Identifying regions for asymptotic expansions of amplitudes: fundamentals and recent advances

TL;DR

This review discusses the method-of-regions technique for asymptotic expansions of Feynman integrals, emphasizing geometric approaches, challenges at higher loops, and strategies for identifying relevant regions.

Contribution

It provides a systematic geometric approach to identify regions in asymptotic expansions and reviews recent advances and challenges in the field.

Findings

Newton polytope geometry aids region identification

Higher loop complexities introduce subtleties in region determination

Current strategies improve accuracy in complex Feynman integral expansions

Abstract

This review paper discusses the identification of regions, a crucial first step in applying the "method-of-regions" technique. A systematic approach based on Newton polytope geometry has proven successful and efficient for many cases. However, obtaining the correct list of regions becomes increasingly subtle with higher loop numbers or specific Feynman graph topologies. This paper explores the scenarios where such subtleties arise, outlines general strategies to address them, and reviews the current understanding of region structures in various asymptotic expansions of Feynman integrals.