  Using methods from effective field theory, we have recently developed a
novel, systematic framework for the calculation of the cross sections for
electroweak gauge-boson production at small and very small transverse momentum
q_T, in which large logarithms of the scale ratio m_V/q_T are resummed to all
orders. This formalism is applied to the production of Higgs bosons in gluon
fusion at the LHC. The production cross section receives logarithmically
enhanced corrections from two sources: the running of the hard matching
coefficient and the collinear factorization anomaly. The anomaly leads to the
dynamical generation of a non-perturbative scale q_* ~ m_H
e^{-const/\alpha_s(m_H)} ~ 8 GeV, which protects the process from receiving
large long-distance hadronic contributions. We present detailed numerical
predictions for the transverse-momentum spectrum of the Higgs boson, finding
that it is quite insensitive to hadronic effects.
