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Writing the $y^n$ moments of $Q(y, P_3)$ in terms of the combined $x^{n-2l} k_\\perp^{2l}$-moments of the transverse momentum distribution (TMD) ${\\cal F} (x,k_\\perp^2)$, we establish a connection between the large-$|y|$ behavior of $Q(y,P_3)$ and large-$k_\\perp^2$ behavior of ${\\cal F} (x,k_\\perp^2)$. In particular, we show that the $1/k_\\perp^2$ hard tail of TMDs in QCD results in a slowly decreasing $\\"},"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":"1807.07509","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-07-19T16:01:23Z","cross_cats_sorted":["hep-lat"],"title_canon_sha256":"87cd63c196c1ccdf018fb6e5d61e40b3e8107bd4769a30479baf768e5724aa91","abstract_canon_sha256":"73f312a8daa573a8bbd0891911e893098e1cac83c8d718211309fdebb4baa946"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:40.772858Z","signature_b64":"QyJNFEu4adv4TgOsvwpw8ac+QduZkXcLA3nfLjPf8+FoqrgdsD1Sym4OQMm1HgLcOSykhQ/SSv08nlz4EnnoCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35e594909831d5744aa798b6fae41125ffbf5630c03b48555f4b224154b76f0b","last_reissued_at":"2026-05-17T23:57:40.772254Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:40.772254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Structure of parton quasi-distributions and their moments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat"],"primary_cat":"hep-ph","authors_text":"Anatoly Radyushkin","submitted_at":"2018-07-19T16:01:23Z","abstract_excerpt":"We discuss the structure of the parton quasi-distributions (quasi-PDFs) $Q(y, P_3)$ outside the \"canonical\" $-1 \\leq y \\leq 1$ support region of the usual parton distribution functions (PDFs). 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