Infrared Structure at NNLO Using Antenna Subtraction

TL;DR

This paper develops a systematic framework for handling infrared divergences in NNLO calculations of hadron collisions using antenna subtraction, with explicit derivations and applications to gluon jet production.

Contribution

It introduces a general form of subtraction terms at NNLO, relating virtual contributions to integrated dipoles and Catani's IR operators, and applies these methods to gluon jet production.

Findings

Explicit NNLO subtraction terms for gluon jet production

Demonstration of antenna subtraction effectiveness at NNLO

Connection of integrated dipoles to Catani's IR operators

Abstract

We consider the infrared structure of hadron-hadron collisions at next-to-next-to leading order using the antenna subtraction method. The general form of the subtraction terms is presented for double real, real-virtual and double virtual contributions. At NLO and NNLO it is shown that the virtual and double virtual subtraction terms can be written in terms of integrated dipoles, formed by systematically combining the mass factorisation contributions and integrated antenna functions. The integrated dipoles describing $\ell$ unresolved partons, denoted $\bs{J}_{2}^{(\ell)}$, are related to Catani's IR singularity operators, $\bs{I}_{ij}^{(\ell)}(\eps)$. It is shown that the IR pole structure of the virtual and double virtual contributions can be written as a sum over integrated dipoles within the antenna subtraction formalism and the master expressions analogous to Catani's one- and two-loop factorisation formulae are derived. To demonstrate the techniques described in this paper, we apply antenna subtraction to the production of two gluon jets via quark-antiquark scattering at NLO and NNLO. Double real, real-virtual and double virtual subtraction terms are explicitly derived for the leading colour NNLO contribution.