The parton-level structure of Higgs decays to hadrons at N3LO

We present the quantum chromodynamics (QCD) corrections for Higgs boson decays to hadronic final states at next-to-next-to-next-to-leading order (N3LO) in the strong coupling constant αs. In particular, we consider the Higgs boson decay to massless bottom quarks and the Higgs boson decay to a pair of gluons in the limit of a heavy top quark. The tree-level five-parton, the one-loop four-parton, the two-loop three-parton, and the three-loop two-parton matrix elements are integrated separately over the inclusive phase space and classified by partons appearing in the final state and by colour structure. As a check, we reproduce known results for the inclusive hadronic decay rates at N3LO. We study patterns of infrared singularity cancellation within the colour layers of the integrated expressions and we comment on the similarities between H → bb¯ and γ ∗ → qq¯ . We anticipate that our result will be an essential ingredient for the formulation of N3LO subtraction schemes.