Geometric IR subtraction for real radiation

Abstract

A scheme is proposed for the subtraction of soft and collinear divergences present in massless 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. We propose that this scheme can be promoted to a fully local subtraction method. 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 ${}_pF_q$ hypergeometric - functions. As a proof of principle the poles in the dimensional regulator of the $H\to gggg$ double real emission contribution to the $H\to gg$ decay rate are reproduced.