NNLO subtraction for any massless final state: a complete analytic expression

We use the Local Analytic Sector Subtraction scheme to construct a completely analytic set of expressions implementing a fully local infrared subtraction at NNLO for generic coloured massless final states. The cancellation of all explicit infrared poles appearing in the double-virtual contribution, in the real-virtual correction and in the integrated local infrared counterterms is explicitly verified, and all finite contributions arising from integrated local counterterms are analytically evaluated in terms of ordinary polylogarithms up to weight three. The resulting subtraction formula can readily be implemented in any numerical framework containing the relevant matrix elements up to NNLO.

Automated summary

In this study, we have successfully constructed a completely analytic set of expressions using the Local Analytic Sector Subtraction scheme, which implements a fully local infrared subtraction for generic coloured massless final states. We have explicitly verified the cancellation of all explicit infrared poles in the double-virtual contribution, real-virtual correction, and integrated local infrared counterterms. Additionally, we have analytically evaluated all finite contributions from the integrated local counterterms using ordinary polylogarithms up to weight three. The resulting subtraction formula can be readily implemented in any numerical framework containing the relevant matrix elements up to NNLO.