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 $ggto ZZto 4ell$ 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 $qbar{q}to4ell$ 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.
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