Real-Virtual corrections for gluon scattering at NNLO

TL;DR

This paper develops a method using antenna functions to systematically cancel infrared singularities in gluon scattering amplitudes at NNLO, enabling precise numerical calculations.

Contribution

It introduces a new subtraction scheme for real-virtual corrections in gluon scattering at NNLO using antenna functions with initial- and final-state partons.

Findings

Infrared poles are explicitly canceled in all phase space regions.

The subtraction term accurately approximates matrix elements in unresolved configurations.

The method allows for finite, numerically integrable results in four dimensions.

Abstract

We use the antenna subtraction method to isolate the mixed real-virtual infrared singularities present in gluonic scattering amplitudes at next-to-next-to-leading order. In a previous paper, we derived the subtraction term that rendered the double real radiation tree-level process finite in the single and double unresolved regions of phase space. Here, we show how to construct the real-virtual subtraction term using antenna functions with both initial- and final-state partons which removes the explicit infrared poles present in the one-loop amplitude, as well as the implicit singularities that occur in the soft and collinear limits. As an explicit example, we write down the subtraction term that describes the single unresolved contributions from the five-gluon one-loop process. The infrared poles are explicitly and locally cancelled in all regions of phase space prior to integration, leaving a finite remainder that can be safely evaluated numerically in four-dimensions. We show numerically that the subtraction term correctly approximates the matrix elements in the various single unresolved configurations.