{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:QMUW4R225DWST7ADAGBDMHSKT5","short_pith_number":"pith:QMUW4R22","schema_version":"1.0","canonical_sha256":"83296e475ae8ed29fc030182361e4a9f6239528719eb133f9fcbc9b9993717f4","source":{"kind":"arxiv","id":"1610.07059","version":2},"attestation_state":"computed","paper":{"title":"30 years, some 700 integrals, and 1 dessert, or: Electroweak two-loop corrections to the Zbb vertex","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"A. Freitas (Univ. Pittsburgh), I. Dubovyk (Univ. Hamburg), J. Gluza (Univ. Katowice), J. Usovitsch (Humboldt-Univ. zu Berlin), T. Riemann (K\\\"onigs Wusterhausen, Univ. Katowice)","submitted_at":"2016-10-22T14:52:53Z","abstract_excerpt":"The one-loop corrections to the weak mixing angle $\\sin^2\\theta_{eff}^b$ derived from the $Z{\\bar b}b$ vertex, are known since 1985. It took another 30 years to calculate the complete electroweak two-loop corrections to $\\sin^2\\theta_{eff}^b$. The main obstacle was the calculation of the O(700) bosonic two-loop vertex integrals with up to three mass scales, at $s=M_Z^2$. We did not perform the usual integral reduction and master evaluation, but chose a completely numerical approach, using two different calculational chains. One method relies on publicly available sector decomposition implement"},"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":"1610.07059","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"hep-ph","submitted_at":"2016-10-22T14:52:53Z","cross_cats_sorted":[],"title_canon_sha256":"25b29e88bfd4bf9f3d90bc931f6e9f987dec3b2346fb6293c86f08a0ffd3570c","abstract_canon_sha256":"81c91f1e79a96c34f2c4cdf31718d074eed985c70e6a782eb2cf95817de5aa55"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:05.281305Z","signature_b64":"btA4ClK3CE1326P9YcHx2+dqWsGkthrzobgvv3grbruIGDlFmoImXDovscxK+dSHxVt3+U7MaKMg943u0MJBCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83296e475ae8ed29fc030182361e4a9f6239528719eb133f9fcbc9b9993717f4","last_reissued_at":"2026-05-18T01:00:05.280771Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:05.280771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"30 years, some 700 integrals, and 1 dessert, or: Electroweak two-loop corrections to the Zbb vertex","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"A. Freitas (Univ. Pittsburgh), I. Dubovyk (Univ. Hamburg), J. Gluza (Univ. Katowice), J. Usovitsch (Humboldt-Univ. zu Berlin), T. Riemann (K\\\"onigs Wusterhausen, Univ. Katowice)","submitted_at":"2016-10-22T14:52:53Z","abstract_excerpt":"The one-loop corrections to the weak mixing angle $\\sin^2\\theta_{eff}^b$ derived from the $Z{\\bar b}b$ vertex, are known since 1985. It took another 30 years to calculate the complete electroweak two-loop corrections to $\\sin^2\\theta_{eff}^b$. The main obstacle was the calculation of the O(700) bosonic two-loop vertex integrals with up to three mass scales, at $s=M_Z^2$. We did not perform the usual integral reduction and master evaluation, but chose a completely numerical approach, using two different calculational chains. One method relies on publicly available sector decomposition implement"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07059","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.07059","created_at":"2026-05-18T01:00:05.280868+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.07059v2","created_at":"2026-05-18T01:00:05.280868+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07059","created_at":"2026-05-18T01:00:05.280868+00:00"},{"alias_kind":"pith_short_12","alias_value":"QMUW4R225DWS","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"QMUW4R225DWST7AD","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"QMUW4R22","created_at":"2026-05-18T12:30:39.010887+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QMUW4R225DWST7ADAGBDMHSKT5","json":"https://pith.science/pith/QMUW4R225DWST7ADAGBDMHSKT5.json","graph_json":"https://pith.science/api/pith-number/QMUW4R225DWST7ADAGBDMHSKT5/graph.json","events_json":"https://pith.science/api/pith-number/QMUW4R225DWST7ADAGBDMHSKT5/events.json","paper":"https://pith.science/paper/QMUW4R22"},"agent_actions":{"view_html":"https://pith.science/pith/QMUW4R225DWST7ADAGBDMHSKT5","download_json":"https://pith.science/pith/QMUW4R225DWST7ADAGBDMHSKT5.json","view_paper":"https://pith.science/paper/QMUW4R22","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.07059&json=true","fetch_graph":"https://pith.science/api/pith-number/QMUW4R225DWST7ADAGBDMHSKT5/graph.json","fetch_events":"https://pith.science/api/pith-number/QMUW4R225DWST7ADAGBDMHSKT5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QMUW4R225DWST7ADAGBDMHSKT5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QMUW4R225DWST7ADAGBDMHSKT5/action/storage_attestation","attest_author":"https://pith.science/pith/QMUW4R225DWST7ADAGBDMHSKT5/action/author_attestation","sign_citation":"https://pith.science/pith/QMUW4R225DWST7ADAGBDMHSKT5/action/citation_signature","submit_replication":"https://pith.science/pith/QMUW4R225DWST7ADAGBDMHSKT5/action/replication_record"}},"created_at":"2026-05-18T01:00:05.280868+00:00","updated_at":"2026-05-18T01:00:05.280868+00:00"}