We summarize our recent results on the resummation of hard-scattering coefficient functions and on-shell form factors in massless perturbative QCD. The threshold resummation has been extended to the fourth logarithmic order for deep-inelastic scattering, Drell--Yan lepton pair production and Higgs production via gluon--gluon fusion. The leading six infrared pole terms have been derived to all orders in the strong coupling constant for the photon--quark--quark and the (heavy-top) Higgs--gluon--gluon form factors. These results have many implications, most notably they lead to a new best estimate for the Higgs production cross section at the LHC.

PACS numbers: 12.38.Bx, 12.38.Cy, 13.60.--r, 13.85.--t