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This new contribution reduces the theoretical uncertainty in the relevant parameter P_c from +/-22% down to +/-7%, corresponding to scale uncertainties of +/-3% and +/-6% in the short-distance part of the branching ratio and the determination of the Wolfenstein parameter rhobar from K_L -> mu^+ mu^-. The error in P_c = 0.115 +/- 0.018 is now in equal shares due to the combined scale uncertainties and the current uncertainty in the charm-quark mass. We find BR (K_L -> mu^+ mu^-)_SD ="},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"hep-ph/0605203","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2006-05-18T16:58:53Z","cross_cats_sorted":[],"title_canon_sha256":"322befc2413a3b7163a130e5e9ff5a86af684a091281d2398c62903c58881f23","abstract_canon_sha256":"9601d9ef977c57a9bc72c8f96d528bba64ce63f39f37a6e3709c309feab6235c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:12.814512Z","signature_b64":"gCC+NWagQJX3LQrSI5EJ/mat7M9MwGG/OgMsMaxONH4xw4I4xniO4oI9+5wGkcURLO8KGdYCAdQ2JpGgV0u6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a326e41ab8a245c162f0c5156286d076036c9bdbe782a1311935f578699653c","last_reissued_at":"2026-05-18T03:45:12.813852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:12.813852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Charm-Quark Contribution to K_L -> mu^+ mu^- at Next-to-Next-to-Leading","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Martin Gorbahn, Ulrich Haisch","submitted_at":"2006-05-18T16:58:53Z","abstract_excerpt":"We calculate the charm-quark contribution to the decay K_L -> mu^+ mu^- in next-to-next-to-leading order of QCD. 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