Speaker
Description
I review recent progress in methodology and applications of the Method of Regions, the central approach to performing asymptotic expansions of Feynman integrals. In this method, general log-power expansions in singular kinematic limits are obtained through a sum over “region integrals”, each of which is defined by a Taylor expansion of the integrand under certain assumptions regarding the behaviour of the integration variables in the limit considered. In certain cases, there is a geometric algorithm in parameter space to find the complete set of regions. Recent progress, stemming from Landau singularity analysis, elucidated under what conditions the latter set is complete, and how to determine the remaining “hidden regions” otherwise. This analysis also led to a graph-theoretical momentum-space interpretation of both type of regions in certain expansions.
Turning to applications, a novel use of the geometric method is the recent computation of the three-loop soft anomalous dimension for scattering of a heavy particle and any number of massless ones. In this way the MoR contributes to our state-of-the-art knowledge of the multiloop IR structure of multileg amplitudes in general (wide-angle) kinematics. Next, I show that while in wide-angle kinematics hidden regions are only relevant for multiple hard scattering, in special kinematic limits, such as the (multi) Regge limit and the spacelike collinear limit, they are essential to understanding the dynamics, which is govern by Glauber effects.