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To improve the accuracy of the sum rules, we expand both the quark propagator and the vertex $(z\\cdot \\tensor{D})^n$ of the correlator up to dimension-six operators in the background field theory. The sum rules for the pion DA moments are obtained, in which all condensates up to dimension-six have been taken into consideration. Using the sum rules, we obtain $\\left<\\xi^2\\right>|_{\\rm 1\\;GeV} = 0.338 \\pm 0.032$, $\\left<\\xi^4\\right>|_{\\rm 1\\;GeV} = 0.211 \\pm 0.030$"},"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":"1405.0774","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2014-05-05T03:44:41Z","cross_cats_sorted":[],"title_canon_sha256":"8e286a1688103fd9ae76bb8ae961021ce818bd6e1501f87c68dc06ec48e7acdf","abstract_canon_sha256":"5353187b5ec761caabae5c898bdd7871a35905811e519918be16246e8c04d473"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:22.871371Z","signature_b64":"eV4fOD2nzetRME1flZy18PxJnY8rb+s5enUSnFurqHTUJmikoawdagZa/LCZMRPAeK5BjrpZkJamTno8s0CICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b70d5dfc4ab0fec7e4ab85ccfeb52739c6d9d316d0699767f65cd0ca34b1b1fd","last_reissued_at":"2026-05-18T02:47:22.870773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:22.870773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Revisiting the Pion Leading-Twist Distribution Amplitude within the QCD Background Field Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Hai-Bing Fu, Hua-Yong Han, Tao Huang, Tao Zhong, Xing-Gang Wu, Zhi-Gang Wang","submitted_at":"2014-05-05T03:44:41Z","abstract_excerpt":"We study the pion leading-twist distribution amplitude (DA) within the framework of SVZ sum rules under the background field theory. 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