A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the iterated singly-unresolved subtraction terms

TL;DR

This paper develops a method to analytically integrate subtraction terms for NNLO QCD jet cross section calculations, facilitating more precise theoretical predictions in particle physics.

Contribution

It introduces a comprehensive integration scheme for unresolved subtraction terms, including explicit computation of basic integrals and their Laurent expansions, advancing NNLO QCD calculations.

Findings

Explicit form of the insertion operator in terms of basic integrals

Laurent expansion coefficients computed via Mellin-Barnes and sector decomposition

Application to electron-positron annihilation into jets

Abstract

We perform the integration of all iterated singly-unresolved subtraction terms, as defined in ref. [1], over the two-particle factorized phase space. We also sum over the unresolved parton flavours. The final result can be written as a convolution (in colour space) of the Born cross section and an insertion operator. We spell out the insertion operator in terms of 24 basic integrals that are defined explicitly. We compute the coefficients of the Laurent-expansion of these integrals in two different ways, with the method of Mellin-Barnes representations and sector decomposition. Finally, we present the Laurent-expansion of the full insertion operator for the specific examples of electron-positron annihilation into two and three jets.