Compute the two-loop one-real-emission amplitudes at NNLO

Determine the two-loop amplitudes for Higgs boson pair production via gluon fusion with one additional real parton, retaining the full top-quark-mass dependence required for a complete NNLO analysis.

Background

A full NNLO calculation requires both virtual and real-radiation ingredients with finite top-quark-mass dependence. Although one-loop amplitudes with two additional real emissions can be generated using automated tools, the corresponding two-loop amplitudes with one additional real emission remain unavailable.

Obtaining these amplitudes would complete another essential building block for a fully massive NNLO prediction of Higgs boson pair production via gluon fusion.

References

A full NNLO analysis also needs the top quark mass dependence of the real radiation amplitudes. While the one-loop amplitudes with two additional real emissions can be obtained with automated tools, the two-loop amplitudes with one additional real emission are not known yet and constitute another computational challenge.

— Higgs Boson Pair Production via Gluon Fusion: Higher-Order Corrections and Theoretical Uncertainties  (2609.04868 - H et al., 4 Sep 2026) in Section 2, subsection “Towards NNLO with full top quark mass dependence”