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We compute the helicity amplitudes for the processes $gg\to Zg$ and $gg\toZ\gamma$ to two loops in massless QCD. The perturbative expansion of theseprocesses starts only at the one-loop level, such that our results are acrucial ingredient to the NLO corrections to $Z\gamma$ and $Z+$jet productionthrough gluon fusion.

Two-loop QCD helicity amplitudes for $g\,g \to Z\,g$ and $g\,g \to Z\,\gamma $