{"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/heavy-to-light-form-factors-to-three-loops","title":"Heavy-to-light form factors to three loops","arxiv_id":"2406.08182","date":"2024-06-12","proceeding":null,"authors":["Matteo Fael","Tobias Huber","Fabian Lange","Jakob Müller","Kay Schönwald","Matthias Steinhauser"],"abstract":"We compute three-loop corrections of $\\mathcal{O}(\\alpha_{s}^3)$ to form factors with one massive and one massless quark coupling to an external vector, axialvector, scalar, pseudoscalar, or tensor current. We obtain analytic results for the color-planar contributions, for the contributions of light-quark loops, and the contributions with two heavy-quark loops. For the computation of the remaining master integrals we use the \"expand and match\" approach which leads to semi-analytic results for the form factors. We implement our results in a {\\tt Mathematica} and a {\\tt Fortran} code which allows for fast and precise numerical evaluations in the physically relevant phase space. The form factors are used to compute the hard matching coefficients in Soft-Collinear Effective Theory for all currents. The tensor coefficients at light-like momentum transfer are used to extract the hard function in $\\bar B \\to X_s \\gamma$ to three loops.","url_abs":"https://arxiv.org/abs/2406.08182v2","url_pdf":"https://arxiv.org/pdf/2406.08182v2.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":"heavy-to-light-form-factors-to-three-loops","repo_url":"https://gitlab.com/formfactors3l/ffh2l","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}