{"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/khuri-treiman-equations-for-3p-decays-of","title":"Khuri-Treiman equations for $3π$ decays of particles with spin","arxiv_id":"1910.03107","date":"2019-10-07","proceeding":null,"authors":["JPAC Collaboration","M. Albaladejo","D. Winney","I. V. ~Danilkin","C. Fernandez-Ramirez","V. Mathieu","M. Mikhasenko","A. Pilloni","J. A. Silva-Castro","A. P. Szczepaniak"],"abstract":"Khuri-Treiman equations have proven to be a useful theoretical tool in the analysis of 3-body decays, specially into the $3\\pi$ final state. In this work we present in full detail the necessary generalization of the formalism to study the decays of particles with arbitrary spin, parity, and charge conjugation. To this extent, we find it most convenient to work with helicity amplitudes instead of the so-called invariant amplitudes, specially when dealing with the unitarity relations. The isobar expansions in the three possible ($s$-, $t$-, and $u$-) final channels are related with the appropriate crossing matrices. We pay special attention to the kinematical singularities and constraints of the helicity amplitudes, showing that these can be derived by means of the crossing matrix.","url_abs":"https://arxiv.org/abs/1910.03107v1","url_pdf":"https://arxiv.org/pdf/1910.03107v1.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":"khuri-treiman-equations-for-3p-decays-of","repo_url":"https://github.com/dwinney/jpacTriangle","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"khuri-treiman-equations-for-3p-decays-of","repo_url":"https://github.com/dwinney/kt_triangle","is_official":0,"mentioned_in_paper":0,"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}