Higgs boson production at the LHC: NNLO partonic cross sections through order $ϵ$ and convolutions with splitting functions to N${}^3$LO

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.