A Caltech Library Service

Towards positive geometry of multi scalar field amplitudes. Accordiohedron and effective field theory

Jagadale, Mrunmay and Laddha, Alok (2022) Towards positive geometry of multi scalar field amplitudes. Accordiohedron and effective field theory. Journal of High Energy Physics, 2022 (4). Art. No. 100. ISSN 1126-6708. doi:10.1007/JHEP04(2022)100.

[img] PDF - Published Version
Creative Commons Attribution.

[img] PDF - Submitted Version
Creative Commons Public Domain Dedication.


Use this Persistent URL to link to this item:


The geometric structure of S-matrix encapsulated by the “Amplituhedron program” has begun to reveal itself even in non-supersymmetric quantum field theories. Starting with the seminal work of Arkani-Hamed, Bai, He and Yan [1] it is now understood that for a wide class of scalar quantum field theories, tree-level amplitudes are canonical forms associated to polytopes known as accordiohedra. Similarly the higher loop scalar integrands are canonical forms associated to so called type-D cluster polytopes for cubic interactions or recently discovered class of polytopes termed pseudo-accordiohedron for higher order scalar interactions. In this paper, we continue to probe the universality of these structures for a wider class of scalar quantum field theories. More in detail, we discover new realisations of the associahedron in planar kinematic space whose canonical forms generate (colour-ordered) tree-level S matrix of external massless particles with n − 4 massless poles and one massive pole at m². The resulting amplitudes are associated to λ₁ϕ₁³+λ₂ϕ₁²ϕ₂ potential where ϕ₁ and ϕ₂ are massless and massive scalar fields with bi-adjoint colour indices respectively. We also show how in the “decoupling limit” (where m → ∞, λ₂ → ∞ such that g :λ₂m/m = finite) these associahedra project onto a specific class of accordiohedron which are known to be positive geometries of amplitudes generated by λϕ₁³+gϕ₁⁴.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Jagadale, Mrunmay0000-0002-7950-4636
Laddha, Alok0000-0003-3193-9291
Additional Information:© 2022 The Authors. 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. Article funded by SCOAP3. Received 06 May 2021; Accepted 29 December 2021; Published 19 April 2022. We are indebted to Nima Arkani-Hamed for a number of insightful discussions, many clarifications and encouragement. We would like to thank Ashoke Sen and Nemani Suryanarayana for valuable inputs and Sujay Ashok, Pinaki Banerjee, Miguel Campiglia, Dileep Jatkar, Nikhil Kalyanapuram, Madhusudan Raman, Prashanth Raman and Arnab Priya Saha for many discussions over the years on related issues. We also thank Pinaki Banerjee for comments on the manuscript. We would especially like to thank Vincent Pilaud for his guidance and crucial insights in the early stages of this work.
Funding AgencyGrant Number
Subject Keywords:Scattering Amplitudes; Differential and Algebraic Geometry; Effective Field Theories
Issue or Number:4
Record Number:CaltechAUTHORS:20210809-220317459
Persistent URL:
Official Citation:Jagadale, M., Laddha, A. Towards positive geometry of multi scalar field amplitudes. Accordiohedron and effective field theory. J. High Energ. Phys. 2022, 100 (2022).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110184
Deposited By: George Porter
Deposited On:10 Aug 2021 15:23
Last Modified:06 May 2022 18:00

Repository Staff Only: item control page