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Samuel (McGill, SLAC)","submitted_at":"1996-11-29T10:23:54Z","abstract_excerpt":"We predict that the four-loop contribution \\beta_3 to the QCD \\beta function in the MS-bar prescription is given by\n  \\beta_3\\simeq 23,600(900) - 6,400(200) N_f + 350(70) N_f^2 + 1.5 N_f^3, where N_f is the number of flavours and the coefficient of N_f^3 is an exact result from large-N_f expansion. In the phenomenologically-interesting case N_f=3, we estimate \\beta_3 = (7.6 \\pm 0.1) x 10^3. We discuss our estimates of the errors in these QCD predictions, basing them on the demonstrated accuracy of our method in test applications to the O(N) \\Phi^4 theory, and on variations in the details of ou"},"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":"hep-ph/9612202","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"1996-11-29T10:23:54Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th"],"title_canon_sha256":"63133a22f47dd4e645e767594d72a8706d9d9da71e5e0e71aab260b9156cfb86","abstract_canon_sha256":"e68d6b0d4438c56626e7ff0506bf131886dd77a297ee58b5eac90a62f4358343"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:09.818578Z","signature_b64":"HUfkgj+B0tO1hxOS70xcG6I6XzsIXMiAPV+QMwdIZcOOUITsDR4WMGictDGA9/jzaS7od4ra0ulKVOv8Gga3Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3805c64d4fa064b98a2fdd04d412951e04421f571acebb05f4c59bbbe37d87e9","last_reissued_at":"2026-05-18T01:06:09.817872Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:09.817872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Prediction for the 4-Loop \\beta Function","license":"","headline":"","cross_cats":["cond-mat.stat-mech","hep-th"],"primary_cat":"hep-ph","authors_text":"John Ellis (CERN), Marek Karliner (Tel-Aviv Univ.), Mark. 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