Factorisation and Local Subtraction of Infrared Divergences for QCD Processes

We review a recently proposed subtraction procedure at next-to- and next-to-next-to-leading order in quantum chromodynamics (QCD), based on the introduction of a set of minimal, local and analytically integrable counterterms. We also provide an operator definition for the counterterms by investigating the factorisation properties of a generic massless virtual amplitude. Our local, analytic scheme is designed for massless final state radiation only, but its main features are extensible to initial state radiation.