Work

Serendipitous syzygies of scattering amplitudes

Year: 2025

Type: article

Abstract: We study linear relations between color-ordered all-plus amplitudes at one loop in Yang-Mills theory. We show that on general grounds, there are ( n − 1 ) ! / 2 − 2 relations for n ≥ 5 , leaving only two independent color-ordered amplitudes. We present two complementary approaches to finding such relations; one using numerical linear algebra and the other using syzygies in computational algebraic geometry. We obtain explicit forms for all relations through n = 7 . We also study relations for the tree-level maximally helicity violating amplitudes through n = 8 . The latter relations include the well-known color and Bern-Carrasco-Johansson identities.

Source: Zurich Open Repository and Archive (University of Zurich)

DOI: 10.5167/uzh-291641

Authors: Kosower, David A., Pögel, Sebastian

Language: English

Topic: Particle physics theoretical and experimental studies

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7128959334

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