\midheading{$H \to W^+W^-$ production, ($m_t=$~finite), processes 123-127}
These processes represent the production of a Higgs boson that decays to $W^+ W^-$,
with subsequent decay into leptons. For process {\tt 123}, the exact form of the triangle
loop coupling a Higgs boson to two gluons is included, with both top and bottom quarks
circulating in the loop. This is to be contrasted with process {\tt 113} in which only the
top quark contribution is included in the effective coupling approach.

Process {\tt 124} includes only the effect of the interference of the
Higgs and $gg \to W^+W^-$ amplitudes, as described in ref.~\cite{Campbell:2011cu}.
The calculation is available at LO only. LO corresponds to $O(\alpha_s^2)$ in this case.
The calculation of loops containing the third quark generation
includes the effect of the top quark mass (but $m_b=0$), while the first two
generations are considered massless. For numerical stability, a small cut on the
transverse momentum of the $W$ bosons is applied: $p_T(W)>0.05$~GeV for loops
containing massless (first or second generation) quarks, $p_T(W)>2$~GeV for $(t,b)$
loops. This typically removes less than $0.1$\% of the cross section. The
values of these cutoffs can be changed by editing \verb|src/HWW/gg_WW_int.f| and recompiling.

Process {\tt 125} includes all $gg$-initiated diagrams that have a Higgs boson in the $s$-channel,
namely the square of the $s$-channel Higgs boson production and the interference with the diagrams
that do not contain a Higgs boson, (i.e. $gg \to W^+W^- \to \nu_e e^+ e^- \bar{\nu_e}$),
i.e.~$|M_H|^2+2 |M_H^* M_{WW}|$.

The result for the square of the box diagrams alone, i.e. the process
$gg \to W^+W^- \to \nu_e e^+ e^- \bar{\nu_e}$, may be obtained by running process
{\tt nproc=61} with {\tt part=virt} and {\tt ggonly=.true.}

Process {\tt 126} calculates the full result for this process from  $gg$-initiated diagrams.
This includes diagrams that have a Higgs boson in the $s$-channel, the continuum $W^+W^-$
diagrams described above and their interference, i.e.~$|M_{H}+M_{WW}|^2$.

Process {\tt 127} calculates the full result for this process for  $gg$-initiated box
diagrams alone, $gg \to W^+W^-$, i.e.~$|M_{WW}|^2$.
