We present a calculation of the helicity amplitudes for the process gg → γγ in three-loop massless QCD. We employ a recently proposed method to calculate scattering amplitudes in the ’t Hooft-Veltman scheme that reduces the amount of spurious non-physical information needed at intermediate stages of the computation. Our analytic results for the three-loop helicity amplitudes are remarkably compact, and can be efficiently evaluated numerically. This calculation provides the last missing building block for the computation of NNLO QCD corrections to diphoton production in gluon fusion.

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We present recent advancements in the computation of three-loop four-particle helicity amplitudes in full-color massless QCD. In this contribution, we focus on the → process. We show how to obtain compact analytic formulae for the three-loop scattering amplitude. Our results can be expressed in terms of harmonic polylogarithms, which allows for an efficient numerical evaluation. The results presented here can be used for improving theoretical predictions relevant for Higgs physics at hadron colliders.

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