From five-loop scattering amplitudes to open trees with the Loop-Tree Duality

TL;DR

This paper uses the Loop-Tree Duality formalism to analyze five-loop topologies in quantum field theory, introducing a universal topology and recursive methods to simplify multiloop scattering amplitudes, aiding high-precision calculations.

Contribution

It introduces the N$^7$MLT universal topology and recursive relations for multiloop topologies, advancing the analysis of high-order scattering amplitudes in quantum field theory.

Findings

Identification of the N$^7$MLT universal topology.

Development of factorization and recursion relations.

Application to multiloop topologies up to five loops.

Abstract

Characterizing multiloop topologies is an important step towards developing novel methods at high perturbative orders in quantum field theory. In this article, we exploit the Loop-Tree Duality (LTD) formalism to analyse multiloop topologies that appear for the first time at five loops. Explicitly, we open the loops into connected trees and group them according to their topological properties. Then, we identify a kernel generator, the so-called N$^7$MLT universal topology, that allow us to describe any scattering amplitude of up to five loops. Furthermore, we provide factorization and recursion relations that enable us to write these multiloop topologies in terms of simpler subtopologies, including several subsets of Feynman diagrams with an arbitrary number of loops. Our approach takes advantage of many symmetries present in the graphical description of the original fundamental five-loop topologies. The results obtained in this article might shed light into a more efficient determination of higher-order corrections to the running couplings, which are crucial in the current and future precision physics program.