Sudakov resummation of multiparton QCD cross sections

We present the general expressions for the resummation, up to next-to-leading logarithmic accuracy, of Sudakov-type logarithms in processes with an arbirtrary number of hard-scattering partons. These results document the formulae used by the authors in several previous phenomenological studies. The resummation formulae presented here, which are valid for phase-space factorizable observables, determine the resummation correction in a process-independent fashion. All process dependence is encoded in the colour and flavour structure of the leading order and virtual one-loop amplitudes, and in Sudakov weights associated to the cross section kinematics. We explicitly illustrate the application to the case of Drell--Yan and prompt-photon production.