Cutting Deep Into The Amplituhedron

TL;DR

This paper computes the deepest cuts of MHV amplitudes in planar N=4 SYM, revealing complex Feynman diagrams through a geometric approach using the amplituhedron in momentum-twistor space, applicable to many loops and particles.

Contribution

It introduces a novel geometric method to compute the deepest cuts of scattering amplitudes using the amplituhedron reformulation in momentum-twistor space.

Findings

First non-trivial results for arbitrary loops and multiplicities.

Deepest cuts probe complex Feynman diagrams.

Geometric facets of the amplituhedron relate to amplitude cuts.

Abstract

In this letter we compute a canonical set of cuts of the integrand for MHV amplitudes in planar ${\cal N}=4$ SYM, where all internal propagators are put on-shell. These "deepest cuts" probe the most complicated Feynman diagrams and on-shell processes that can possibly contribute to the amplitude, but are also naturally associated with remarkably simple geometric facets of the amplituhedron. The recent reformulation of the amplituhedron in terms of combinatorial geometry directly in the kinematic (momentum-twistor) space plays a crucial role in understanding this geometry and determining the cut. This provides us with the first non-trivial results on scattering amplitudes in the theory valid for arbitrarily many loops and external particle multiplicities.