Revealing Hidden Regions in Wide-Angle and Forward Scattering

TL;DR

This paper investigates hidden regions in Feynman integrals relevant to wide-angle and forward scattering, revealing their structure using Landau singularity analysis and proposing methods to handle their numerical evaluation.

Contribution

It introduces a novel approach to identify and analyze hidden regions in Feynman integrals that are not detected by traditional geometric methods.

Findings

Hidden regions can be exposed in both momentum and parametric representations.

Landau singularities prevent direct numerical evaluation in certain limits.

Re-parameterisation techniques can circumvent evaluation issues.

Abstract

We discuss a class of Feynman Integrals containing hidden regions that are not straightforwardly identified using the geometric, or Newton polytope, approach to the method of regions. Using Landau singularity analysis and existing analytic results, we study the appearance of such regions in wide-angle and forward scattering and discuss how they can be exposed in both the momentum and parametric representations. We demonstrate that in the strict on-shell limit such integrals contain Landau singularities that prevent their direct numerical evaluation in parameter space and describe how they can be re-parameterised and dissected to circumvent this problem.