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

This talk considers Higgs boson production at hadron colliders via gluon fusion and the computation of higher order terms in the regularization parameter ε. In particular, the next-to-next-to-leading order cross section needs to be 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. A clear account is given on the solution of the occurring convolution integrals involving harmonic polylogarithms and generalized functions.