Four-loop scattering amplitudes journey into the forest

TL;DR

This paper explores four-loop scattering amplitudes, introducing a universal topology, and discusses novel methods including Loop-Tree Duality and quantum algorithms for analyzing multiloop Feynman diagrams.

Contribution

It presents the first analysis of four-loop topologies, constructs a universal topology, and applies quantum algorithms for causal analysis of multiloop diagrams.

Findings

Introduction of the N$^4$MLT universal topology

Application of Loop-Tree Duality to multiloop amplitudes

Use of quantum algorithms for causal singularity identification

Abstract

We present an overview of the analysis of the multiloop topologies that appear for the first time at four loops and the assembly of them in a general expression, the N$^4$MLT universal topology. Based on the fact that the Loop-Tree Duality enables to open any scattering amplitude in terms of convolutions of known subtopologies, we go through the dual representation of the universal N$^4$MLT topology and the manifestly causal representation. Additionally, we expose the application of a quantum algorithm as an alternative methodology to identify the causal singular configurations of multiloop Feynman diagrams.