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Journal of High Energy Physics

, 2019:271 | Cite as

The positive geometry for 𝜙p interactions

  • Prashanth RamanEmail author
Open Access
Regular Article - Theoretical Physics
  • 275 Downloads

Abstract

Starting with the seminal work of Arkani-Hamed et al. [1], in [2], the “Ampli- tuhedron program” was extended to analyzing (planar) amplitudes in massless 𝜙 4 theory. In this paper we show that the program can be further extended to include 𝜙p (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.

Keywords

Scattering Amplitudes Differential and Algebraic Geometry 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Institute of Mathematical SciencesChennaiIndia
  2. 2.Homi Bhabha National InstituteMumbaiIndia

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