
The process $gg\to h\to WW^*$ can lead to the purely leptonic channel
in Eq.~(\ref{sigww}), where we identify the final state signal as two
isolated opposite-sign charged leptons and large missing transverse
energy.  Such a signature has been shown to be a sensitive way to
search for the Higgs in the mass range 155-180 GeV/$c^2$ at the LHC \cite{dreiner}.

At the Tevatron the leading SM background processes in this search are
%
\begin{eqnarray}
%\label{wpwm}
p\bar p &\to& W^+W^-\to  \ell \bar \nu \bar \ell \nu,\ \ 
 Z Z(\gamma^*)\to \nu \bar \nu \ell \bar \ell,\ \  
 W Z(\gamma^*)\to \ell \bar \nu \ell \bar \ell,
\nonumber\\
p\bar p &\to& t \bar t\to  \ell \bar \nu \bar \ell \nu b\bar b,
\ \  
p\bar p \to Z(\gamma^*)\to  \tau^+\tau^- \to 
\ell \bar \nu \bar \ell \nu \nu_\tau \bar \nu_\tau .
\label{dy}
\end{eqnarray}
%

\vspace{0.2in}
{\bf Selection Criteria}\\ 

We first impose basic acceptance cuts for the 
leptons \footnote{The cuts for leptons were chosen to reflect
realistic trigger considerations. It is desirable to
extend the acceptance in $\eta_\ell^{}$.}
%
\begin{eqnarray}
\nonumber
&&p^{}_T(e)  > 10\ {\gev},\ \ |\eta^{}_e| < 1.5,\nonumber\\
&&p^{}_T(\mu_1)>10\ {\gev},\ \  p^{}_T(\mu_2)>5\ {\gev},\ \ 
|\eta^{}_\mu| < 1.5,\nonumber \\
&&m(\ell\ell)>10\ {\gev},\ \ \Delta R(\ell j)>0.4,\ \ 
\etmiss > 10\ {\gev},
\label{basic}
\end{eqnarray}
%
where $p^{}_T$ is the transverse momentum and $\eta$ the
pseudo-rapidity.
The cut on the invariant mass $m(\ell\ell)$ is to remove the
photon conversions and leptonic $J/\psi$ and $\Upsilon$ decays.
The isolation cut on $\Delta R(\ell j)$ removes the muon events 
from heavy quark ($c, b$) decays.\footnote{The electron identification
in the SHW simulation imposes strict isolation requirements already.} 

\begin{figure}[t!]
  \begin{center}
    \parbox{3.75in}{\epsfxsize=\hsize\epsffile{highmass/phi_ll.eps}}
  \end{center}
  \caption{Normalized azimuthal angle distributions for the
           signal $gg\to h\to \ww\to\llnn$ with $\mh=170$ GeV
           and backgrounds $WW$, $t \bar t$, $\tau^+\tau^-$, $WZ$ and $ZZ$.}
  \label{phis}
%\end{figure}
\vskip1pc
%\begin{figure}[b!]
  \begin{center}
    \parbox{3.75in}{\epsfxsize=\hsize\epsffile{highmass/theta_ll.eps}}
  \end{center}
  \caption{Normalized distributions 
           for the opening angle in Eq.~(\ref{phi}) for the signal 
           $gg \to h \to \ww \to \llnn$ with $\mh=170$ GeV and backgrounds $WW$, 
           $t \bar t$, $\tau^+\tau^-$, $WZ$ and $ZZ$. }
  \label{thes}
\end{figure}

