The Momentum Amplituhedron

Understand

In this paper we define a new object, the momentum amplituhedron, which is the long sought-after positive geometry for tree-level scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills theory in spinor helicity space.

• Inspired by the construction of the ordinary amplituhedron, we introduce bosonized spinor helicity variables to represent our external kinematical data, and restrict them to a particular positive region.
• The momentum amplituhedron $\mathcal{M}_{n,k}$ is then the image of the positive Grassmannian via a map determined by such kinematics.
• The scattering amplitudes are extracted from the canonical form with logarithmic singularities on the boundaries of this geometry.