Two-loop QCD helicity amplitudes for gg → Z g and gg →Zγ

We compute the helicity amplitudes for the processes gg → Zg and gg → Zγ to two loops in massless QCD. The perturbative expansion of these processes starts only at the one-loop level, such that our results are a crucial ingredient to the NLO corrections to Zγ and Z+jet production through gluon fusion.