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arXiv · 1906.12148

Accordiohedra as positive geometries for generic scalar field theories

P. B. Aneesh·Mrunmay Jagadale·Nikhil Kalyanapuram
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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 $\lambda_3\phi^{3}\ +\lambda_4 \phi^{4}$, 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.

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P. B. Aneesh, Mrunmay Jagadale, Nikhil Kalyanapuram. 2019-06-28. Accordiohedra as positive geometries for generic scalar field theories. https://doi.org/10.1103/physrevd.100.106013

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