Accordiohedra as positive geometries for generic scalar field theories

Abstract

We build upon the prior works of [1-3] to study tree-level planar amplitudes for a massless scalar field theory with polynomial interactions. Focusing on a specific example, where the interaction is given by ${\lambda }_3{\varphi }^3+{\lambda }_4{\varphi }^4$, we show that a specific convex realization of a simple polytope known as the accordiohedron in kinematic space is the positive geometry for this theory. As in the previous cases, there is a unique planar scattering form in kinematic space, associated to each positive geometry which yields planar scattering amplitudes.

v2: updated references and closest to journal version; v1: 24 pages, 7 figures