{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1992:WQAGASDDTIDTVGITVVGKXH4Y7E","short_pith_number":"pith:WQAGASDD","schema_version":"1.0","canonical_sha256":"b4006048639a073a9913ad4cab9f98f915c9991ab8e0dbb102bf2d741ca06dfd","source":{"kind":"arxiv","id":"hep-ph/9211304","version":1},"attestation_state":"computed","paper":{"title":"The Two-Loop Anomalous Dimension Matrix for $\\Delta S=1$ Weak Non-Leptonic Decays I: ${\\cal O}(\\alpha_s^2)$","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Andrzej J. Buras, Markus E. Lautenbacher, Matthias Jamin, Peter H. Weisz","submitted_at":"1992-11-25T14:03:51Z","abstract_excerpt":"We calculate the two-loop $10 \\times 10$ anomalous dimension matrix ${\\cal O}(\\alpha_s^{2})$ involving current-current operators, QCD penguin operators, and electroweak penguin operators especially relevant for $\\Delta S=1$ weak non-leptonic decays, but also important for $\\Delta B=1$ decays. The calculation is performed in two schemes for $\\gamma_{5}$: the dimensional regularization scheme with anticommuting $\\gamma_{5}$ (NDR), and in the 't Hooft-Veltman scheme. We demonstrate how a direct calculation of diagrams involving $\\gamma_{5}$ in closed fermion loops can be avoided thus allowing a c"},"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/9211304","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"1992-11-25T14:03:51Z","cross_cats_sorted":[],"title_canon_sha256":"00bb5b09c76702179e6c11513dd1bed667d1d9670423e666fef8d5f3098729d0","abstract_canon_sha256":"d9ce64db4e5ced7f4558205eaadfedefcffdb9016d2300bfd6121cb3fef618e3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:55:17.866610Z","signature_b64":"HMThk0+QV6cZj/HqaT3HOo5GrGx3FdE9DbSkJfYc02CHG0kNKK13b8fLXMcSC9apI6WuGuQPnrLg8QqAMR9JBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4006048639a073a9913ad4cab9f98f915c9991ab8e0dbb102bf2d741ca06dfd","last_reissued_at":"2026-07-04T15:55:17.866201Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:55:17.866201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Two-Loop Anomalous Dimension Matrix for $\\Delta S=1$ Weak Non-Leptonic Decays I: ${\\cal O}(\\alpha_s^2)$","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Andrzej J. Buras, Markus E. Lautenbacher, Matthias Jamin, Peter H. Weisz","submitted_at":"1992-11-25T14:03:51Z","abstract_excerpt":"We calculate the two-loop $10 \\times 10$ anomalous dimension matrix ${\\cal O}(\\alpha_s^{2})$ involving current-current operators, QCD penguin operators, and electroweak penguin operators especially relevant for $\\Delta S=1$ weak non-leptonic decays, but also important for $\\Delta B=1$ decays. The calculation is performed in two schemes for $\\gamma_{5}$: the dimensional regularization scheme with anticommuting $\\gamma_{5}$ (NDR), and in the 't Hooft-Veltman scheme. We demonstrate how a direct calculation of diagrams involving $\\gamma_{5}$ in closed fermion loops can be avoided thus allowing a c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9211304","kind":"arxiv","version":1},"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/hep-ph/9211304/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/9211304","created_at":"2026-07-04T15:55:17.866266+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/9211304v1","created_at":"2026-07-04T15:55:17.866266+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/9211304","created_at":"2026-07-04T15:55:17.866266+00:00"},{"alias_kind":"pith_short_12","alias_value":"WQAGASDDTIDT","created_at":"2026-07-04T15:55:17.866266+00:00"},{"alias_kind":"pith_short_16","alias_value":"WQAGASDDTIDTVGIT","created_at":"2026-07-04T15:55:17.866266+00:00"},{"alias_kind":"pith_short_8","alias_value":"WQAGASDD","created_at":"2026-07-04T15:55:17.866266+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.08384","citing_title":"Two-Loop Anomalous Dimensions in the LEFT: Dimension-Six Four-Fermion Operators in NDR","ref_index":14,"is_internal_anchor":true},{"citing_arxiv_id":"2604.24841","citing_title":"Next-to-next-to-leading QCD corrections to the $\\mathbf{B^+}$-$\\mathbf{B_d^0}$, $\\mathbf{D^+}$-$\\mathbf{D^0}$, and $\\mathbf{D_s^+}$-$\\mathbf{D^0}$ lifetime ratios","ref_index":34,"is_internal_anchor":false},{"citing_arxiv_id":"2604.16691","citing_title":"Four-loop QCD mixing of current-current operators","ref_index":26,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WQAGASDDTIDTVGITVVGKXH4Y7E","json":"https://pith.science/pith/WQAGASDDTIDTVGITVVGKXH4Y7E.json","graph_json":"https://pith.science/api/pith-number/WQAGASDDTIDTVGITVVGKXH4Y7E/graph.json","events_json":"https://pith.science/api/pith-number/WQAGASDDTIDTVGITVVGKXH4Y7E/events.json","paper":"https://pith.science/paper/WQAGASDD"},"agent_actions":{"view_html":"https://pith.science/pith/WQAGASDDTIDTVGITVVGKXH4Y7E","download_json":"https://pith.science/pith/WQAGASDDTIDTVGITVVGKXH4Y7E.json","view_paper":"https://pith.science/paper/WQAGASDD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-ph/9211304&json=true","fetch_graph":"https://pith.science/api/pith-number/WQAGASDDTIDTVGITVVGKXH4Y7E/graph.json","fetch_events":"https://pith.science/api/pith-number/WQAGASDDTIDTVGITVVGKXH4Y7E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WQAGASDDTIDTVGITVVGKXH4Y7E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WQAGASDDTIDTVGITVVGKXH4Y7E/action/storage_attestation","attest_author":"https://pith.science/pith/WQAGASDDTIDTVGITVVGKXH4Y7E/action/author_attestation","sign_citation":"https://pith.science/pith/WQAGASDDTIDTVGITVVGKXH4Y7E/action/citation_signature","submit_replication":"https://pith.science/pith/WQAGASDDTIDTVGITVVGKXH4Y7E/action/replication_record"}},"created_at":"2026-07-04T15:55:17.866266+00:00","updated_at":"2026-07-04T15:55:17.866266+00:00"}