Higgs boson production at the LHC: NNLO partonic cross sections through order ϵ and convolutions with splitting functions to N3LO

We consider Higgs boson production at hadron colliders in the gluon fusion channel and compute higher order terms in the regularization parameter ϵ. In particular, the next-to-next-to-leading order cross section is evaluated including order ϵ terms. These results are used to compute all convolutions with the splitting functions entering the next-to-next-to-next-to-leading order cross section.