On the interplay between the loop-tree duality and helicity amplitudes

TL;DR

This paper explores the synergy between the loop-tree duality and spinor-helicity formalisms to improve the calculation of scattering amplitudes, emphasizing local renormalization and automation in four dimensions.

Contribution

It introduces a novel combination of LTD and spinor-helicity formalisms for efficient, automated amplitude calculations at one- and two-loop levels.

Findings

Efficient numerical implementation for four-dimensional integrals.

Successful analysis of one- and two-loop scattering processes.

Enhanced local UV renormalization techniques.

Abstract

The spinor-helicity formalism has proven to be very efficient in the calculation of scattering amplitudes in quantum field theory, while the loop tree duality (LTD) representation of multi-loop integrals exhibits appealing and interesting advantages with respect to other approaches. In view of the most recent developments in LTD, we exploit the synergies with the spinor-helicity formalism to analyse illustrative one- and two-loop scattering processes. We focus our discussion on the local UV renormalisation of IR and UV finite amplitudes and present a fully automated numerical implementation that provides efficient expressions which are integrable directly in four space-time dimensions.