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Towards Positive Geometry of Multi Scalar Field Amplitudes: Accordiohedron and Effective Field Theory

Jagadale, Mrunmay and Laddha, Alok (2021) Towards Positive Geometry of Multi Scalar Field Amplitudes: Accordiohedron and Effective Field Theory. . (Unpublished)

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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 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: = λ₂/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:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Jagadale, Mrunmay0000-0002-7950-4636
Laddha, Alok0000-0003-3193-9291
Additional Information:CC0 1.0 Universal (CC0 1.0) Public Domain Dedication. Dedicated to the memory of Nila; Teacher, Mentor and Friend. 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.
Record Number:CaltechAUTHORS:20210809-220317459
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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:10 Aug 2021 15:23

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