{"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/two-loop-form-factors-for-p-wave-quarkonium","title":"Two-loop form factors for $P$-wave quarkonium production and decay","arxiv_id":"2501.04188","date":"2025-01-07","proceeding":null,"authors":["Melih A. Ozcelik"],"abstract":"We present the analytical results for the two-loop form factors needed for $\\chi_{Q,J}$ production and decay. We consider the two-loop corrections to the process $\\gamma \\gamma \\leftrightarrow {^3 P_J^{[1]}}$, that has been known only numerically before, and the processes $gg \\leftrightarrow {^3 P_J^{[1]}}$, $\\gamma g \\leftrightarrow {^3 P_J^{[8]}}$ and $gg \\leftrightarrow {^3 P_J^{[8]}}$, which have not been computed before. We observe that the NRQCD pole structure of the two-loop amplitude in the $gg$ channel is more involved for the spin-triplet $P$-wave case than for the pseudo-scalar $S$-wave case. It involves in addition to the standard Coulomb singularity also a new singularity whose cancellation requires the inclusion of the $gg \\leftrightarrow {^3S_1^{[8]}}$ form factor. We give the high precision numerical results for the hard functions that can be used to compute $\\chi_{Q,J}$ production and decay up to NNLO accuracy.","url_abs":"https://arxiv.org/abs/2501.04188v2","url_pdf":"https://arxiv.org/pdf/2501.04188v2.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":"two-loop-form-factors-for-p-wave-quarkonium","repo_url":"https://gitlab.com/onium_p_wave/two_loop_amplitudes","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}