{"paper":{"title":"RI-(S)MOM to $\\overline{\\rm MS}$ conversion for $B_K$ at two-loop order","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-lat"],"primary_cat":"hep-ph","authors_text":"Martin Gorbahn, Sandra Kvedarait\\.e, Sebastian J\\\"ager","submitted_at":"2024-11-29T17:24:30Z","abstract_excerpt":"The Kaon bag parameter $ {\\hat{B}}_K $ plays a critical role in constraining the parameters of the CKM matrix and in probing physics beyond the Standard Model. In this work, we improve the precision of $ \\hat{B}_K $ to next-to-next-to-leading order (NNLO) and provide world averages for both $3$- and $4$-flavour theories. In the course of this, as our main technical development, we carry out the two-loop matching between the RI-(S)MOM and $\\overline{\\mathrm{MS}}$ schemes. Our world averages combine all available lattice data, including conversion between the 3- and 4-flavour theories as appropr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19861","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.19861/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}