Geometry and causality for efficient multiloop representations

TL;DR

This paper introduces a geometric and causal approach to rewriting multi-loop Feynman integrands, reducing non-physical singularities, enhancing numerical stability, and improving efficiency in high-energy physics computations.

Contribution

It presents a new method inspired by Loop-Tree Duality that leverages geometry and causality to produce more stable multi-loop integrand representations.

Findings

Reduces non-physical singularities in integrands

Enhances numerical stability and computational speed

Facilitates new interpretations of higher-order quantum corrections

Abstract

Multi-loop scattering amplitudes constitute a serious bottleneck in current high-energy physics computations. Obtaining new integrand level representations with smooth behaviour is crucial for solving this issue, and surpassing the precision frontier. In this talk, we describe a new technology to rewrite multi-loop Feynman integrands in such a way that non-physical singularities are avoided. The method is inspired by the Loop-Tree Duality (LTD) theorem, and uses geometrical concepts to derive the causal structure of any multi-loop multi-leg scattering amplitude. This representation makes the integrand much more stable, allowing faster numerical simulations, and opens the path for novel re-interpretations of higher-order corrections in QFT.