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The vertex function with one off-shell gluon is shown to have the form (valid for $| q_1^2 | > m_{\\eta^\\prime}^2$) $F_{\\eta^\\prime g^* g} (q_1^2, 0, m_{\\eta^\\prime}^2) = m_{\\eta^\\prime}^2 H(q_1^2)/(q_1^2 - m_{\\eta^\\prime}^2)$, where $H(q_1^2)$ is a "},"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/0307092","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2003-07-07T16:19:38Z","cross_cats_sorted":[],"title_canon_sha256":"f2d9ba69e3dcfb1d3d2b2b549d1b77442265d8ddf63f05f80e909addbb15465e","abstract_canon_sha256":"02c6bd8ea41b3b5013297b2a6485de10845b5b4d4cff8f6b441724a595439591"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:36.737907Z","signature_b64":"/NfJrI9ssZ8Ui7YbPnNAUUh9eOPETsQ07P+F7gMfN+FEJ+qa9SrK0m8q8qaUvMpz5jdgkbkyw8BE9kcY8dr6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22ef1e7c1b0971e5642c9df4c94b10e2962236e89e37e259b6afeba75303b683","last_reissued_at":"2026-05-18T04:13:36.737182Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:36.737182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $\\eta^\\prime g^* g^{(*)}$ Vertex Including the $\\eta^\\prime$-Meson Mass","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"A. 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The vertex function with one off-shell gluon is shown to have the form (valid for $| q_1^2 | > m_{\\eta^\\prime}^2$) $F_{\\eta^\\prime g^* g} (q_1^2, 0, m_{\\eta^\\prime}^2) = m_{\\eta^\\prime}^2 H(q_1^2)/(q_1^2 - m_{\\eta^\\prime}^2)$, where $H(q_1^2)$ is a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0307092","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":""},"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/0307092","created_at":"2026-05-18T04:13:36.737312+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0307092v1","created_at":"2026-05-18T04:13:36.737312+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0307092","created_at":"2026-05-18T04:13:36.737312+00:00"},{"alias_kind":"pith_short_12","alias_value":"ELXR47A3BFY6","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_16","alias_value":"ELXR47A3BFY6KZBM","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_8","alias_value":"ELXR47A3","created_at":"2026-05-18T12:25:51.375804+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.15224","citing_title":"Investigate the glueball-like particle $X(2370)$ in $B$ meson decays","ref_index":52,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ELXR47A3BFY6KZBMTX2MSSYQ4K","json":"https://pith.science/pith/ELXR47A3BFY6KZBMTX2MSSYQ4K.json","graph_json":"https://pith.science/api/pith-number/ELXR47A3BFY6KZBMTX2MSSYQ4K/graph.json","events_json":"https://pith.science/api/pith-number/ELXR47A3BFY6KZBMTX2MSSYQ4K/events.json","paper":"https://pith.science/paper/ELXR47A3"},"agent_actions":{"view_html":"https://pith.science/pith/ELXR47A3BFY6KZBMTX2MSSYQ4K","download_json":"https://pith.science/pith/ELXR47A3BFY6KZBMTX2MSSYQ4K.json","view_paper":"https://pith.science/paper/ELXR47A3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-ph/0307092&json=true","fetch_graph":"https://pith.science/api/pith-number/ELXR47A3BFY6KZBMTX2MSSYQ4K/graph.json","fetch_events":"https://pith.science/api/pith-number/ELXR47A3BFY6KZBMTX2MSSYQ4K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ELXR47A3BFY6KZBMTX2MSSYQ4K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ELXR47A3BFY6KZBMTX2MSSYQ4K/action/storage_attestation","attest_author":"https://pith.science/pith/ELXR47A3BFY6KZBMTX2MSSYQ4K/action/author_attestation","sign_citation":"https://pith.science/pith/ELXR47A3BFY6KZBMTX2MSSYQ4K/action/citation_signature","submit_replication":"https://pith.science/pith/ELXR47A3BFY6KZBMTX2MSSYQ4K/action/replication_record"}},"created_at":"2026-05-18T04:13:36.737312+00:00","updated_at":"2026-05-18T04:13:36.737312+00:00"}