Causal representation and numerical evaluation of multi-loop Feynman integrals

TL;DR

This paper discusses the development of a causal representation for multi-loop Feynman integrals using loop-tree duality, enhancing numerical evaluation stability for complex scattering amplitudes.

Contribution

It introduces an all-loop causal representation based on loop topology features, improving the understanding and numerical stability of multi-loop integrands.

Findings

Causal representation simplifies multi-loop integrands to physical information.

Numerical evaluations of two-loop triangles demonstrate improved stability.

Application to planar and non-planar cases confirms effectiveness.

Abstract

The loop-tree duality (LTD) has become a novelty alternative to bootstrap the numerical evaluation of multi-loop scattering amplitudes. It has indeed been found that Feynman integrands, after the application of LTD, display a representation containing only physical information, the so-called causal representation. In this talk, we discuss the all-loop causal representation of multi-loop Feynman integrands, recently found in terms of features that describe a loop topology, vertices and edges. Likewise, in order to elucidate the numerical stability in LTD integrands, we present applications that involve numerical evaluations of two-loop planar and non-planar triangles with presence of several kinematic invariants.