Integration of collinear-type doubly unresolved counterterms in NNLO jet cross sections

TL;DR

This paper develops an integrated approach for collinear-type counterterms in NNLO jet cross sections, enhancing precision in QCD calculations by analytically computing phase space integrals within a subtraction framework.

Contribution

It introduces a novel method to analytically integrate collinear counterterms in NNLO jet cross section calculations, expressed as convolutions involving master integrals and the Born cross section.

Findings

Derived explicit expressions for integrated counterterms

Expressed results as convolutions in colour space

Expanded master integrals in dimensional regularisation

Abstract

In the context of a subtraction method for jet cross sections at NNLO accuracy in the strong coupling, we perform the integration over the two-particle factorised phase space of the collinear-type contributions to the doubly unresolved counterterms. We present the final result as a convolution in colour space of the Born cross section and of an insertion operator, which is written in terms of master integrals that we expand in the dimensional regularisation parameter.