From tree- to loop-simplicity in affine Toda theories II: higher-order poles and cut decompositions

Dorey, Patrick; Polvara, Davide

Abstract

Recently we showed how, in two-dimensional scalar theories, one-loop threshold diagrams can be cut into the product of one or more tree-level diagrams [1]. Using this method on the ADE series of Toda models, we computed the double- and single-pole coefficients of the Laurent expansion of the S-matrix around a pole of arbitrary even order, finding agreement with the bootstrapped results. Here we generalise the cut method explained in [1] to multiple loops and use it to simplify large networks of singular diagrams. We observe that only a small number of cut diagrams survive and contribute to the expected bootstrapped result, while most of them cancel each other out through a mechanism inherited from the tree-level integrability of these models. The simplification mechanism between cut diagrams inside networks is reminiscent of Gauss’s theorem in the space of Feynman diagrams.

Citation

Dorey, P., & Polvara, D. (2023). From tree- to loop-simplicity in affine Toda theories II: higher-order poles and cut decompositions. Journal of High Energy Physics, 2023(10), Article 177. https://doi.org/10.1007/jhep10%282023%29177

• Journal Article Type: Article
• Acceptance Date: Oct 6, 2023
• Online Publication Date: Oct 30, 2023
• Publication Date: 2023-10
• Deposit Date: Nov 10, 2023
• Publicly Available Date: Nov 10, 2023
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2023
• Issue: 10
• Article Number: 177
• DOI: https://doi.org/10.1007/jhep10%282023%29177
• Keywords: Field Theories in Lower Dimensions, Scattering Amplitudes, Integrable Field Theories, Higher Spin Symmetry
• Public URL: https://durham-repository.worktribe.com/output/1883681