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.