From Momentum Amplituhedron Boundaries to Amplitude Singularities and Back

Understand

The momentum amplituhedron is a positive geometry encoding tree-level scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills directly in spinor-helicity space.

• In this paper we classify all boundaries of the momentum amplituhedron $\mathcal{M}_{n,k}$ and explain how these boundaries are related to the expected factorization channels, and soft and collinear limits of tree amplitudes.
• Conversely, all physical singularities of tree amplitudes are encoded in this boundary stratification.
• Finally, we find that the momentum amplituhedron $\mathcal{M}_{n,k}$ has Euler characteristic equal to one, which provides a first step towards proving that it is homeomorphic to a ball.