{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1997:KWQUBDMI7GVQHIVXT4GS565RLS","short_pith_number":"pith:KWQUBDMI","schema_version":"1.0","canonical_sha256":"55a1408d88f9ab03a2b79f0d2efbb15c8cac667c0f03ad35024b62ab30bcbb68","source":{"kind":"arxiv","id":"hep-ph/9708255","version":2},"attestation_state":"computed","paper":{"title":"Decoupling Relations to O(alpha_s^3) and their Connection to Low-Energy Theorems","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"B.A. Kniehl, K.G. Chetyrkin, M. Steinhauser (MPI Munich)","submitted_at":"1997-08-05T20:36:09Z","abstract_excerpt":"If quantum chromodynamics (QCD) is renormalized by minimal subtraction (MS), at higher orders, the strong coupling constant alpha_s and the quark masses m_q exhibit discontinuities at the flavour thresholds, which are controlled by so-called decoupling constants, zeta_g and zeta_m, respectively. Adopting the modified MS (MS-bar) scheme, we derive simple formulae which reduce the calculation of zeta_g and zeta_m to the solution of vacuum integrals. This allows us to evaluate zeta_g and zeta_m through three loops. We also establish low-energy theorems, valid to all orders, which relate the effec"},"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/9708255","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"1997-08-05T20:36:09Z","cross_cats_sorted":[],"title_canon_sha256":"5272cc9d71cc54ec2e5090f191b802b71bc04c276429713a040c125b9b82e0bd","abstract_canon_sha256":"1fee11a6086f5c9581428d89d53479cfc39f93849dd931e683438df36f80eb4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:05:10.339333Z","signature_b64":"WPHcK8HPUx2DaDHA9zS4WEV0JsUIdfpAWfWIwPcCUy5wDV6YDoH0hVNwN7+XO0sIIds6yEvSPSVfvebFqAzwBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55a1408d88f9ab03a2b79f0d2efbb15c8cac667c0f03ad35024b62ab30bcbb68","last_reissued_at":"2026-07-04T16:05:10.338870Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:05:10.338870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decoupling Relations to O(alpha_s^3) and their Connection to Low-Energy Theorems","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"B.A. Kniehl, K.G. Chetyrkin, M. Steinhauser (MPI Munich)","submitted_at":"1997-08-05T20:36:09Z","abstract_excerpt":"If quantum chromodynamics (QCD) is renormalized by minimal subtraction (MS), at higher orders, the strong coupling constant alpha_s and the quark masses m_q exhibit discontinuities at the flavour thresholds, which are controlled by so-called decoupling constants, zeta_g and zeta_m, respectively. Adopting the modified MS (MS-bar) scheme, we derive simple formulae which reduce the calculation of zeta_g and zeta_m to the solution of vacuum integrals. This allows us to evaluate zeta_g and zeta_m through three loops. We also establish low-energy theorems, valid to all orders, which relate the effec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9708255","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/hep-ph/9708255/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/9708255","created_at":"2026-07-04T16:05:10.338945+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/9708255v2","created_at":"2026-07-04T16:05:10.338945+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/9708255","created_at":"2026-07-04T16:05:10.338945+00:00"},{"alias_kind":"pith_short_12","alias_value":"KWQUBDMI7GVQ","created_at":"2026-07-04T16:05:10.338945+00:00"},{"alias_kind":"pith_short_16","alias_value":"KWQUBDMI7GVQHIVX","created_at":"2026-07-04T16:05:10.338945+00:00"},{"alias_kind":"pith_short_8","alias_value":"KWQUBDMI","created_at":"2026-07-04T16:05:10.338945+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":8,"internal_anchor_count":5,"sample":[{"citing_arxiv_id":"2606.27022","citing_title":"Dyeing form factors as amplitudes","ref_index":16,"is_internal_anchor":true},{"citing_arxiv_id":"2606.12929","citing_title":"Double copy of form factors with multiple operator insertions","ref_index":25,"is_internal_anchor":true},{"citing_arxiv_id":"2606.28494","citing_title":"Soft Contributions Stabilize NNLO QCD Corrections to Quarkonium Production and Decay","ref_index":36,"is_internal_anchor":true},{"citing_arxiv_id":"2508.02862","citing_title":"New high-precision $b$, $c$, and $s$ masses from pseudoscalar-pseudoscalar correlators in $n_f=4$ lattice QCD","ref_index":44,"is_internal_anchor":true},{"citing_arxiv_id":"2603.29803","citing_title":"Perturbative QCD fitting of KEDR and BESIII $e^+e^-$ data for R(s) and $\\alpha_s$ determination","ref_index":75,"is_internal_anchor":true},{"citing_arxiv_id":"2605.04009","citing_title":"Two-loop leading-color QCD corrections for Higgs plus two-jet production in the heavy-top limit","ref_index":71,"is_internal_anchor":false},{"citing_arxiv_id":"2604.23526","citing_title":"Smooth Threshold Effects from Dimensional Regularization","ref_index":12,"is_internal_anchor":false},{"citing_arxiv_id":"2604.10889","citing_title":"Heavy-quark transport across the QCD crossover driven by a lattice-constrained in-medium potential","ref_index":36,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KWQUBDMI7GVQHIVXT4GS565RLS","json":"https://pith.science/pith/KWQUBDMI7GVQHIVXT4GS565RLS.json","graph_json":"https://pith.science/api/pith-number/KWQUBDMI7GVQHIVXT4GS565RLS/graph.json","events_json":"https://pith.science/api/pith-number/KWQUBDMI7GVQHIVXT4GS565RLS/events.json","paper":"https://pith.science/paper/KWQUBDMI"},"agent_actions":{"view_html":"https://pith.science/pith/KWQUBDMI7GVQHIVXT4GS565RLS","download_json":"https://pith.science/pith/KWQUBDMI7GVQHIVXT4GS565RLS.json","view_paper":"https://pith.science/paper/KWQUBDMI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-ph/9708255&json=true","fetch_graph":"https://pith.science/api/pith-number/KWQUBDMI7GVQHIVXT4GS565RLS/graph.json","fetch_events":"https://pith.science/api/pith-number/KWQUBDMI7GVQHIVXT4GS565RLS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KWQUBDMI7GVQHIVXT4GS565RLS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KWQUBDMI7GVQHIVXT4GS565RLS/action/storage_attestation","attest_author":"https://pith.science/pith/KWQUBDMI7GVQHIVXT4GS565RLS/action/author_attestation","sign_citation":"https://pith.science/pith/KWQUBDMI7GVQHIVXT4GS565RLS/action/citation_signature","submit_replication":"https://pith.science/pith/KWQUBDMI7GVQHIVXT4GS565RLS/action/replication_record"}},"created_at":"2026-07-04T16:05:10.338945+00:00","updated_at":"2026-07-04T16:05:10.338945+00:00"}