Double Virtual corrections for gluon scattering at NNLO

TL;DR

This paper develops a method using antenna functions to subtract infrared singularities in two-loop gluon scattering amplitudes at NNLO, enabling finite, numerical evaluation of complex QCD processes.

Contribution

It introduces a systematic way to construct double virtual subtraction terms with antenna functions for initial- and final-state partons at NNLO.

Findings

Explicit subtraction term for four-gluon two-loop process provided.

Infrared poles are locally canceled, leaving finite results.

Method facilitates numerical evaluation of NNLO gluon scattering amplitudes.

Abstract

We use the antenna subtraction method to isolate the double virtual infrared singularities present in gluonic scattering amplitudes at next-to-next-to-leading order. In previous papers, we derived the subtraction terms that rendered (a) the double real radiation tree-level process finite in the single and double unresolved regions of phase space and (b) the mixed single real radiation one-loop process both finite and well behaved in the unresolved regions of phase space. Here, we show how to construct the double virtual subtraction term using antenna functions with both initial- and final-state partons which remove the explicit infrared poles present in the two-loop amplitude. As an explicit example, we write down the subtraction term for the four-gluon two-loop process. The infrared poles are explicitly and locally cancelled in all regions of phase space leaving a finite remainder that can be safely evaluated numerically in four-dimensions.