Triangular tessellations of one-loop scattering amplitudes in �3 theory

Das, AB (2024) Triangular tessellations of one-loop scattering amplitudes in �3 theory. In: European Physical Journal: Special Topics .

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Abstract

Inspired by the recent work of Nima Arkani Hamed and collaborators who introduced the notion of positive geometry to account for the structure of tree-level scattering amplitudes in bi-adjoint �3 theory, which led to one-loop descriptions of the integrands. Here, we consider the one-loop integrals themselves in �3 theory. In order to achieve this end, the geometrical construction offered by Schnetz for Feynman diagrams is hereby extended, and the results are presented. The extension relies on masking the loop momentum variable with a constant and proceeding with the calculations. The results appear as a construction given in a diagrammatic manner. The significance of the resulting triangular diagrams is that they have a common side amongst themselves for the corresponding Feynman diagrams they pertain to. Further extensions to this mathematical construction can lead to additional insights into higher loops. A mathematica code has been provided in order to generate the final results given the initial parameters of the theory. © 2024, The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature.

Item Type:	Journal Article
Publication:	European Physical Journal: Special Topics
Publisher:	Springer Science and Business Media Deutschland GmbH
Additional Information:	The copyright for this article belongs to Springer Science and Business Media Deutschland GmbH
Department/Centre:	Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited:	01 Mar 2024 09:02
Last Modified:	01 Mar 2024 09:02
URI:	https://eprints.iisc.ac.in/id/eprint/83947

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