  We consider the one-loop effective vertex for the interaction of a gluon with
a Reggeized gluon and a Higgs boson in the infinite-top-mass limit, which is
described by a dimension-5 non-renormalizable operator. This vertex enters the
calculation of differential cross sections for the forward inclusive production
of a Higgs boson in high-energy proton-proton collisions, possibly in
association with a backward jet or identified hadron, in a framework where
next-to-leading logarithms of the energy are resummed to all orders. The
effective vertex is extracted from the high-energy behavior of two-to-two
amplitudes for the Higgs production in parton-parton collisions and relies on
the validity of the Regge form for these amplitudes. We find that the usual
eikonal approximation (Gribov prescription) for the Regge limit and the known
region-expansion technique in this limit lead to an incomplete result for the
amplitude. The discrepancy is traced back to the non-renormalizable nature of
the involved operator. However, the Regge limit of the exact QCD amplitude
agrees with the Regge-pole exchange form at one loop, nontrivially supporting
the Reggeization hypothesis.
