{"paper":{"title":"Feynman Integral Reduction without Integration-By-Parts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Equivalence relations among Feynman integration contours yield universal reduction formulas for any one-loop integral without integration-by-parts.","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Li Lin Yang, Ziwen Wang","submitted_at":"2024-12-20T14:57:51Z","abstract_excerpt":"We present an interesting study of Feynman integral reduction that does not employ integration-by-parts identities. Our approach proceeds by studying the equivalence relations of integral contours in the Feynman parameterization. We find that the integration contour can take a more general form than that given by the Cheng-Wu theorem. We apply this idea to one-loop integrals, and derive universal reduction formulas that can be used to efficiently reduce any one-loop integral. We expect that this approach can be useful in the reduction of multi-loop integrals as well."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We apply this idea to one-loop integrals, and derive universal reduction formulas that can be used to efficiently reduce any one-loop integral.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that the more general integration contours identified via equivalence relations produce mathematically valid and physically correct reductions for arbitrary one-loop integrals, extending beyond the Cheng-Wu theorem without introducing new errors.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Contour equivalence in Feynman parameterization yields universal reduction formulas for one-loop integrals without integration-by-parts.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Equivalence relations among Feynman integration contours yield universal reduction formulas for any one-loop integral without integration-by-parts.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c5a763863d14b741e4544396cae7f79a26aea39936362cedf6fff5741066fe31"},"source":{"id":"2412.15962","kind":"arxiv","version":3},"verdict":{"id":"4a467722-ceca-49b8-a26f-42062ef66e53","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-23T07:01:40.127821Z","strongest_claim":"We apply this idea to one-loop integrals, and derive universal reduction formulas that can be used to efficiently reduce any one-loop integral.","one_line_summary":"Contour equivalence in Feynman parameterization yields universal reduction formulas for one-loop integrals without integration-by-parts.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that the more general integration contours identified via equivalence relations produce mathematically valid and physically correct reductions for arbitrary one-loop integrals, extending beyond the Cheng-Wu theorem without introducing new errors.","pith_extraction_headline":"Equivalence relations among Feynman integration contours yield universal reduction formulas for any one-loop integral without integration-by-parts."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.15962/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":81,"sample":[{"doi":"","year":1991,"title":"Kotikov,Differential equations method: New technique for massive Feynman diagrams calculation,Phys","work_id":"33186b09-1d15-4e42-9c72-bee9b5b81396","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1991,"title":"Kotikov,Differential equation method: The Calculation of N point Feynman diagrams, Phys","work_id":"b7a0bb2f-9aed-452c-adaf-bc7386c58120","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1997,"title":"Remiddi,Differential equations for Feynman graph amplitudes,Nuovo Cim","work_id":"7868074a-d80a-4d75-8d71-11b3962dcdd3","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2000,"title":"Differential Equations for Two-Loop Four-Point Functions","work_id":"ea2b1724-ca22-4b19-8346-1bfb930b5e78","ref_index":4,"cited_arxiv_id":"hep-ph/9912329","is_internal_anchor":true},{"doi":"","year":2001,"title":"Calculation of master integrals by difference equations","work_id":"e2f94328-3ace-4621-8ea2-d0108da80303","ref_index":5,"cited_arxiv_id":"hep-ph/0102032","is_internal_anchor":true}],"resolved_work":81,"snapshot_sha256":"e79737bb0bb233902837ac49b3e5c5220f1bf80f45a752e1d34d05fb202ecdd6","internal_anchors":31},"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"}