At this level, the largest background comes from the Drell-Yan
process for $\tau^+\tau^-$ production. However, the charged
leptons in this background are very much back-to-back and this
feature is also true, although to a lesser extent, for other 
background processes as well.
On the other hand, due to the spin correlation of the Higgs boson
decay products, the two charged leptons tend to move in 
parallel~\cite{dreiner}.
We demonstrate this point in Figs.~\ref{phis} and \ref{thes}
where the distributions of the azimuthal angle in the transverse 
plane [$\phi(\ell\ell)$] and the three-dimensional opening-angle 
between the two leptons [$\theta(\ell\ell)$] for the signal 
and backgrounds are shown.\footnote{Since we are mainly interested
in the shapes of the kinematic distributions, we present them
normalized to unity with respect to the total cross section
with appropriate preceding cuts.}
This comparison motivates us to impose the cuts 
%
\begin{equation}
\phi(\ell\ell) < 160^\circ,\ \ 
\theta(\ell\ell) < 160^\circ.
\label{phi}
\end{equation}
%
The $\tau^+\tau^-$ background can be essentially 
eliminated with the help of additional cuts
%
\begin{equation}
p_T^{}(\ell\ell) > 20\ {\gev},\ \ 
\cos\theta_{\ell\ell-\etmiss} < 0.5,\ \ 
M_T^{}(\ell \etmiss) >20\ {\gev},
\label{ptll}
\end{equation}
%
where 
$\theta_{\ell\ell-\etmiss}$ is the relative angle between the lepton 
pair transverse momentum and the missing transverse momentum, 
which is close to 180$^\circ$ for the signal and near 0$^\circ$
for the Drell-Yan $\tau^+\tau^-$ background. The
two-body transverse-mass is defined for each
lepton and the missing energy as 
\begin{equation}
M_T^2(\ell \etmiss)=2 p_T(\ell)\etmiss(1-\cos\theta_{\ell-\etmiss}),
\label{tm}
\end{equation}
%
and the distributions are shown in Fig.~\ref{mtlnu}.
\clearpage

%\begin{figure}[t!]
%  \begin{center}
%    \parbox{3.7in}{\epsfxsize=\hsize\epsffile{highmass/phi_ll.eps}}
%  \end{center}
%  \caption{Normalized azimuthal angle distributions for the
%           signal $gg\to h\to \ww\to\llnn$ with $\mh=170$ GeV
%           and backgrounds $WW$, $t \bar t$, $\tau^+\tau^-$, $WZ$ and $ZZ$.}
%  \label{phis}
%%\end{figure}
%\vskip1pc
%%\begin{figure}[b!]
%  \begin{center}
%    \parbox{3.7in}{\epsfxsize=\hsize\epsffile{highmass/theta_ll.eps}}
%  \end{center}
%  \caption{Normalized distributions 
%           for the opening angle in Eq.~(\ref{phi}) for the signal 
%           $gg \to h \to \ww \to \llnn$ with $\mh=170$ GeV and backgrounds $WW$, 
%           $t \bar t$, $\tau^+\tau^-$, $WZ$ and $ZZ$. }
%  \label{thes}
%\end{figure}

\begin{figure}[t!]
  \begin{center}
    \parbox{3.75in}{\epsfxsize=\hsize\epsffile{highmass/minmtliet.eps}}
  \end{center}
  \caption{Normalized distributions 
           for the two-body transverse-mass defined in Eq.~(\ref{tm}) 
           for the signal $gg \to h \to \ww \to \llnn$ with $\mh=170$ GeV
           and backgrounds $WW$, $t \bar t$, $\tau^+\tau^-$, $WZ$ and $ZZ$. 
           The minimum of $M_T(\ell_1 \etmiss)$ and $M_T(\ell_2 \etmiss)$ is shown.}
  \label{mtlnu}
\end{figure}

