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 →$$ b\overline{b} $$ b b ¯ and γ∗→$$ q\overline{q} $$ q q ¯ . We anticipate that our result will be an essential ingredient for the formulation of N3LO subtraction schemes.

In view of the forthcoming High-Luminosity phase of the LHC, next-to-next-to-next-to-leading (N3LO) calculations for the most phenomenologically relevant processes become necessary. In this work, we take the first step towards this goal for H+jet production by computing the one- and two-loop helicity amplitudes for the two contributing processes, H → ggg, $$ H\to q\overline{q}g $$ H → q q ¯ g , in an effective theory with infinite top quark mass, to higher orders in the dimensional regulator. We decompose the amplitude in scalar form factors related to the helicity amplitudes and in a new basis of tensorial structures. The form factors receive contributions from Feynman integrals which were reduced to a novel canonical basis of master integrals. We derive and solve a set of differential equations for these integrals in terms of Multiple Polylogarithms (MPLs) of two variables up to transcendental weight six.

We investigate the quantum chromodynamics (QCD) corrections to hadronic final states in electron-positron collisions at $$ \mathcal{O} $$ O ($$ {\alpha}_s^3 $$ α s 3 ) in the strong coupling constant αs. Namely, we analytically compute the total cross section for this process by separately integrating the tree-level five-parton, the one-loop four-parton, the two-loop three-parton, and the three-loop two-parton matrix elements over the respective phase space. All the contributions to the calculation are treated in a common framework whereby phase space integrals are expressed as physical cuts of the four-loop two-point function. We check the cancellation of infrared poles at all colour levels and we reproduce the known result for the R-ratio at order $$ {\alpha}_s^3 $$ α s 3 .

We investigate the quantum chromodynamics (QCD) corrections to hadronic final states in electron-positron collisions at O(α 3 s ) in the strong coupling constant α s . Namely, we analytically compute the total cross section for this process by separately integrating the tree-level five-parton, the one-loop four-parton, the two-loop three-parton, and the three-loop two-parton matrix elements over the respective phase space. All the contributions to the calculation are treated in a common framework whereby phase space integrals are expressed as physical cuts of the four-loop two-point function. We check the cancellation of infrared poles at all colour levels and we reproduce the known result for the R-ratio at order α 3 s .