{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:Q5QPC26YMKSFPOVVPYZFIHEWE4","short_pith_number":"pith:Q5QPC26Y","schema_version":"1.0","canonical_sha256":"8760f16bd862a457bab57e32541c962721f89e173b4e653d1eeb0e10304b60ea","source":{"kind":"arxiv","id":"2201.04075","version":1},"attestation_state":"computed","paper":{"title":"Two-loop leading colour helicity amplitudes for $W^\\pm\\gamma+j$ production at the LHC","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Heribertus Bayu Hartanto, Jakub Kry\\'s, Simon Badger, Simone Zoia","submitted_at":"2022-01-11T17:12:32Z","abstract_excerpt":"We present the two-loop leading colour QCD helicity amplitudes for the process $pp\\to W(\\to l\\nu)\\gamma+j$. We implement a complete reduction of the amplitudes, including the leptonic decay of the $W$-boson, using finite field arithmetic, and extract the analytic finite remainders using a recently identified basis of special functions. Simplified analytic expressions are obtained after considering permutations of a rational kinematic parametrisation and multivariate partial fractioning. We demonstrate efficient numerical evaluation of the two-loop colour and helicity summed finite remainders f"},"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":"2201.04075","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2022-01-11T17:12:32Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"64461f3f5b053f884acb0fee2ba93cf674e55edb3ba7bfd9560347ed39df4116","abstract_canon_sha256":"bcbd0d235489c4dd27e8f88114a2a5a088a24ee627c730c7ad6b37bc4c0576cf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:25:52.206503Z","signature_b64":"J/vxAh6tp+Oi4/rY3qImxPOI0t8d/JG0oP151O5V3xW0JiYDLj9q4VJPvf6Uf49FsfcKv1zbRH6ZkQMVZh/TBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8760f16bd862a457bab57e32541c962721f89e173b4e653d1eeb0e10304b60ea","last_reissued_at":"2026-07-05T04:25:52.206032Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:25:52.206032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two-loop leading colour helicity amplitudes for $W^\\pm\\gamma+j$ production at the LHC","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Heribertus Bayu Hartanto, Jakub Kry\\'s, Simon Badger, Simone Zoia","submitted_at":"2022-01-11T17:12:32Z","abstract_excerpt":"We present the two-loop leading colour QCD helicity amplitudes for the process $pp\\to W(\\to l\\nu)\\gamma+j$. We implement a complete reduction of the amplitudes, including the leptonic decay of the $W$-boson, using finite field arithmetic, and extract the analytic finite remainders using a recently identified basis of special functions. Simplified analytic expressions are obtained after considering permutations of a rational kinematic parametrisation and multivariate partial fractioning. We demonstrate efficient numerical evaluation of the two-loop colour and helicity summed finite remainders f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.04075","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2201.04075/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2201.04075","created_at":"2026-07-05T04:25:52.206088+00:00"},{"alias_kind":"arxiv_version","alias_value":"2201.04075v1","created_at":"2026-07-05T04:25:52.206088+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.04075","created_at":"2026-07-05T04:25:52.206088+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q5QPC26YMKSF","created_at":"2026-07-05T04:25:52.206088+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q5QPC26YMKSFPOVV","created_at":"2026-07-05T04:25:52.206088+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q5QPC26Y","created_at":"2026-07-05T04:25:52.206088+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2505.10406","citing_title":"One-loop amplitudes for $t\\bar{t}j$ and $t\\bar{t}\\gamma$ productions at the LHC through $\\mathcal{O}(\\epsilon^2)$","ref_index":40,"is_internal_anchor":false},{"citing_arxiv_id":"2511.11424","citing_title":"Double virtual QCD corrections to $t\\bar{t}+$jet production at the LHC","ref_index":44,"is_internal_anchor":false},{"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":58,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Q5QPC26YMKSFPOVVPYZFIHEWE4","json":"https://pith.science/pith/Q5QPC26YMKSFPOVVPYZFIHEWE4.json","graph_json":"https://pith.science/api/pith-number/Q5QPC26YMKSFPOVVPYZFIHEWE4/graph.json","events_json":"https://pith.science/api/pith-number/Q5QPC26YMKSFPOVVPYZFIHEWE4/events.json","paper":"https://pith.science/paper/Q5QPC26Y"},"agent_actions":{"view_html":"https://pith.science/pith/Q5QPC26YMKSFPOVVPYZFIHEWE4","download_json":"https://pith.science/pith/Q5QPC26YMKSFPOVVPYZFIHEWE4.json","view_paper":"https://pith.science/paper/Q5QPC26Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2201.04075&json=true","fetch_graph":"https://pith.science/api/pith-number/Q5QPC26YMKSFPOVVPYZFIHEWE4/graph.json","fetch_events":"https://pith.science/api/pith-number/Q5QPC26YMKSFPOVVPYZFIHEWE4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q5QPC26YMKSFPOVVPYZFIHEWE4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q5QPC26YMKSFPOVVPYZFIHEWE4/action/storage_attestation","attest_author":"https://pith.science/pith/Q5QPC26YMKSFPOVVPYZFIHEWE4/action/author_attestation","sign_citation":"https://pith.science/pith/Q5QPC26YMKSFPOVVPYZFIHEWE4/action/citation_signature","submit_replication":"https://pith.science/pith/Q5QPC26YMKSFPOVVPYZFIHEWE4/action/replication_record"}},"created_at":"2026-07-05T04:25:52.206088+00:00","updated_at":"2026-07-05T04:25:52.206088+00:00"}