Positive geometries for all scalar theories from twisted intersection theory

Open Access

Positive geometries for all scalar theories from twisted intersection theory

Nikhil Kalyanapuram and Raghav G. Jha

Phys. Rev. Research 2, 033119 – Published 22 July 2020

Abstract

We show that accordiohedra furnish polytopes which encode amplitudes for all massive scalar field theories with generic interactions. This is done by deriving integral formulas for the Feynman diagrams at the tree level and integrands at the one-loop level in the planar limit using the twisted intersection theory of convex realizations of the accordiohedron polytopes.

Received 20 April 2020
Accepted 26 June 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.033119

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Feynman diagrams Scattering amplitudes

Particles & Fields

Authors & Affiliations

Nikhil Kalyanapuram^1,2,* and Raghav G. Jha ^1,†

¹Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada N2L 2Y5
²Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1