Next-to-next-to-next-to-leading-order soft-gluon corrections in hard-scattering processes near threshold

I present a unified calculation of soft-gluon corrections to hard-scattering cross sections through next-to-next-to-next-to-leading order (NNNLO). Master formulas are derived, from a threshold resummation formalism, that can be applied to total and differential cross sections for hard-scattering processes in hadron colliders. I also present numerical results for charged Higgs production at the LHC where these corrections are large, and for top quark production at the Tevatron where these corrections greatly reduce the scale dependence of the cross section.

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