Momentum Amplituhedron meets Kinematic Associahedron

Understand

In this paper we study a relation between two positive geometries: the momentum amplituhedron, relevant for tree-level scattering amplitudes in $\mathcal{N} = 4$ super Yang-Mills theory, and the kinematic associahedron, encoding tree-level amplitudes in bi-adjoint scalar $\phi^3$ theory.

• We study the implications of restricting the latter to four spacetime dimensions and give a direct link between its canonical form and the canonical form for the momentum amplituhedron.
• After removing the little group scaling dependence of the gauge theory, we find that we can compare the resulting reduced form with the pull-back of the associahedron form.
• In particular, the associahedron form is the sum over all helicity sectors of the reduced momentum amplituhedron forms.