Speaker
Description
The method of regions (MoR), a systematic way to compute Feynman integrals involving multiple kinematic scales, states that a Feynman integral can be approximated, and even reproduced, by summing over integrals that are expanded in certain regions. A modern perspective of the MoR is to consider any given Feynman integral as a certain Newton polytope, which is defined as the convex hull of the points associated to the terms of the Symanzik polynomials. The regions then, has a one-to-one correspondence to the "lower facets" of this polytope. Since the Symanzik polynomials are further related to the spanning trees and spanning 2-trees of the Feynman graph, a graph-theoretical study of these polynomials may allow us to unveil all the possible regions that are needed in the MoR. In this talk we mainly focus on three specific expansions of the wide-angle scattering process: the on-shell expansion, threshold expansion and mass expansion. After introducing the background knowledge, we will describe the basic strategy of the grah-theoretical approach, and formulate the generic form of the regions appearing in each of the three expansions above. The results, which hold for graphs at all orders, can be further applied to construct graph-finding algorithms for the MoR, and investigate the properties of the Soft-Collinear Effective Theory (SCET).
