On Positive Geometry and Scattering Forms for Matter Particles
Abstract
We initiate the study of positive geometry and scattering forms for tree-level amplitudes with matter particles in the (anti-)fundamental representation of the color/flavor group. As a toy example, we study the bi-color scalar theory, which supplements the bi-adjoint theory with scalars in the (anti-)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.
Cite
@article{arxiv.1912.08307,
title = {On Positive Geometry and Scattering Forms for Matter Particles},
author = {Aidan Herderschee and Song He and Fei Teng and Yong Zhang},
journal= {arXiv preprint arXiv:1912.08307},
year = {2020}
}
Comments
47 pages and 9 figures; v2: more references added and typos corrected; v3: published version and typos corrected