Four-loop scattering amplitudes through the loop-tree duality

TL;DR

This paper explores four-loop scattering amplitudes using the Loop-Tree Duality framework, introducing a universal topology and a novel quantum algorithm approach to identify causal singularities.

Contribution

It presents a unified description of four-loop topologies and proposes a modified Grover's quantum algorithm for causal analysis of Feynman diagrams.

Findings

Introduction of the N$^4$MLT universal topology

Application of a modified Grover's algorithm for causal singularity search

Discussion of the importance of a causal representation in four-loop amplitudes

Abstract

A general outlook is presented on the study of multiloop topologies appearing for the first time at four loops. A unified description and representation of this family is provided, the so-called N$^4$MLT universal topology. Based on the Loop-Tree Duality framework, we discuss the dual opening of this family and expose the relevance of a causal representation. We explore an alternative procedure for the search of causal singular configurations of selected N$^4$MLT Feynman diagrams through the application of a modified Grover's quantum algorithm.