  We compute next-to-leading order (NLO) QCD corrections to the production of
two massive electroweak bosons in gluon fusion. We consider both the prompt
production process $gg \to VV$ and the production mediated by an exchange of an
s-channel Higgs boson, $gg \to H^* \to V V$. We include final states with both
on- and off-shell vector bosons with leptonic decays. The gluonic production of
vector bosons is a loop-induced process, including both massless and massive
quarks in the loop. For $gg \to ZZ$ production, we obtain the NLO QCD
corrections to the massive loops through an expansion around the heavy top
limit. This approximation is valid below the top production threshold, giving a
broad range of invariant masses between the Higgs production and the top
production thresholds in which our results are valid. We explore the NLO QCD
effects in $gg \to ZZ$ focusing, in particular, on the interference between
prompt and Higgs-mediated processes. We find that the QCD corrections to the
interference are large and similar in size to the corrections to both the
signal and the background processes. At the same time, we observe that
corrections to the interference change rapidly with the four-lepton invariant
mass in the region around the ZZ production threshold. We also study the
interference effects in $gg \to WW$ production where, due to technical
limitations, we only consider contributions of massless loops. We find that the
QCD corrections to the interference in this case are somewhat larger than those
for either the signal or the background.
