
This section describes a neural network analysis applied to the
$ZH\rightarrow\nu\bar{\nu}\bb$ final state.  The technique is
identical to that for the neural network analysis for the
$WH\rightarrow\ell\nu\bb$ section.

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

The $ZH$ events were generated using PYTHIA for Higgs masses of 90, 100, 110,
120 and 130 GeV/c$^2$.  The principal backgrounds to $ZH$ production are $ZZ$,
$Zb\bar{b}$, single top and $t\bar{t}$. The $Zb\bar{b}$ background sample was
generated using CompHEP, with fragmentation done using PYTHIA, while all other
samples were generated using PYTHIA.  We used SHW to simulate the detector
response and, as in the $WH$ study, we assumed that two jets are $b$-tagged.
The cross sections for signal and background are shown in Table~\ref{table6}.
As in the other two analyses, no $\bb$ dijet background is considered.

\begin{table}[h!]
\caption{$ZH\rightarrow \nu\bar{\nu}\bb$ channel, neural network selection. Accepted
         cross section times branching ratio for signal and background processes.}
\label{table6}
\begin{center}
\begin{tabular}{lr}
$M_H$ (GeV/c$^2$) & $\sigma\times BR(\mbox{pb})$ \\ \tableline
90                      &  0.041\\
100                     &  0.030\\
110                     &  0.022\\
120                     &  0.016\\
130                     &  0.013\\ \tableline
Backgrounds             &                   \\
$Zb\bar{b}$             & 0.700\\
$tbq$                             & 0.800\\ \tableline
                                  & $\sigma$ (pb) \\ 
$ZZ$                              & 1.235\\ 
$tb$                              & 1.000 \\
$t\bar{t}$              & 7.500\\ 
\end{tabular}
%\caption{$ZH\rightarrow \nu\bar{\nu}\bb$ channel, neural network selection. Accepted
%         cross section times branching ratio for signal and background processes.}
%\label{table6}
\end{center}
\end{table}

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

We applied the following requirements to produce a base sample to which the
neural network was then applied:
\begin{itemize}
\item
the missing transverse momentum
$\met > 20$ ~GeV 
\item
two or more jets in the event 
with $E_T^{jet} > 10$~GeV and $|{\eta}_{jet}| < 2$
\end{itemize}
In order to reduce the dominant $Wb\bar{b}$ background, we  assumed
that the two jets will be  $b$-tagged.

A network was trained for each Higgs mass
and for each of the backgrounds with the following variables
\begin{itemize}
\item
$E_T$ of the $b$-tagged jets
\item
$M_{b\bar{b}}$ -- invariant mass of the $b$-tagged jets
\item
$H_T$ -- sum of jet transverse energies
\item
$\met$
\item
$S$ -- sphericity
\item
Centrality ($\sum{E_T(jets)}/\sum{E(jets)}$)
\item
$\frac{\met}{\sqrt{E^{b1}_t}}$
\item
Minimum $\Delta\phi$(jet,$\met$)
\end{itemize}

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

Figure~\ref{fig:zhnn-net} shows the network output distributions $Z
\rightarrow \nu\bar{\nu}$, respectively.  From these figures it is
clear that discriminating between $ZH$ and its principal backgrounds
is much more difficult than for $WH$ and that further study is needed
to identify better variables. Nonetheless, the $ZH$ channel
contributes usefully to the final result.  The results for the
$ZH\rightarrow \nu\bar{\nu}\bb$ channel are in Table~\ref{table7}.

\begin{table}[h!]
\caption{$ZH$, $Z\to\nn$ channel, neural network selection.
         Expected number of $\met\bb$ signal and background
         events in 1 fb$^{-1}$ of data (per experiment) for various
         Higgs masses, assuming 10\% $\bb$ mass resolution.}
\label{table7}
\begin{center}
\begin{tabular}{lrrrrr} 
$M_H$ (GeV/c$^2$) &        90 &    100 &   110 &   120 &   130\\ \tableline
number of events &&&&& \\
$ZH$           &  6.66 &    4.37 &   3.53 &   2.76 &   2.16 \\ 
$WH$           &  5.59 &    3.75 &   2.79 &   1.98 &   1.70 \\ \tableline
signal         & 12.25 &    8.12 &   6.32 &   4.74 &   3.86 \\ \tableline 
$Zb\bar{b}$    &  8.12 &    4.97 &   4.83 &   3.85 &   3.92 \\
$Wbb$          & 21.70 &   13.12 &  10.68 &   8.22 &   7.53 \\    
$ZZ$           & 11.24 &    6.14 &   2.59 &   1.05 &   0.59 \\
$WZ$           &  7.95 &    4.49 &   1.99 &   0.90 &   0.54 \\
$tqb$          &  0.63 &    0.27 &   0.37 &   0.24 &   0.29 \\
$tb$           &  6.83 &    2.99 &   4.27 &   5.12 &   6.40 \\ 
$t\bar{t}$     &  5.10 &    2.70 &   3.00 &   3.00 &   4.35 \\ \tableline
background$^a$ & 61.57 &   34.80 &  27.73 &  22.38 &  23.62 \\ %\hline
% $S/B$        &  0.20 &    0.23 &   0.23 &   0.21 &   0.16 \\
% $S/\sqrt{B}$ &  1.56 &    1.38 &   1.20 &   1.00 &   0.79 \\
\end{tabular}
$^a$This does not include generic $\bb$ dijet production
processes, which must be estimated from data; see text.\\ 
%\vspace{0.2in}
%\caption{$ZH$, $Z\to\nn$ channel, neural network selection.
%         Expected number of $\met\bb$ signal and background
%         events in 1 fb$^{-1}$ of data (per experiment) for various
%         Higgs masses, assuming 10\% $\bb$ mass resolution.}
%\label{table7}
\end{center}
\vspace{2pc}
\end{table}

%12
\begin{figure}
\begin{center}
\centerline{\epsfsize=0.9\hsize\epsfbox{zhvv/net_plots_zhnn.eps} }
\caption{$ZH\rightarrow \nn\bb$ channel, neural network analysis.
Distributions of neural network outputs for
networks trained using signal (heavy shading) vs. 
the backgrounds $ZZ$, $Zb\bar{b}$, $t\bar{t}$, and single top.}
\end{center}
\label{fig:zhnn-net}
\end{figure}
