  In this paper, we compute the soft-virtual corrections to Higgs boson
production in gluon fusion for infinite top quark mass at
next-to-next-to-next-to-leading order in QCD. In addition, we present analogous
soft-virtual terms for both Drell-Yan lepton production in QCD and scalar pair
production in N = 4 super Yang-Mills theory. The result for Drell-Yan lepton
production is derived from the result for Higgs boson production using Casimir
scaling arguments together with well-known results available in the literature.
For scalar pair production in the N = 4 model, we show by explicit calculation
that the result is equal to the part of the Higgs boson soft-virtual term which
is of maximal transcendentality weight.
