  We consider the production of four charged leptons in hadron collisions and
compute the next-to-leading order (NLO) QCD corrections to the loop-induced
gluon fusion contribution by consistently accounting for the Higgs boson
signal, its corresponding background and their interference. The contribution
from heavy-quark loops is exactly included in the calculation except for the
two-loop $gg\to ZZ\to 4\ell$ continuum diagrams, for which the unknown
heavy-quark effects are approximated through a reweighting procedure. Our
calculation is combined with the next-to-next-to-leading order QCD and NLO
electroweak corrections to the $q\bar{q}\to4\ell$ process, including all
partonic channels and consistently accounting for spin correlations and
off-shell effects. The computation is implemented in the MATRIX framework and
allows us to separately study the Higgs boson signal, the background and the
interference contributions, whose knowledge can be used to constrain the Higgs
boson width through off-shell measurements. Our state-of-the-art predictions
for the invariant-mass distribution of the four leptons are in good agreement
with recent ATLAS data.
