The method of regions, a systematic approach to the asymptotic expansions of Feynman integrals, suggests that a Feynman integral can be reconstructed by summing over integrals expanded in certain regions. This technique not only facilitates the computation of Feynman integrals but also provides valuable insights for formulating an EFT, such as the Soft-Collinear Effective Theory (SCET). However, a fundamental question remains unanswered for most cases: how does one systematically determine the entire list of regions?
This talk aims to address this question by drawing from some recent research works. The following results will be presented and demonstrated. 1. For the "on-shell expansion" and the "soft expansion" of massless wide-angle scattering, an all-order result is validated: each region involves only the hard mode, collinear modes, and ultrasoft mode, with their interactions following certain structures. 2. For the heavy-to-light decay processes, more modes are involved as the loop number increases. 3. For the high-energy expansion of two-to-two forward scattering, the Glauber mode is also involved, starting from three loops. Some important implications from these results will be discussed in the talk.
