  We discuss the resummation of Sudakov effects in a cross section from the
viewpoint of its underlying factorization near the edge of phase space. We
perform the resummation of Sudakov threshold logarithms in Higgs (Standard
Model and Minimal Supersymmetric SM) production at the LHC, using an evolution
equation in the Higgs mass that is derived from this factorization. We extend
the class of universal large terms that is resummed to include additional
universal contributions, which, when included, help to reproduce the exact
result to within a few percent for the full allowed range of Higgs boson masses
in the SM and MSSM. Using the analytic resummed formula as a generating
functional for approximate perturbation theory, we show results for
next-to-next-to-leading order corrections in Higgs production, and find they
are potentially sizable.
