Two-loop amplitudes in massless QCD for diphoton-plus-jet production via gluon fusion at hadron colliders

The ability to calculate analytic full-colour two-to-three two-loop helicity amplitudes in massless QCD has been a recent triumph of the field, driving phenomenology towards one percent precision. In this contribution, we focus on the virtual correction of diphoton-plus-jet production via gluon fusion, $gg\to g\gamma \gamma$. We outline state-of-the-art strategies to optimise the reconstruction over finite fields of the rational coefficients of the amplitude. We also present an updated performance analysis of our publicly-available C++ implementation of the amplitude, demonstrating its typical speed and stability, and study its stability in infrared regions of phase space. These results are relevant for improving predictions in Higgs physics at hadron colliders.