I will present a computation of the cross section for Higgs production via gluon fusion that is differential in the Higgs momentum and inclusive with respect to associated QCD radiation.
This calculation is carried out through NNLO in perturbative QCD and includes the O(d-4) pieces which are necessary for UV renormalisation and mass factorisation at N3LO.
First, I will discuss the restriction to observables that only depend on the Higgs kinematics. This choice renders the subtraction of infrared singularities straightforward and makes our strategy well suited to be generalised to higher orders.
I will then show some predictions for differential cross sections for Higgs production in the fiducial volume, which can be directly obtained including the decay of the Higgs on top of the discussed computation.