Higgs boson gluon-fusion production beyond threshold in N3LO QCD

In this article, we compute the gluon fusion Higgs boson cross-section at (NLO)-L-3 through the second term in the threshold expansion. This calculation constitutes a major milestone towards the full (NLO)-L-3 cross section. Our result has the best formal accuracy in the threshold expansion currently available, and includes contributions from collinear regions besides subleading corrections from soft and hard regions, as well as certain logarithmically enhanced contributions for general kinematics. We use our results to perform a critical appraisal of the validity of the threshold approximation at (NLO)-L-3 in perturbative QCD.