Towards a Numerical Unitarity Approach for Two-loop Amplitudes in QCD

TL;DR

This paper extends the numerical unitarity method to two-loop amplitudes in QCD, enabling more accurate predictions for LHC physics by constructing suitable surface terms and master integrands.

Contribution

It introduces a new approach for parametrizing multi-loop integrands in QCD, focusing on the construction of surface terms matching Feynman propagator structures.

Findings

Development of a classification scheme for surface terms

Enhanced integral reduction techniques for two-loop amplitudes

Potential for improved precision in QCD predictions

Abstract

The numerical unitarity approach has been important for obtaining reliable QCD predictions for the LHC. Here I discuss the extension of the approach beyond the leading quantum corrections for computing multi-loop amplitudes. The numerical unitarity approach requires a suitable parametrisation of the loop integrands as a sum of terms that integrate to zero (surface terms) and master integrands. The construction and classification of suitable surface terms which match the propagators structures of Feynman amplitudes is the main technical advance discussed. A number of spin-offs for integral reduction and further formal questions are briefly reviewed.