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In addition we evaluate the twist-3 contribution $d_2$. Our computations make use of $N_f=2+1$ gauge field ensembles generated by the Coordinated Lattice Simulations (CLS) effort. Neglecting quark-line disconnected contributions we obtain as our best estimates $a_2^{(p)}= 0.069(17)$, $d_2^{(p)}= 0.0105(68)$ and $a_2^{(n)}= 0.0068(88)$, $d_2^{(n)}= -0.0009(70)$ for the proton and the neutron, respectively, where we use the normalizations given"},"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":"2111.08306","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2021-11-16T09:00:06Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"f5d7f226b5a20a3f847394de35faa2376cae704e3f02e5d62695cecf3e26c6b0","abstract_canon_sha256":"de304e7e61733ae0f95beb0f83712a7fb4dbb9b9c25f22bc2ea40cdc7e936e47"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:07:27.860438Z","signature_b64":"dfqrpc0DWLFNKBk7x9uqYs1vZrcXlxUsWSrfycLUXINXSzZ+OIiyzbjd6vTDgYn14u2/DZxYgMUKOi1tPAVhAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31e813ec417536bf8ba18d83a70106649656dda710c82943514b68ca1b48156f","last_reissued_at":"2026-07-05T04:07:27.859953Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:07:27.859953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lattice results for the longitudinal spin structure and color forces on quarks in a nucleon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-lat","authors_text":"A. 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Neglecting quark-line disconnected contributions we obtain as our best estimates $a_2^{(p)}= 0.069(17)$, $d_2^{(p)}= 0.0105(68)$ and $a_2^{(n)}= 0.0068(88)$, $d_2^{(n)}= -0.0009(70)$ for the proton and the neutron, respectively, where we use the normalizations given"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.08306","kind":"arxiv","version":2},"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/2111.08306/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":"2111.08306","created_at":"2026-07-05T04:07:27.860008+00:00"},{"alias_kind":"arxiv_version","alias_value":"2111.08306v2","created_at":"2026-07-05T04:07:27.860008+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.08306","created_at":"2026-07-05T04:07:27.860008+00:00"},{"alias_kind":"pith_short_12","alias_value":"GHUBH3CBOU3L","created_at":"2026-07-05T04:07:27.860008+00:00"},{"alias_kind":"pith_short_16","alias_value":"GHUBH3CBOU3L7C5B","created_at":"2026-07-05T04:07:27.860008+00:00"},{"alias_kind":"pith_short_8","alias_value":"GHUBH3CB","created_at":"2026-07-05T04:07:27.860008+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2607.01866","citing_title":"Phenomenology of genuine twist-three distributions from a global QCD analysis","ref_index":65,"is_internal_anchor":false},{"citing_arxiv_id":"2511.09019","citing_title":"The color force acting on a quark in the pion and nucleon","ref_index":39,"is_internal_anchor":false},{"citing_arxiv_id":"2605.02808","citing_title":"Third moments of nucleon unpolarized, polarized, and transversity parton distribution functions from physical-point lattice QCD","ref_index":56,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GHUBH3CBOU3L7C5BRWB2OAIGMS","json":"https://pith.science/pith/GHUBH3CBOU3L7C5BRWB2OAIGMS.json","graph_json":"https://pith.science/api/pith-number/GHUBH3CBOU3L7C5BRWB2OAIGMS/graph.json","events_json":"https://pith.science/api/pith-number/GHUBH3CBOU3L7C5BRWB2OAIGMS/events.json","paper":"https://pith.science/paper/GHUBH3CB"},"agent_actions":{"view_html":"https://pith.science/pith/GHUBH3CBOU3L7C5BRWB2OAIGMS","download_json":"https://pith.science/pith/GHUBH3CBOU3L7C5BRWB2OAIGMS.json","view_paper":"https://pith.science/paper/GHUBH3CB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2111.08306&json=true","fetch_graph":"https://pith.science/api/pith-number/GHUBH3CBOU3L7C5BRWB2OAIGMS/graph.json","fetch_events":"https://pith.science/api/pith-number/GHUBH3CBOU3L7C5BRWB2OAIGMS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GHUBH3CBOU3L7C5BRWB2OAIGMS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GHUBH3CBOU3L7C5BRWB2OAIGMS/action/storage_attestation","attest_author":"https://pith.science/pith/GHUBH3CBOU3L7C5BRWB2OAIGMS/action/author_attestation","sign_citation":"https://pith.science/pith/GHUBH3CBOU3L7C5BRWB2OAIGMS/action/citation_signature","submit_replication":"https://pith.science/pith/GHUBH3CBOU3L7C5BRWB2OAIGMS/action/replication_record"}},"created_at":"2026-07-05T04:07:27.860008+00:00","updated_at":"2026-07-05T04:07:27.860008+00:00"}