A general algorithm to build mixed real and virtual antenna functions for higher-order calculations

TL;DR

This paper introduces a comprehensive algorithm for constructing mixed real and virtual antenna functions at NNLO, enhancing the automation and consistency of subtraction schemes for higher-order QCD calculations relevant to collider physics.

Contribution

It extends previous methods to include mixed real-virtual radiation, providing a full set of antenna functions and integration techniques for NNLO predictions.

Findings

Developed a new algorithm for mixed real-virtual antenna functions

Constructed a full set of NNLO antenna functions with phase space integration

Demonstrated the consistency of the subtraction scheme for NNLO calculations

Abstract

The antenna-subtraction technique has demonstrated remarkable effectiveness in providing next-to-next-to-leading order in $\alpha_s$ (NNLO) predictions for a wide range of processes relevant for the Large Hadron Collider. In a previous paper [1], we demonstrated how to build real-radiation antenna functions for any number of real emissions directly from a specified list of unresolved limits. Here, we extend this procedure to the mixed case of real and virtual radiation, for any number of real and virtual emissions. A novel feature of the algorithm is the requirement to match the antenna constructed with the correct unresolved limits to the other elements of the subtraction scheme. We discuss how this can be achieved and provide a full set of real-virtual NNLO antenna functions (together with their integration over the final-final unresolved phase space). We demonstrate that these antennae can be combined with the real-radiation antennae of Ref. [1] to form a consistent NNLO subtraction scheme that cancels all explicit and implicit singularities at NNLO. We anticipate that the improved antenna functions should be more amenable to automation, thereby making the construction of subtraction terms for more complicated processes simpler at NNLO.