The positive geometry for \(\phi^{p}\) interactions

Starting with the seminal work of Arkani-Hamed et al arXiv:1711.09102, in arXiv:1811.05904, the "Amplituhedron program" was extended to analyzing (planar) amplitudes in massless \(\phi^{4}\) theory. In this paper we show that the program can be further extended to include \(\phi^{p}\) (\(p...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2019-06
Main Author: Raman, Prashanth
Format: Article
Language:English
Subjects:
Amplitudes
Canonical forms
Polytopes
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Starting with the seminal work of Arkani-Hamed et al arXiv:1711.09102, in arXiv:1811.05904, the "Amplituhedron program" was extended to analyzing (planar) amplitudes in massless \(\phi^{4}\) theory. In this paper we show that the program can be further extended to include \(\phi^{p}\) (\(p>4\)) interactions. We show that tree-level planar amplitudes in these theories can be obtained from geometry of polytopes called accordiohedron which naturally sits inside kinematic space. As in the case of quartic interactions the accordiohedron of a given dimension is not unique, and we show that a weighted sum of residues of the canonical form on these polytopes can be used to compute scattering amplitudes. We finally provide a prescription to compute the weights and demonstrate how it works in various examples.
ISSN:2331-8422
DOI:10.48550/arxiv.1906.02985