{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:JVRL75NSVFJLJ46ABL37QXUUQV","short_pith_number":"pith:JVRL75NS","schema_version":"1.0","canonical_sha256":"4d62bff5b2a952b4f3c00af7f85e948576463bcb10c1b038bc7a1ec22d311b0d","source":{"kind":"arxiv","id":"0712.1851","version":4},"attestation_state":"computed","paper":{"title":"Scalar one-loop integrals for QCD","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Giulia Zanderighi, R. Keith Ellis","submitted_at":"2007-12-12T17:26:45Z","abstract_excerpt":"We construct a basis set of infra-red and/or collinearly divergent scalar one-loop integrals and give analytic formulas, for tadpole, bubble, triangle and box integrals, regulating the divergences (ultra-violet, infra-red or collinear) by regularization in $D=4-2\\epsilon$ dimensions. For scalar triangle integrals we give results for our basis set containing 6 divergent integrals. For scalar box integrals we give results for our basis set containing 16 divergent integrals. We provide analytic results for the 5 divergent box integrals in the basis set which are missing in the literature. Buildin"},"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":"0712.1851","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2007-12-12T17:26:45Z","cross_cats_sorted":[],"title_canon_sha256":"3437bd509b4b150b2517280cf1820fbe0a77b25c01e878d425b05c2167649791","abstract_canon_sha256":"5820c2348fcf15f027a99c26c71dd571eaf865dbf60736fd2433623091b8cc71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:12.522408Z","signature_b64":"pM4EZbY1NMB1LXtpAiF5e5SlbvTdgz/s+XGs/OVoeUOWleTPV4QEjkAN+RLjooHmToG6OW3jGjTsqOnDZlw9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d62bff5b2a952b4f3c00af7f85e948576463bcb10c1b038bc7a1ec22d311b0d","last_reissued_at":"2026-05-18T04:19:12.521855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:12.521855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scalar one-loop integrals for QCD","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Giulia Zanderighi, R. Keith Ellis","submitted_at":"2007-12-12T17:26:45Z","abstract_excerpt":"We construct a basis set of infra-red and/or collinearly divergent scalar one-loop integrals and give analytic formulas, for tadpole, bubble, triangle and box integrals, regulating the divergences (ultra-violet, infra-red or collinear) by regularization in $D=4-2\\epsilon$ dimensions. For scalar triangle integrals we give results for our basis set containing 6 divergent integrals. For scalar box integrals we give results for our basis set containing 16 divergent integrals. We provide analytic results for the 5 divergent box integrals in the basis set which are missing in the literature. Buildin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1851","kind":"arxiv","version":4},"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":"0712.1851","created_at":"2026-05-18T04:19:12.521938+00:00"},{"alias_kind":"arxiv_version","alias_value":"0712.1851v4","created_at":"2026-05-18T04:19:12.521938+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1851","created_at":"2026-05-18T04:19:12.521938+00:00"},{"alias_kind":"pith_short_12","alias_value":"JVRL75NSVFJL","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"JVRL75NSVFJLJ46A","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"JVRL75NS","created_at":"2026-05-18T12:25:55.427421+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"1906.11862","citing_title":"A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons","ref_index":92,"is_internal_anchor":true},{"citing_arxiv_id":"2511.11537","citing_title":"Two-loop all-plus helicity amplitudes for self-dual Higgs boson with gluons via unitarity cut constraints","ref_index":96,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JVRL75NSVFJLJ46ABL37QXUUQV","json":"https://pith.science/pith/JVRL75NSVFJLJ46ABL37QXUUQV.json","graph_json":"https://pith.science/api/pith-number/JVRL75NSVFJLJ46ABL37QXUUQV/graph.json","events_json":"https://pith.science/api/pith-number/JVRL75NSVFJLJ46ABL37QXUUQV/events.json","paper":"https://pith.science/paper/JVRL75NS"},"agent_actions":{"view_html":"https://pith.science/pith/JVRL75NSVFJLJ46ABL37QXUUQV","download_json":"https://pith.science/pith/JVRL75NSVFJLJ46ABL37QXUUQV.json","view_paper":"https://pith.science/paper/JVRL75NS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0712.1851&json=true","fetch_graph":"https://pith.science/api/pith-number/JVRL75NSVFJLJ46ABL37QXUUQV/graph.json","fetch_events":"https://pith.science/api/pith-number/JVRL75NSVFJLJ46ABL37QXUUQV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JVRL75NSVFJLJ46ABL37QXUUQV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JVRL75NSVFJLJ46ABL37QXUUQV/action/storage_attestation","attest_author":"https://pith.science/pith/JVRL75NSVFJLJ46ABL37QXUUQV/action/author_attestation","sign_citation":"https://pith.science/pith/JVRL75NSVFJLJ46ABL37QXUUQV/action/citation_signature","submit_replication":"https://pith.science/pith/JVRL75NSVFJLJ46ABL37QXUUQV/action/replication_record"}},"created_at":"2026-05-18T04:19:12.521938+00:00","updated_at":"2026-05-18T04:19:12.521938+00:00"}