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In the SU(2) instanton background of size $\\rho$, the spinor effective action $\\Gamma^F$ (in the minimal subtraction scheme), which gives rise to the prefactor $\\exp (-\\Gamma^F)$, is shown to have the small-$m \\rho$ behavior\n  \\Gamma^F = -\\ln (m /\\mu) - \\ln (\\mu\\rho)/3 -2 \\alpha(1/2) -(m \\rho)^2 \\{\\ln (m \\rho /2) +\\gamma+1/2\\} -2 (m \\rho)^4 \\{-\\ln ^2(m \\rho)/4+\\ln (m \\rho) (1/2-\\gamma +\\ln 2)/2+C \\} +O((m \\rho)^6), where $\\gamma=0.577216...$, $\\alpha(1/2)=0.1458"},"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":"0909.5515","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-09-30T06:16:34Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"50fd122686b3b7e66decccbf60900b94533b321ac52897595dff094d0f6ea5ed","abstract_canon_sha256":"2e9d4842ac22858cce0a6bfa4e1ac41d415d3ba10207525a6d3a79edb0e7fbff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:23:57.485489Z","signature_b64":"1sEatUmwY09I/qC8UN2ldfTH6qgKODe9n4LyZOpL9m4Bcs3leCLDf+VbrkvSvSXUqdueLAhx7Kp5Pfmm5AVTCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1869ea1effded9d0ec43a2c89fdcaa790efbce87a94bc077dc6bb59d0b453203","last_reissued_at":"2026-05-18T03:23:57.484832Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:23:57.484832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytic Form of the QCD Instanton Determinant for Small Quark Mass","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Choonkyu Lee, Hyunsoo Min, Jin Hur","submitted_at":"2009-09-30T06:16:34Z","abstract_excerpt":"We use a novel method to calculate analytically the QCD instanton prefactor due to a quark field carrying a small mass parameter $m$. In the SU(2) instanton background of size $\\rho$, the spinor effective action $\\Gamma^F$ (in the minimal subtraction scheme), which gives rise to the prefactor $\\exp (-\\Gamma^F)$, is shown to have the small-$m \\rho$ behavior\n  \\Gamma^F = -\\ln (m /\\mu) - \\ln (\\mu\\rho)/3 -2 \\alpha(1/2) -(m \\rho)^2 \\{\\ln (m \\rho /2) +\\gamma+1/2\\} -2 (m \\rho)^4 \\{-\\ln ^2(m \\rho)/4+\\ln (m \\rho) (1/2-\\gamma +\\ln 2)/2+C \\} +O((m \\rho)^6), where $\\gamma=0.577216...$, $\\alpha(1/2)=0.1458"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.5515","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":"0909.5515","created_at":"2026-05-18T03:23:57.484944+00:00"},{"alias_kind":"arxiv_version","alias_value":"0909.5515v2","created_at":"2026-05-18T03:23:57.484944+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.5515","created_at":"2026-05-18T03:23:57.484944+00:00"},{"alias_kind":"pith_short_12","alias_value":"DBU6UHX733M5","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_16","alias_value":"DBU6UHX733M5B3CD","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_8","alias_value":"DBU6UHX7","created_at":"2026-05-18T12:25:59.703012+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/DBU6UHX733M5B3CDULEJ7XFKPE","json":"https://pith.science/pith/DBU6UHX733M5B3CDULEJ7XFKPE.json","graph_json":"https://pith.science/api/pith-number/DBU6UHX733M5B3CDULEJ7XFKPE/graph.json","events_json":"https://pith.science/api/pith-number/DBU6UHX733M5B3CDULEJ7XFKPE/events.json","paper":"https://pith.science/paper/DBU6UHX7"},"agent_actions":{"view_html":"https://pith.science/pith/DBU6UHX733M5B3CDULEJ7XFKPE","download_json":"https://pith.science/pith/DBU6UHX733M5B3CDULEJ7XFKPE.json","view_paper":"https://pith.science/paper/DBU6UHX7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0909.5515&json=true","fetch_graph":"https://pith.science/api/pith-number/DBU6UHX733M5B3CDULEJ7XFKPE/graph.json","fetch_events":"https://pith.science/api/pith-number/DBU6UHX733M5B3CDULEJ7XFKPE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DBU6UHX733M5B3CDULEJ7XFKPE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DBU6UHX733M5B3CDULEJ7XFKPE/action/storage_attestation","attest_author":"https://pith.science/pith/DBU6UHX733M5B3CDULEJ7XFKPE/action/author_attestation","sign_citation":"https://pith.science/pith/DBU6UHX733M5B3CDULEJ7XFKPE/action/citation_signature","submit_replication":"https://pith.science/pith/DBU6UHX733M5B3CDULEJ7XFKPE/action/replication_record"}},"created_at":"2026-05-18T03:23:57.484944+00:00","updated_at":"2026-05-18T03:23:57.484944+00:00"}