Universal opening of four-loop scattering amplitudes to trees

TL;DR

This paper introduces a universal method to convert complex four-loop scattering amplitudes into simpler tree-like structures using loop-tree duality, enhancing computational efficiency and stability in high-energy physics calculations.

Contribution

It develops a universal topology expression for four-loop amplitudes, enabling their factorized opening into simpler subtopologies and confirming the causal structure properties.

Findings

Universal topology expression for four-loop amplitudes

Factorized opening into simpler subtopologies

Manifestly free of noncausal thresholds

Abstract

The perturbative approach to quantum field theories has made it possible to obtain incredibly accurate theoretical predictions in high-energy physics. Although various techniques have been developed to boost the efficiency of these calculations, some ingredients remain specially challenging. This is the case of multiloop scattering amplitudes that constitute a hard bottleneck to solve. In this paper, we delve into the application of a disruptive technique based on the loop-tree duality theorem, which is aimed at an efficient computation of such objects by opening the loops to nondisjoint trees. We study the multiloop topologies that first appear at four loops and assemble them in a clever and general expression, the N$^4$MLT {\it universal topology}. This general expression enables to open any scattering amplitude of up to four loops, and also describes a subset of higher order configurations to all orders. These results confirm the conjecture of a factorized opening in terms of simpler known subtopologies, which also determines how the causal structure of the entire loop amplitude is characterized by the causal structure of its subtopologies. In addition, we confirm that the loop-tree duality representation of the N$^4$MLT universal topology is manifestly free of noncausal thresholds, thus pointing towards a remarkably more stable numerical implementation of multiloop scattering amplitudes.