{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/kinematic-hopf-algebra-and-bcj-numerators-at","title":"Kinematic Hopf algebra and BCJ numerators at finite $α'$","arxiv_id":"2403.04614","date":"2024-03-07","proceeding":null,"authors":["Gang Chen","Laurentiu Rodina","Congkao Wen"],"abstract":"In this letter, starting from a kinematic Hopf algebra, we first construct a closed-form formula for all Bern-Carrasco-Johansson (BCJ) numerators in Yang-Mills (YM) theory with infinite orders of $\\alpha'$ corrections, known as $\\rm DF^2+YM$ theory, when coupled to two heavy particles which can be removed through a simple factorization limit. The full $\\alpha'$ dependence appears simply in massive physical propagator factors, with factorization strongly constraining the construction. The intricate structure induced by the massive poles also naturally leads us to find a novel closed-form and local expression for BCJ numerators in usual pure YM theory, based directly on the kinematic Hopf algebra.","url_abs":"https://arxiv.org/abs/2403.04614v1","url_pdf":"https://arxiv.org/pdf/2403.04614v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"kinematic-hopf-algebra-and-bcj-numerators-at","repo_url":"https://github.com/amplitudegravity/kinematichopfalgebra","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}