We can further purify the signal by removing the high
$m(\ell\ell)$ events from $Z\to \ell\bar \ell$ 
as well as from $t\bar t, W^+W^-$, 
as demonstrated in Fig.~\ref{mlls}. We therefore impose
%
\begin{eqnarray}
\nonumber
m(\ell\ell)&<& 78\ {\gev}\ \ {\rm for}\ e^+e^-,\mu^+\mu^-,\\ 
m(\ell\ell)&<& 110\ {\gev}\ \ {\rm for}\ e\mu.
\label{zout}
\end{eqnarray}
%
As suggested in ref.~\cite{5}, the lepton correlation angle
between the momentum vector of the lepton pair and the momentum of
the higher $p_T$ lepton ($\ell_1$) in the lepton-pair rest frame, 
$\theta^*_{\ell_1}$, also has discriminating power between the
signal and backgrounds. This is shown in Fig.~\ref{thetas}. 
We thus select events with
%
\begin{equation}
-0.3 < \cos\theta^*_{\ell_1} < 0.8.
\label{theta}
\end{equation}
%
A characteristic feature of the top-quark background is the presence
of hard $b$-jets. We thus devise the following jet-veto 
criteria:
\begin{eqnarray}
{\rm veto\ if}\ \ p_T^{j_1}>95\ {\gev},\ \  |\eta^{}_j| < 3,\nonumber\\ 
{\rm veto\ if}\ \ p_T^{j_2}>50\ {\gev},\ \  |\eta^{}_j| < 3,\nonumber\\ 
{\rm veto\ if}\ \ p_T^{j_3}>15\ {\gev},\ \  |\eta^{}_j| < 3.
\label{jetveto}
\end{eqnarray}

Furthermore, if either of the two hard jets ($j_1,j_2$) is identified
as a $b$ quark, the event will be also vetoed. The $b$-tagging 
efficiency is taken from SHW.

The results up to this stage are summarized in Table~\ref{tabI} for thqqqe signal
$\mh=140$--190~GeV as well as the SM backgrounds.  The acceptance cuts discussed
above are fairly efficient, approximately 35\% of the signal is retained while
backgrounds are substantially suppressed. We see that the dominant background
comes from the electroweak $WW$ production, about a factor of 30 higher than
the signal rate. The sub-leading backgrounds $t\bar t$ and $W$+fake (the
background where a jet mimics an electron with a probability of $P(j\to
e)=10^{-4}$~\cite{fake}) are also bigger than the signal.  We note that
although the $b$-jet veto is effective against the $t\bar t$ background, the
final results are not affected if the veto efficiency is significantly worse.

\begin{figure}[t!]
  \begin{center}
    \parbox{3.75in}{\epsfxsize=\hsize\epsffile{highmass/mll_like.eps}}
  \end{center}
  \caption{Normalized like-flavor lepton-pair invariant mass distributions 
           for the signal $gg \to h \to \ww \to \llnn$ with $\mh=170$ GeV
           and backgrounds $WW$, $t \bar t$, $\tau^+\tau^-$, $WZ$ and $ZZ$.}
  \label{mlls}
%\end{figure}
\vskip1pc
%\begin{figure}[b!]
  \begin{center}
    \parbox{3.75in}{\epsfxsize=\hsize\epsffile{highmass/helang1.eps}}
  \end{center}
  \caption{Normalized angular distributions for the correlation angle 
           defined above Eq.~(\ref{theta}) for the signal 
           $gg \to h \to \ww \to \llnn$ with $\mh=170$ GeV and backgrounds $WW$, 
           $t \bar t$, $\tau^+\tau^-$, $WZ$ and $ZZ$.}
  \label{thetas}
\end{figure}
\clearpage

