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%%JDH\newcommand{\WWstar}    {{\mathrm{W}\mathrm{W}^*}}
%\newcommand{\WpWm}      {{\mathrm{W}^+\mathrm{W}^-}}
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%%JDH\newcommand{\Brbb} {B_{\mathrm{b}\bar{\mathrm{b}}}}
%%JDH\newcommand{\BrWW} {B_{\mathrm{W}\mathrm{W}}}
%%JDH\newcommand{\Brl}  {B_\ell}
\newcommand{\Lumi}  {\cal{L}}
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\vspace{0.2in}
{\bf Merged Analysis} \\ \nopagebreak
\par
As described in the previous section, a final state with two {\em
same-sign} leptons arises in the associated production process
$\ppbar\rightarrow Wh$ with $h$ decaying to $\WpWm$ (we suppress the
stars for clarity of notation).  One of the $W$'s produced in the $h$
decay will have the same sign as the primary $W$ boson, and if these
two $W$'s both decay leptonically, a particularly clean signature
results.  This signature has been

developed in the search for supersymmetric particles at Run~1
in which very low background rates have been achieved.  We have
attempted to exploit this channel in the search for high-mass
Higgs bosons.  
%As before, all results have been obtained
%using the SHW simulation package.
%
%-------------
%
\par
This channel was explored in parallel by two members of the group.
One of these efforts has been published~\cite{htz} and is 
described in the previous section.  Later, the two analyses 
were merged and
better performance obtained.  We describe this ``merged analysis''
briefly in this section.
\pagebreak

\par
The definition of leptons and jets is retained from the analysis
described above.  Leptons are identified in the range $|\eta| < 1.5$
and are accepted if $p_t > 10$~GeV.  They must be separated from
all hadronic jets by $dR > 0.3$, and in addition for muons, the
sum of momenta of charged tracks in a $30^\circ$ cone around the
muon must be less than 60\% of the muon's momentum.
Jets must fall in the range $|\eta| < 3$ and have $\Et > 15$~GeV.
\par
The selection requirements are as follows.  There must be exactly
two identified leptons of the same sign, and their invariant mass
must be at least 2~GeV.  Their isolation, computed as the $\Et$ sum
over towers in a cone around the lepton, must be less than 3.4~GeV.
Back-to-back leptons occur in background processes but rarely in
the signal, so we require an acoplanarity $\Delta\phi < 179^\circ$ and 
and acollinearity $\alpha < 174^\circ$. 
\par
In contrast to the trilepton channel, we want the candidate events
to show significant jet activity, expected from the hadronic decay
of the third (opposite-sign) $W$ boson.
There should be at least two jets but no more than six, and
none of them should pass the b-tagging algorithm (impact-parameter
method).  To avoid $\tau$-jets coming from di-boson backgrounds,
we require that the two highest-$\Et$ jets have at least two
charged tracks.  Keeping in mind the mass of the $\mathrm{W}$,
we require that these two jets have an invariant mass of no more
than 200~GeV.  Finally, as further evidence of high-$p_T$ activity,
we require that the scalar $\Et$ sum over all calorimeter towers
and muon tracks be at least 170~GeV.
\par
The numerical values for the cuts listed above were chosen by
a simple optimization program which varied all cuts simultaneously
to obtain the best value for $S/\sqrt{B}$ assuming in integrated
luminosity of $30~\invfb$.  This optimization procedure showed
that some of the cuts of the two original analyses were no longer
effective, and have been dropped.  The signal was computed for
both $Wh$ and $Zh$ production, and included $W \rightarrow
\tau\nu$ decays.
\par
Estimated backgrounds from Drell-Yan, $\WpWm$ and $ZZ$ production
are negligible.  The $WZ$ background is serious however, and
is estimated to be 0.15~fb.  The $t\bar{t}$ background is significantly
reduced with respect to the previous analysis, but still is important
at 0.024~fb.  Background from a $W$ or $Z$ and jets
is 0.15~fb based on D\O\ data.  Contributions from triple-boson and
$t\bar{t}+V$ production have been estimated and are rather small.  The
total background expecation is 0.48~fb.  
\par
For a SM Higgs of mass
$160~\gev$, for which the cuts above were designed, the accepted
cross section is $0.41$~fb, giving $S/B = 0.84$ (Table~\ref{tab:ssdlmerged}).  
For ${\Lumi} = 30~\invfb$, $12$ signal events would be expected,
corresponding to $S/\sqrt{B} = 3.2$, for one experiment.

%------------------------
\begin{table}
\caption[.]{Accepted cross section and significance for the merged
same-sign dilepton selection.  The effective cross section, 
$\sigma_{\mathrm{eff}}$,
includes the leptonic branching ratio factors for $Wh$ 
and $Zh$ production.
\label{tab:ssdlmerged}}
\begin{center}
\begin{tabular}{c|cccc}
\noalign{\vskip-6pt}
$M_h$ & $\sigma_{\mathrm{eff}}$ (fb) & $\sigma_{\mathrm{acc}}$ (fb) &
  $S/B$ & $S/B$ ($30~\invfb$) \cr
  \tableline
 100 &  5.1 & 0.01 & 0.02 & 0.07 \cr
 110 & 15.8 & 0.04 & 0.08 & 0.32 \cr
 120 & 28   & 0.08 & 0.16 & 0.60 \cr
 130 & 59   & 0.15 & 0.30 & 1.15 \cr
 140 & 77   & 0.29 & 0.60 & 2.3  \cr
 150 & 84   & 0.36 & 0.75 & 2.8  \cr
 160 & 84   & 0.41 & 0.84 & 3.2  \cr
 170 & 69   & 0.38 & 0.77 & 3.0  \cr
 180 & 55   & 0.26 & 0.53 & 2.0  \cr
 190 & 44   & 0.20 & 0.41 & 1.55 \cr
 200 & 35   & 0.16 & 0.33 & 1.24 \cr 
\end{tabular}
\end{center}
\end{table}
%------------------------
