{"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/decay-time-integrals-in-neutral-meson-mixing","title":"Decay time integrals in neutral meson mixing and their efficient evaluation","arxiv_id":"1407.0748","date":"2014-07-03","proceeding":null,"authors":["Till Moritz Karbach","Gerhard Raven","Manuel Schiller"],"abstract":"In neutral meson mixing, a certain class of convolution integrals is required whose solution involves the error function $\\mathrm{erf}(z)$ of a complex argument $z$. We show the the general shape of the analytic solution of these integrals, and give expressions which allow the normalisation of these expressions for use in probability density functions. Furthermore, we derive expressions which allow a (decay time) acceptance to be included in these integrals, or allow the calculation of moments. We also describe the implementation of numerical routines which allow the numerical evaluation of $w(z)=e^{-z^2}(1-\\mathrm{erf}(-iz))$, sometimes also called Faddeeva function, in C++. These new routines improve over the old CERNLIB routine(s) WWERF/CWERF in terms of both speed and accuracy. These new routines are part of the RooFit package, and have been distributed with it since ROOT version 5.34/08.","url_abs":"https://arxiv.org/abs/1407.0748v1","url_pdf":"https://arxiv.org/pdf/1407.0748v1.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":"decay-time-integrals-in-neutral-meson-mixing","repo_url":"https://github.com/aoeftiger/faddeevas","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}