\begin{table}[h!]
\caption[]{$h\rightarrow \ww \rightarrow \llnn$ signal cross section
(in fb) for $\mh=140-$190 GeV and various SM backgrounds after 
the kinematic cuts of Eqs.~(\ref{basic})$-$(\ref{jetveto}). 
The signal efficiencies are also shown (in percentage). 
$W+$fake refers to the background where a jet mimics
an electron with a probability of $P(j\to e)=10^{-4}$.
The backgrounds are independent of $\mh$.
}
\label{tabI}
\begin{tabular}{|l|c|c|c|c|c|c|}%\hline
\noalign{\vskip-6pt}
 $\mh$ [GeV] & 140 & 150 & 160 & 170 & 180   & 190\\  \tableline
 signal [fb] & 3.9 & 4.4 & 5.2 & 4.8 & 3.6   & 2.5\\  %\hline
 efficiency. [\%] & 35  & 34  & 38  & 39  & 36    & 37\\   \hline \hline
{}&$WW$ & $t\bar t$ & $\tau^+\tau^-$& $WZ$ & $ZZ$ & $W+$fake\\ 
\hline
backgrounds [fb]& 130 & 13  & 0   & 4.4 & 2.4   & 18 \\ 
\end{tabular}
%\vspace{0.2in}
%\caption[]{$h\rightarrow \ww \rightarrow \llnn$ signal cross section
%(in fb) for $\mh=140-$190 GeV and various SM backgrounds after 
%the kinematic cuts of Eqs.~(\ref{basic})$-$(\ref{jetveto}). 
%The signal efficiencies are also shown (in percentage). 
%$W+$fake refers to the background where a jet mimics
%an electron with a probability of $P(j\to e)=10^{-4}$.
%The backgrounds are independent of $\mh$.
%}
%\label{tabI}
\end{table}

\vspace{0.2in}
{\bf Further Selection: Likelihood Analysis}\\ 

One can improve the signal observability by
constructing a likelihood based on some characteristic
kinematic variables. We choose the variables as
%
\begin{itemize}
\item[1.] $\cos\theta_{\ell\ell}$, the polar angle with respect 
to the beam axis of the dilepton~\cite{dreiner};
\item[2.] $\phi(\ell\ell)$ as in Eq.~(\ref{phi});
\item[3.] $\theta(\ell\ell)$ as in Eq.~(\ref{phi});
\item[4.] $\cos\theta_{\ell\ell-\etmiss}$ as in Eq.~(\ref{ptll});
\item[5.] $p_T^{j1}$ as in Eq.~(\ref{jetveto});
\item[6.] $p_T^{j2}$ as in Eq.~(\ref{jetveto}).
\end{itemize}
%
We wish to evaluate the likelihood for a candidate event
to be consistent with one of five event classes: a Higgs
boson signal ($140 < \mh <$ 190 GeV), 
$WW$, $t\bar t$, $WZ$ or $ZZ$. For a single variable $x_i$, 
the probability for an event to belong to class $j$ is given by
%
\begin{equation}
P^j_i(x_i) = \frac{f^j_i(x_i)}{\Sigma_{k=1}^5\ f^k_i(x_i)},
\end{equation}
%
where $f_i^j$ denotes the probability density for 
class $j$ and variable $i$. 
The likelihood of an event to belong
to class $j$ is given by the normalized products of the individual
$P^j_i(x_i)$ for the $n=6$ kinematic variables:
%
\begin{equation}
{\cal L}^j = \frac{ \Pi_{i=1}^n\  P^j_i(x_i)}
{\Sigma_{k=1}^5\ \Pi_{i=1}^n\  P^k_i(x_i)},
\label{like}
\end{equation}
%
The value of ${\cal L}^j$ for a Higgs boson signal hypothesis 
($j=1$) is shown in Fig.~\ref{likeli} 
where it can be seen that a substantial fraction
of the $t\bar t$ and $WW$ background can be removed for a modest loss
of efficiency. The $WZ$ and $ZZ$ backgrounds
have similar distributions to the
$WW$ and have been omitted for clarity. 
We thus impose the requirement
%
\begin{equation}
{\cal L}^{j=1} > 0.10.
\label{likec}
\end{equation}
%
The improved results are summarized in Table~\ref{tabII}.

