On Positive Geometry and Scattering Forms for Matter Particles

Authors: Aidan Herderschee, Song He, Fei Teng and Yong Zhang

Preprint number: UUITP-52/19

Abstract: We initiate the study of positive geometry and scattering forms for tree-level amplitudes with (massive) matter particles in (anti-)fundamental representation of color/flavor group. As a toy example, we study the bi-color scalar theory, which supplement the bi-adjoint theory with scalars in fundamental representations of both groups. Using a recursive construction we obtain a class of unbounded polytopes called open associahedra (or associahedra with certain facets at infinity) whose canonical form computes amplitudes in bi-color theory, for arbitrary number of legs and flavor assignments. In addition, we discuss the duality between color factors and wedge products, or ”color is kinematics”, for amplitudes with matter particles as well.