Universal opening of four-loop scattering amplitudes to trees

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.

21 pages, 9 figures. Explicit causal formulae included, discussion and explanations extended

References in corpus (12)

• Higgs boson gluon-fusion production in N3LO QCD
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs
• From loops to trees by-passing Feynman's theorem
• Four-dimensional unsubtraction with massive particles
• A Tree-Loop Duality Relation at Two Loops and Beyond
• A four-dimensional approach to quantum field theories
• On the singular behaviour of scattering amplitudes in quantum field theory
• Universal four-dimensional representation of $H\to \gamma \gamma$ at two loops through the Loop-Tree Duality
• Mixed QCD$\otimes$QED corrections to exclusive Drell Yan production using the $q_T$-subtraction method
• Mathematical properties of nested residues and their application to multi-loop scattering amplitudes
• Causal representation of multi-loop Feynman integrands within the loop-tree duality

Cited by in corpus (8)

• Geometrical approach to causality in multi-loop amplitudes
• Quantum algorithm for Feynman loop integrals
• Loop-tree duality from vertices and edges
• Numerical integration of loop integrals through local cancellation of threshold singularities
• Exposing the threshold structure of loop integrals
• Rewording Theoretical Predictions at Colliders with Vacuum Amplitudes
• Loop Feynman integration on a quantum computer
• Quantum integration of decay rates at second order in perturbation theory