%
\begin{table}[t!]
\caption[]{$h\rightarrow \ww \rightarrow \llnn$ signal cross section
(in fb) for $\mh=140-$190 GeV and various SM backgrounds after the kinematic 
cuts of Eqs.~(\ref{basic})$-$(\ref{jetveto}) and the likelihood cut
Eq.~(\ref{likec}). $W+$fake refers to the background where a jet mimics
an electron with a probability of $P(j\to e)=10^{-4}$.
The backgrounds are independent of $\mh$.
}
\label{tabII}
\begin{tabular}{|l|c|c|c|c|c|c|}%\hline
\noalign{\vskip-6pt} 
$\mh$ [GeV] & 140 & 150 & 160 & 170 & 180   & 190\\  \tableline
 signal [fb] & 3.1 & 3.6 & 4.5 & 4.1 & 2.9   & 2.0\\  \hline
\hline
{}&$WW$ & $t\bar t$ & $\tau^+\tau^-$& $WZ$ & $ZZ$ & $W+$fake\\ 
\hline
backgrounds [fb]& 83 & 4.5  & 0   & 3.1 & 1.8   & 13 \\ [2pt] 
\end{tabular}
%\vspace{0.2in}
%\caption[]{$h\rightarrow \ww \rightarrow \llnn$ signal cross section
%(in fb) for $\mh=140-$190 GeV and various SM backgrounds after the kinematic 
%cuts of Eqs.~(\ref{basic})$-$(\ref{jetveto}) and the likelihood cut
%Eq.~(\ref{likec}). $W+$fake refers to the background where a jet mimics
%an electron with a probability of $P(j\to e)=10^{-4}$.
%The backgrounds are independent of $\mh$.
%}
%\label{tabII}
\vspace{1pc}
\end{table}
%

\begin{figure}[h!]
  \begin{center}
    \parbox{3.5in}{\epsfxsize=\hsize\epsffile{highmass/lhoods.eps}}
  \end{center}
  \caption{Distributions for the likelihood variable
           defined in Eq.~(\ref{like}) for the signal $\mh=170$ GeV
           and the leading SM backgrounds $WW$ and $t\bar t$.}
  \label{likeli}
\end{figure}



In identifying the signal events, it is crucial to
reconstruct the mass peak of $\mh$. Unfortunately,
the $\ww$ mass from the $h$ decay cannot be accurately 
reconstructed due to the two undetectable neutrinos. 
However, both the transverse mass $M_T$ and the 
cluster transverse mass $M_C$ \cite{bho}, defined as
%
\begin{eqnarray}
M_T &=& 2\sqrt{ p^2_T(\ell\ell)+m^2(\ell\ell)},\label{mt} \\ 
M_C &=&  \sqrt{ p^2_T(\ell\ell)+m^2(\ell\ell)}\ + \etmiss,
\label{mc}
\end{eqnarray}
%
yield a broad peak near $\mh$ and have a long tail below.
The cluster transverse mass $M_C$ has a Jacobian structure
with a well defined edge at $m_h$.
We show the nature of these two variables for the signal
with $\mh=170$ GeV and the leading $WW$ background
in Fig.~\ref{masses}(a) for $M_T$ and (b) for $M_C$ after application
of the likelihood cut.
For a given $m_h$ to be studied, one can perform additional cut optimization.
In Table~\ref{tabcut}, we list $m_h$-dependent criteria for
the signal region defined as
%
\begin{equation}
\mh - 60 < M_C < \mh + 5\ \gev.
\end{equation}
%

%
\begin{table}
\caption[]{Summary of the optimized cuts additional to those
in Eqs.~(\ref{basic})$-$(\ref{jetveto}) for various Higgs boson mass.
}
\label{tabcut}
\begin{tabular}{|l|c|c|c|c|c|c|}%\hline
\noalign{\vskip-6pt}
 $\mh$ [GeV] & 140 & 150 & 160 & 170 & 180   & 190\\  \tableline
 $\cos\theta^*_{\ell_1}$ & - & $<$0.6 & 0.35 & 0.35 & 0.55   & 0.75\\ %\hline
 $\etmiss$ & $>$25 & 25 & 30 & 35 & 40 & 40\\  %\hline
min[$M_T^{}(\ell_1 \etmiss),M_T^{}(\ell_2 \etmiss)$]  
& $>$40 & 40 & 75 & 80 & 85   & 75\\  %\hline
$M_T^{}(\ell_1 \etmiss)$ & $>$60 & 60 & - & - & - & -\\  %\hline
$m(\ell\ell)$ & $<$65 & 65 & 65 & 75 & 85 & -\\  %\hline
$p_T^{}(\ell\ell)$ & $>$40 & 50 & 65 & 70 & 70 & 70\\  %\hline
$\theta(\ell\ell)$ & $<$100 & 100 & 70 & 70 & 90  & 90\\ %5\hline
$M_T^{}$ & - & $>$110 & 120 & 130 & 140 & 140\\
\end{tabular}
%\vspace{0.2in}
%\caption[]{Summary of the optimized cuts additional to those
%in Eqs.~(\ref{basic})$-$(\ref{jetveto}) for various Higgs boson mass.
%}
%\label{tabcut}
\end{table}

