{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:Y7PRCLBFXWXR36LGRXL7M5DECN","short_pith_number":"pith:Y7PRCLBF","schema_version":"1.0","canonical_sha256":"c7df112c25bdaf1df9668dd7f674641368b2f699796be8976221773ac1c03705","source":{"kind":"arxiv","id":"2409.09667","version":3},"attestation_state":"computed","paper":{"title":"Evolution of unpolarized transverse momentum dependent parton distributions of twist-3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"An-Ping Chen, Ping-An Liu, Xue-Tao Liu, Yu-Lu Liu","submitted_at":"2024-09-15T08:39:10Z","abstract_excerpt":"We revisit the calculation of the evolution equations for four unpolarized twist-3 transverse momentum dependent (TMD) parton distribution functions (PDFs) at $\\mathcal {O}(\\alpha_s)$. Unlike the existing calculations in the literature, which are based on the background field method, we derive the evolution equations directly through diagram expansion. Additionally, instead of using the $\\delta$ regulator, we employ the exponential regulator to regularize the rapidity divergences. We find that the evolutions of the four twist-3 TMD PDFs are governed by eight homogeneous equations. Our evolutio"},"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":"2409.09667","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2024-09-15T08:39:10Z","cross_cats_sorted":[],"title_canon_sha256":"3acf9826f997364be8dc643e0673fd02b9f6ddd22183ae7501cbe52dbddf438d","abstract_canon_sha256":"80a2e996f7d60097c22515d3df0d93fdc5fa2c90d44114d43c8b17924a05d4d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:29:01.719254Z","signature_b64":"ZNpj/vNxchqSQGTD+bcrVvF86GYDW5gDE2qGs2xsnUJfobdz38ZBKHcONj9F2abfm/G0tWola2W63HV+c5VIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7df112c25bdaf1df9668dd7f674641368b2f699796be8976221773ac1c03705","last_reissued_at":"2026-07-05T11:29:01.718615Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:29:01.718615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Evolution of unpolarized transverse momentum dependent parton distributions of twist-3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"An-Ping Chen, Ping-An Liu, Xue-Tao Liu, Yu-Lu Liu","submitted_at":"2024-09-15T08:39:10Z","abstract_excerpt":"We revisit the calculation of the evolution equations for four unpolarized twist-3 transverse momentum dependent (TMD) parton distribution functions (PDFs) at $\\mathcal {O}(\\alpha_s)$. Unlike the existing calculations in the literature, which are based on the background field method, we derive the evolution equations directly through diagram expansion. Additionally, instead of using the $\\delta$ regulator, we employ the exponential regulator to regularize the rapidity divergences. We find that the evolutions of the four twist-3 TMD PDFs are governed by eight homogeneous equations. Our evolutio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.09667","kind":"arxiv","version":3},"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/2409.09667/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":"2409.09667","created_at":"2026-07-05T11:29:01.718693+00:00"},{"alias_kind":"arxiv_version","alias_value":"2409.09667v3","created_at":"2026-07-05T11:29:01.718693+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.09667","created_at":"2026-07-05T11:29:01.718693+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y7PRCLBFXWXR","created_at":"2026-07-05T11:29:01.718693+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y7PRCLBFXWXR36LG","created_at":"2026-07-05T11:29:01.718693+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y7PRCLBF","created_at":"2026-07-05T11:29:01.718693+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.03072","citing_title":"Soft background fields at next-to-leading power in transverse momentum dependent SIDIS with jets","ref_index":57,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y7PRCLBFXWXR36LGRXL7M5DECN","json":"https://pith.science/pith/Y7PRCLBFXWXR36LGRXL7M5DECN.json","graph_json":"https://pith.science/api/pith-number/Y7PRCLBFXWXR36LGRXL7M5DECN/graph.json","events_json":"https://pith.science/api/pith-number/Y7PRCLBFXWXR36LGRXL7M5DECN/events.json","paper":"https://pith.science/paper/Y7PRCLBF"},"agent_actions":{"view_html":"https://pith.science/pith/Y7PRCLBFXWXR36LGRXL7M5DECN","download_json":"https://pith.science/pith/Y7PRCLBFXWXR36LGRXL7M5DECN.json","view_paper":"https://pith.science/paper/Y7PRCLBF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2409.09667&json=true","fetch_graph":"https://pith.science/api/pith-number/Y7PRCLBFXWXR36LGRXL7M5DECN/graph.json","fetch_events":"https://pith.science/api/pith-number/Y7PRCLBFXWXR36LGRXL7M5DECN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y7PRCLBFXWXR36LGRXL7M5DECN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y7PRCLBFXWXR36LGRXL7M5DECN/action/storage_attestation","attest_author":"https://pith.science/pith/Y7PRCLBFXWXR36LGRXL7M5DECN/action/author_attestation","sign_citation":"https://pith.science/pith/Y7PRCLBFXWXR36LGRXL7M5DECN/action/citation_signature","submit_replication":"https://pith.science/pith/Y7PRCLBFXWXR36LGRXL7M5DECN/action/replication_record"}},"created_at":"2026-07-05T11:29:01.718693+00:00","updated_at":"2026-07-05T11:29:01.718693+00:00"}