A Soft Theorem for the Tropical Grassmannian

Understand

We study the soft limit of a recently proposed generalization of the biadjoint scalar amplitudes $m^{(k)}_{n}$, which have been conjectured to have a relation to the tropical Grassmannian $\text{Tr G}(k,n)$.

• Using the CHY formulation along with the Global Residue Theorem, we prove the soft factorization for $m^{(k)}_{n}$ amplitudes for arbitrary $k$ and $n$.
• We find that the soft factors are in direct correspondence to vertices of the associahedron $\mathcal{A}_{k-1}$, and hence take the form of $m^{(2)}_{n}$ amplitudes.
• This entails that all scattering amplitudes of the ordinary biadjoint scalar theory can be interpreted as an infinite family of soft factors.