We illustrate the effect of the optimized cuts of Table~\ref{tabcut}
in Fig.~\ref{bacuts}, where the cluster transverse mass distribution
for a $\mh=170$ GeV signal and
the summed backgrounds, normalized to 30 $\fbi$, are shown 
before (a) and after the final cuts (b). A clear excess
of events from the Higgs signal can be seen in
Fig.~\ref{bacuts}(b). 
It is important to note that before application of the
final cuts, the dominant backgrounds are $WW$ and the $W$+fake
with other sources accounting for less than 10\% 
of the total. Moreover, for 30 $\fbi$ integrated luminosity, 
the statistical error in the background is less than 2\% 
before application of the final cuts. 
We therefore argue that one should be able 
to normalize the SM background curve ($WW$) with sufficient
precision to unambiguously identify a significant excess 
attributable to Higgs boson signal. It should also be noted that by
selectively loosening the final cuts, it is possible 
to maintain the same $S/\sqrt{B}$ while increasing the accepted 
background by up to factor of 5, and the accepted signal
by a factor of 2.5. This can provide a powerful cross-check
of the predicted background $M_C$ shape and can be used
to demonstrate the stability of any observed excess.

\begin{figure}
  \begin{center}
    \parbox{6.0in}{\epsfxsize=\hsize\epsffile[0 260 530 530]{highmass/mt_mc.eps}}
  \end{center}
\caption{Normalized mass distributions for the signal 
         $gg \to h \to \ww \to \llnn$ with $\mh=170$ GeV (histogram)
         and the leading $WW$ background (shaded) for (a) the transverse mass
         defined in Eq.~(\ref{mt}), and (b) the cluster transverse mass defined in 
         Eq.~(\ref{mc}).}
  \label{masses}
\end{figure}


Our final results for the channel $h\to \ww\to \ell \bar \nu \bar \ell \nu$ are
summarized in Table~\ref{lnln}. We have included the contributions to $h\to
\ww$ from the signal channels in Eqs.~(\ref{whzh}) and (\ref{wwzz}).  Although
they are small to begin with, they actually increase the accepted signal cross
section by 12--18\%.  We have also included the contribution from $W \to \tau
\nu \to \ell\nu_\ell \nu$.\footnote{From consideration of the
$W$+$(j\rightarrow e)$ background, it should be clear that improving the
sensitivity by incorporating hadronic tau decays will be a difficult task.}  It
can be seen that one may achieve a $S/B$ of at least 6\% for 140 GeV$<\mh< 190$
GeV and reach 45\% for $\mh=170$ GeV. The statistical significance, $S/\sqrt
B$, for 30 fb$^{-1}$ integrated luminosity, is 3$\sigma$ or better for $150<
\mh < 180$ GeV.  


