Geometric IR subtraction for final state real radiation

A scheme is proposed for the subtraction of soft and collinear divergences present in massless final state real emission phase space integrals. The scheme is based on a local slicing procedure which utilises the soft and collinear factorisation properties of amplitudes to produce universal counter-terms whose analytic integration is relatively simple. As a first application the scheme is applied to establish a general pole formula for final state real radiation at NLO and NNLO in Yang Mills theory for arbitrary multiplicities. All required counter-terms are evaluated to all orders in the dimensional regulator in terms of Gamma - and F-p(q) hypergeometric - functions. As a proof of principle the poles in the dimensional regulator of the H -> gggg double real emission contribution to the H -> gg decay rate are reproduced.