### Scattering forms and Stokes Polytopes

In a remarkable recent work by Arkani-Hamed et al, the amplituhedron program was extended to the realm of non-supersymmetric scattering amplitudes. In particular it was shown that for tree-level planar diagrams in massless $\phi^3$ theory (and its close cousin, bi-adjoint $\phi^3$ theory) a polytope known as the associahedron sits inside the kinematic space and is the amplituhedron for the theory. Precisely as in the case of amplituhedron, it was shown that scattering amplitude is nothing but residue of the canonical form associated to the associahedron. Combinatorial and geometric properties of associahedron naturally encode properties like locality and unitarity of (tree level) scattering amplitudes.

In this talk after briefly reviewing their work we attempt to extend this program to planar amplitudes in massless $\phi^4$ theory. We show that tree-level planar amplitudes in this theory can be obtained from geometry of objects known as the Stokes polytope which sits naturally inside the kinematic space. As in the case of associahedron we show that residues of the canonical form on these Stokes polytopes can be used to compute scattering amplitudes for quartic interactions. However unlike associahedron, Stokes polytope of a given dimension is not unique and as we show, one must sum over all of them to obtain the complete scattering amplitude. We shall finally discuss some ongoing work about generalisation of the program to all $\phi^p$ ($p>4$) theories.

Wednesday, 10th of April 2019, 14:30, sala Wataghin