\begin{figure}
  \begin{center}
    \parbox{6.0in}{\epsfxsize=\hsize\epsffile[0 260 530 530]{highmass/m170_paper.eps}}
  \end{center}
  \caption{Cluster transverse mass distributions for
           the leading $WW$ background (shaded) and the background
           plus the signal $gg \to h \to \ww \to \llnn$ with $\mh=170$ GeV
           (histogram) (a) before the optimized
           cuts in Table~\ref{tabcut} and (b) after the cuts. The
           vertical axis gives the number of events per 5 GeV bin
           for 30 $\fbi$.}
  \label{bacuts}
\end{figure}


\begin{table}[h!]
\caption[]{Summary table for $h\rightarrow \ww \rightarrow \llnn$ signal 
for $\mh=140-$190 GeV and various SM backgrounds after the kinematic 
cuts of Eqs.~(\ref{basic})$-$(\ref{jetveto}) and the likelihood cut
Eq.~(\ref{likec}). The entry ``fake $j\to e$'' refers to the background where a jet mimics
an electron with a probability of $P(j\to e)=10^{-4}$.
The backgrounds are independent of $\mh$.
}
\label{lnln}
\begin{tabular}{|l|c|c|c|c|c|c|}%\hline
 $\mh$ [GeV] & 140 & 150 & 160 & 170 & 180   & 190\\  \tableline
 $gg\to h$ [fb] & 2.2 & 2.4 & 1.3 & 0.93 & 0.85 & 0.73\\ 
 associated $VH$ [fb] & 0.26 & 0.31 & 0.13 & 0.09 & 0.06   & 0.06\\ 
 $VV$ fusion [fb] & 0.12 & 0.12 & 0.09 & 0.06 & 0.05 & 0.05\\ 
 signal sum [fb] & 2.6 & 2.8 & 1.5 & 1.1 & 0.96 & 0.83\\ 
\hline
SM backgrounds [fb]& 39 & 27  & 4.1 & 2.3 & 3.8 & 7.0 \\ 
fake $j\to e$ [fb]& 5.1 & 3.4  & 0.34 & 0.15 & 0.08 & 0.45 \\ 
backgrounds sum [fb]& 44 & 30  & 4.4 & 2.4 & 3.8 & 7.5 \\ \hline
$S/B$ & 0.058 & 0.094  & 0.34 & 0.45 & 0.25 & 0.11 \\ \hline
$S/\sqrt B$ for 30 fb$^{-1}$ & 2.1 & 2.8  & 3.9 & 3.8 & 2.7 & 1.7 \\ 
\end{tabular}
%\vspace{0.2in}
%\caption[]{Summary table for $h\rightarrow \ww \rightarrow \llnn$ signal 
%for $\mh=140-$190 GeV and various SM backgrounds after the kinematic 
%cuts of Eqs.~(\ref{basic})$-$(\ref{jetveto}) and the likelihood cut
%Eq.~(\ref{likec}). The entry ``fake $j\to e$'' refers to the background where a jet mimics
%an electron with a probability of $P(j\to e)=10^{-4}$.
%The backgrounds are independent of $\mh$.
%}
%\label{lnln}
\end{table}


\break
In Fig.~\ref{intL}(a), we present the integrated luminosities
needed to reach a 3$\sigma$ significance and 95\% CL exclusion computed
assuming Poisson probabilities as a function of $\mh$.

To assess the effect of inherent systematic uncertainties, we
re-evaluate the corresponding curves in Fig.~\ref{intL}(b) assuming a
10\% systematic error for the signal and SM backgrounds.\footnote{For
the purposes of computing the effects of systematic errors on the
sensitivity to a Higgs signal, we have scaled the expected background
upward by a given percentage and the expected signal downward by the
same percentage simultaneously.}  The results are somewhat degraded,
but they are still encouraging.


%
\begin{figure}[h!]
  \begin{center}
    \parbox{6.0in}{\epsfxsize=\hsize\epsffile[0 260 530 530]{highmass/contour_gg_paper.eps}}
  \end{center}
  \caption{The integrated luminosity per experiment required to reach $3\sigma$
           statistical significance and 95\%
           exclusion versus $m_h$ in the $h\to \ww \to \ell\bar \nu
           \bar \ell \nu$ channel for (a) statistical effects only; (b) 10\%
           systematic error for the signal and SM backgrounds included. 
           The contribution from $W\to \tau \to \ell$ decays, associated 
           production and gauge boson fusion have also been included.}
  \label{intL}
\end{figure}
