Applications of the loop-tree duality

TL;DR

This paper introduces a novel loop-tree duality method for NLO calculations that integrates real and virtual amplitudes simultaneously in four dimensions, simplifying the process and enhancing automation.

Contribution

It presents a new integrand-level approach to NLO computations that avoids tensor reduction and master integrals, improving efficiency and numerical stability.

Findings

Allows simultaneous integration of all scattering amplitudes

Eliminates the need for tensor reduction or master integrals

Enables computations directly in four dimensions

Abstract

We describe a new method to perform NLO calculations, combining real and virtual amplitudes at the integrand level, with a fully local compensation between them in the IR, and between the virtual integrand and properly defined counter-terms in the UV, in such a way that physical observables can be computed in 4 dimensions. One of the advantages of the method is that all the scattering amplitudes are integrated simultaneously, without the need for tensor reduction, or projection onto sets of master integrals. As such, it could offer great progress in the automation of NLO calculations, where the actual bottle-necks are the complexity of the analytical calculations for multi-leg processes, and the numerical stability of the result.