  We present results for the production of a pair of on-shell Z bosons via
gluon fusion. This process occurs both through the production and decay of the
Higgs boson, and through continuum production where the Z boson couples to a
loop of massless quarks or to a massive quark. We calculate the interference of
the two processes and its contribution to the cross section up to and including
order O(alpha_s^3). The two-loop contributions to the amplitude are all known
analytically, except for the continuum production through loops of top quarks
of mass m. The latter contribution is important for the invariant mass of the
two Z bosons, (as measured by the mass of their leptonic decay products, m_4l),
in a regime where m_4l > 2m because of the contributions of longitudinal
bosons. We examine all the contributions to the virtual amplitude involving top
quarks, as expansions about the heavy top quark limit. Comparison with the
analytic results, where known, allows us to assess the validity of the heavy
quark expansion, and it extensions. We give results for the NLO corrections to
this interference, including both real and virtual radiation.
