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

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.