Abstract
We present the quantum chromodynamics (QCD) corrections for Higgs boson decays to hadronic final states at next-to-next-to-next-to-leading order (N$^{3}$LO) in the strong coupling constant α$_{s}$. 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 N$^{3}$LO. We study patterns of infrared singularity cancellation within the colour layers of the integrated expressions and we comment on the similarities between H →$$ b\overline{b} $$ and γ$^{∗}$→$$ q\overline{q} $$. We anticipate that our result will be an essential ingredient for the formulation of N$^{3}$LO subtraction schemes.
Chen, Xuan