Weights and recursion relations for $\phi^p$ tree amplitudes from the positive geometry

Understand

Recently, the accordiohedron in kinematic space was proposed as the positive geometry for planar tree-level scattering amplitudes in the $\phi^p$ theory \cite{Raman:2019utu}.

• The scattering amplitudes are given as a weighted sum over canonical forms of some accordiohedra with appropriate weights.
• These weights were determined by demanding that the weighted sum corresponds to the scattering amplitudes.
• It means that we need additional data from the quantum field theory to compute amplitudes from the geometry.