Accordiohedra as positive geometries for generic scalar field theories

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 ${\lambda }_3{\varphi }^3+{\lambda }_4{\varphi }^4$, 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.

arXiv commentv2: updated references and closest to journal version; v1: 24 pages, 7 figures

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Cited by in corpus (22)

• Amplitudes meet Cosmology: A (Scalar) Primer
• On-Shell Electroweak Sector and the Higgs Mechanism
• Soft Gravity by Squaring Soft QED on the Celestial Sphere
• The SAGEX Review on Scattering Amplitudes, Chapter 7: Positive Geometry of Scattering Amplitudes
• Positive Geometries for all Scalar Theories from Twisted Intersection Theory
• Amplituhedra, and Beyond
• Stokes Polytopes and Intersection Theory
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• Celebrating Loday's Associahedron
• Weights and recursion relations for ${\varphi }^p$ tree amplitudes from the positive geometry
• Towards Positive Geometry of Multi Scalar Field Amplitudes : Accordiohedron and Effective Field Theory
• Weights, Recursion relations and Projective triangulations for Positive Geometry of scalar theories
• On Polytopes and Generalizations of the KLT Relations
• Constraining the weights of Stokes Polytopes using BCFW recursions for Phi^4
• Open associahedra and scattering forms
• Gauge and Gravity Amplitudes on the Celestial Sphere
• On the Positive Geometry of Quartic Interactions III : One Loop Integrands from Polytopes
• One-loop integrand from generalised scattering equations
• Double Soft Theorem for Generalised Biadjoint Scalar Amplitudes
• Geometric Recursion from Polytope Triangulations and Twisted Homology
• Triangular tessellations of one-loop scattering amplitudes in ${\varphi }^3$ theory
• BCFW like recursion for Deformed Associahedron