Interference Effects in $\mathbf{gg \to H \to Z \gamma}$ Beyond Leading Order

The ATLAS and CMS collaborations at the LHC have recently announced evidence for the rare Higgs boson decay into a $Z$ boson and a photon. We analyze the interference between the process $gg\! \to \! H \! \to \! Z \gamma$ induced by loops of heavy particles, which is by far the dominant contribution to the signal, and the continuum $gg \to Z \gamma$ QCD background process mediated by light quark loops. This interference modifies the event yield, the resonance line-shape and the apparent mass of the Higgs boson. We calculate the radiative corrections to this interference beyond the leading-order approximation in perturbative QCD and find that, while differing numerically from the corresponding effects on the more studied $gg \! \to \! \gamma \gamma$ signal, they are generally rather small. As such, they do not impact significantly the interpretation of the present measurements of the $H \to Z \gamma$ decay mode.