| Summary: | Abstract 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 → q q ¯ g $$ H\to q\overline{q}g $$ , 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.
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