Positive Geometries for all Scalar Theories from Twisted Intersection Theory

TL;DR

This paper demonstrates that accordiohedra polytopes encode amplitudes for all massive scalar theories, deriving integral formulas for tree-level and one-loop diagrams via twisted intersection theory.

Contribution

It introduces a novel geometric framework using accordiohedra and twisted intersection theory to compute scalar field theory amplitudes.

Findings

Accordiohedra encode amplitudes for massive scalar theories.

Derived integral formulas for tree and one-loop amplitudes.

Established a geometric approach to scalar field computations.

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 formulae for the Feynman diagrams at tree level and integrands at one loop level in the planar limit using the twisted intersection theory of convex realizations of the accordiohedron polytopes.