{"paper":{"title":"Four-loop Anomalous Dimensions of Scalar-QED Theory from Operator Product Expansion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The OPE algorithm computes the four-loop anomalous dimension of the fixed-charge operator in scalar QED.","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Qingjun Jin, Rijun Huang, Yi Li","submitted_at":"2026-04-15T04:34:17Z","abstract_excerpt":"We apply the Operator Product Expansion (OPE) algorithm to the renormalization of scalar-QED theory, with a specific focus on the fixed-charge operator $\\phi^Q$. Within the OPE framework, the anomalous dimension of the $\\phi^Q$ operator is perturbatively computed to four-loop order in the modified minimal subtraction scheme, extending beyond the previously available three-loop result. The beta functions, as well as the mass and field anomalous dimensions, are also computed at this order. An alternative loop-integrand construction method is proposed, based on graph decomposition and skeleton ex"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Within the OPE framework, the anomalous dimension of the φ^Q operator is perturbatively computed to four-loop order in the modified minimal subtraction scheme, extending beyond the previously available three-loop result.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The OPE algorithm previously used in pure scalar theories applies without new obstructions or additional counterterms when extended to scalar-QED at four loops.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Four-loop anomalous dimension of φ^Q in scalar-QED computed via OPE, extending prior three-loop results and validating the method in a gauge theory.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The OPE algorithm computes the four-loop anomalous dimension of the fixed-charge operator in scalar QED.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a047744e8912a63030b4a2f58e72c190abfe04230d970ef8fcf630edd8e2a08a"},"source":{"id":"2604.13464","kind":"arxiv","version":2},"verdict":{"id":"b8a4a01a-de81-45bb-9da6-f538696e4e95","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T13:36:17.249241Z","strongest_claim":"Within the OPE framework, the anomalous dimension of the φ^Q operator is perturbatively computed to four-loop order in the modified minimal subtraction scheme, extending beyond the previously available three-loop result.","one_line_summary":"Four-loop anomalous dimension of φ^Q in scalar-QED computed via OPE, extending prior three-loop results and validating the method in a gauge theory.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The OPE algorithm previously used in pure scalar theories applies without new obstructions or additional counterterms when extended to scalar-QED at four loops.","pith_extraction_headline":"The OPE algorithm computes the four-loop anomalous dimension of the fixed-charge operator in scalar QED."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.13464/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"}