets, which
are required to reside in opposite detector hemispheres. In addition
we can increase the transverse momentum requirement for the $b$-quark
jets to 40~GeV without undue loss of signal acceptance. These
additional cuts reduce the $\bb jj$ background to 30~pb for
$m_{bb}>100$~GeV while keeping a signal rate of $\sigma(qq\to
qqH,\;H\to\bb)=9$~fb.
 

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

The Higgs signal would have to be seen as a $\bb$ invariant mass
peak in this high background environment. Even assuming a $\bb$
invariant mass resolution of $\delta m = \pm 10$~GeV, the signal to
background ratio does not exceed 1/1000 within a 20~GeV invariant mass
bin.  Additional distributions exist which differ somewhat between the
Higgs signal and the $\bb jj$ background. However, we have been
unable to find cuts which significantly improve the statistical
significance of the Higgs signal.  The SM Higgs search via weak gauge
boson fusion does not appear promising at the upgraded Tevatron.



