Two-loop QCD corrections to the Higgs plus three-parton amplitudes with top mass correction

We obtain the two-loop QCD corrections to the Higgs plus three-parton amplitudes with dimension-seven operators in Higgs effective field theory. This provides the two-loop S-matrix elements for Higgs plus one-jet production at the LHC with top-mass correction. We apply efficient unitarity plus IBP methods which are described in detail. We also study the color decomposition of the fermion cuts and find a connection between fundamental and adjoint representations which can be used to reduce non-planar to planar unitarity cuts in the Higgs to three-gluon amplitudes. We obtain final results in simple analytic form which exhibits intriguing hidden structures. The principle of maximal transcendentality is found to be satisfied for all results. The lower transcendentality parts also contain universal building blocks and can be written in compact analytic form, suggesting further hidden structures.