Geometric IR subtraction for real radiation

TL;DR

This paper introduces a local subtraction scheme for soft and collinear divergences in real radiation integrals, enabling universal counter-term calculation and application to higher-order QCD corrections.

Contribution

It proposes a novel local subtraction method based on a slicing procedure, applicable to NLO and NNLO calculations in Yang Mills theory with all counter-terms analytically evaluated.

Findings

Derived a general pole formula for real radiation at NLO and NNLO.

Successfully reproduced poles in the Higgs decay to four gluons.

Evaluated counter-terms using hypergeometric functions.

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.