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

TL;DR

This work advances NNLO subtraction for jet processes by computing the integrals of collinear-type doubly unresolved counterterms over the two-particle factorised phase space. The integrated cross sections are expressed as a colour-space convolution of the Born term with an insertion operator I_2^{(0)}, whose structure is organised into flavour-summed, colour-connected contributions and expressed through master integrals expanded in ε. The authors provide detailed analytic and numerical treatments (including sector decomposition) of triple and double collinear as well as soft-collinear counterterms, and connect these results to modified subtraction terms to improve locality and efficiency. Together with a companion paper handling soft-type contributions, this work completes the integration of the unresolved phase-space pieces for the hadronic NNLO subtraction framework and enables precise, fully differential predictions for multi-jet final states at electron-positron colliders and related processes.

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.