All-order prescription for facet regions in massless wide-angle scattering

TL;DR

This paper develops an all-order method to systematically identify dominant regions in the asymptotic expansion of massless wide-angle scattering Feynman integrals, extending Euclidean-space insights to Minkowski space.

Contribution

It introduces a novel momentum-space prescription for facet regions in multiscale processes, combining graph theory and convex geometry, revealing the algebraic structure of momentum modes.

Findings

Provides a systematic all-order prescription for facet regions.

Extends the Euclidean-space region analysis to Minkowski space.

Uncovers the algebraic structure of momentum modes such as collinear and soft.

Abstract

We take a step toward answering a long-standing question in the asymptotic expansion of Feynman integrals: how to systematically determine the regions in the Expansion-by-Regions technique for multiscale processes? Focusing on generic massless wide-angle scattering, we provide an all-order momentum-space prescription for facet regions, which generally dominate -- and in most cases exhaust -- the contributions in a given asymptotic expansion. This extends the Euclidean-space picture, where regions correspond to specific subgraphs, to the complexities of Minkowski space. Our results are derived from a novel analytical approach combining graph theory and convex geometry; as a key byproduct, we uncover for the first time the algebraic structure underlying momentum modes (collinear, soft, and their hierarchies).