Hadleigh Frost, "Cutting Before, During, and After Loop Integration"

Tuesday 25 Feb 2025, 15:00 → 17:00 Europe/Berlin

A.2.25/27 - Atlas (New)

Abstract: In colored theories, the relationship between integrands and topological surfaces gives a powerful book keeping method for calculations. As a first illustration of this, we review the recently introduced cut equation (https://arxiv.org/abs/2412.21027) that recursively constructs multiloop integrands from tree amplitudes—correctly counting contributions even in the presence of higher poles. Next, we'll look at how the cut equation appears again when doing loop integrals in D=1 spacetime dimensions, where loop integrals are sums of residues (as is familiar from the standard t-space trick). Here, the cut equation recursively computes the final amplitude from tree amplitudes. Finally, we consider how the cut equation applies also to schemes for approximating loop integrals, such as expanding around the so-called Hepp bound. We end by considering how the cut equation might help with loop integrals in D>1 dimensions, and/or augment existing approaches to multiloop amplitudes.