Feynman integrals and the Method of Regions

by STEPHEN JONES

Friday 21 Apr 2023, 14:00 → 16:00 Europe/Zurich

4/3-006 - TH Conference Room (CERN)

Feynman integrals commonly show up in perturbation theory, appearing in a broad range of contexts from collider scattering processes to the inspiral of black holes. I will present ongoing work on the application of the ``method of regions'' to Feynman integrals. Pioneered in the 90s, the method, which underlies effective field theory approaches such as Soft-Collinear Effective Field Theory (SCET), provides a procedure for expanding integrals around one or more small parameters prior to integration. It can also provide a systematic way to compute Feynman integrals involving multiple kinematic scales. I review the method of regions from a geometric perspective and study its application to Feynman integrals with massless propagators contributing to off-shell Green's functions expanded around vanishing external mass. We argue that the Landau equations allow us to connect the momentum space analysis to the Feynman parameter space analysis and use this understanding to construct a graph-based algorithm for finding infra-red regions, relevant for the expansion.

mor_cern.pdf