On Positive Geometry and Scattering Forms for Matter Particles
arXiv:1912.08307 · doi:10.1007/JHEP06(2020)030
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.
arXiv comment47 pages and 9 figures; v2: more references added and typos corrected; v3: published version and typos corrected
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Cited by in corpus (9)
- Generalizations of the Double-Copy: the KLT Bootstrap
- Tropical fans, scattering equations and amplitudes
- Positive geometry, local triangulations, and the dual of the Amplituhedron
- Algebraic branch points at all loop orders from positive kinematics and wall crossing
- Amplituhedra, and Beyond
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