Landau Singularities from the Amplituhedron

TL;DR

This paper introduces a geometric algorithm to identify all branch points of amplitudes in planar N=4 super-Yang-Mills theory directly from the amplituhedron, aiding in translating integrands into integrals and understanding symbol alphabets.

Contribution

It presents a novel geometric method to determine Landau singularities from the amplituhedron without using Feynman integrals, advancing the understanding of amplitude singularities.

Findings

Algorithm successfully applied to one- and two-loop MHV amplitudes.

Provides insights into the symbol alphabets of general amplitudes.

Enables direct extraction of branch points from geometric structures.

Abstract

We propose a simple geometric algorithm for determining the complete set of branch points of amplitudes in planar N=4 super-Yang-Mills theory directly from the amplituhedron, without resorting to any particular representation in terms of local Feynman integrals. This represents a step towards translating integrands directly into integrals. In particular, the algorithm provides information about the symbol alphabets of general amplitudes. We illustrate the algorithm applied to the one- and two-loop MHV amplitudes.