Properties of scattering forms and their relation to associahedra

Understand

We show that the half-integrands in the CHY representation of tree amplitudes give rise to the definition of differential forms -- the scattering forms -- on the moduli space of a Riemann sphere with $n$ marked points.

• These differential forms have some remarkable properties.
• We show that all singularities are on the divisor $\overline{\mathcal M}_{0,n} \backslash {\mathcal M}_{0,n}$.
• Each singularity is logarithmic and the residue factorises into two differential forms of lower points.