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Both for vector and axial vector currents, we find moderate two-loop corrections below 1\\% in magnitude. Using the Brodsky--Lepage--Mackenzie prescription to set the scale in the order-$\\alpha_s$ corrections in the $\\overline{\\rm MS}$ scheme, we obtain $\\mu_V\\simeq 0"},"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/9409453","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"1994-09-30T11:39:58Z","cross_cats_sorted":[],"title_canon_sha256":"44c49557a397ba79c4d17b2ac599694381034ecd0eea34b0d4c592a4ba327534","abstract_canon_sha256":"5eb5e910ce66841e0e83efff0eb035dda67a6ce0a9cdb2a80028ba72a1cefdb6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:01.525354Z","signature_b64":"gWtGdlbaqSpBv9Y3K1Gd/XPsGLrC502eXEHuQd0cOui4GEDMfyYAzyhIi93pf+s61GdD/jwMgGCDRZbPRh4rDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b99ffb9361d7f6e4c5a88ca1ecf27562e1f3652f7b3f87d512c779ccbe1a125d","last_reissued_at":"2026-05-18T04:31:01.524879Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:01.524879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher-Order Perturbative Corrections to $b\\to c$ Transitions at Zero Recoil","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Matthias Neubert","submitted_at":"1994-09-30T11:39:58Z","abstract_excerpt":"We estimate the two-loop perturbative corrections to zero-recoil matrix elements of the flavour-changing currents $\\bar c\\,\\gamma^\\mu b$ and $\\bar c\\,\\gamma^\\mu\\gamma_5\\,b$ by calculating the terms of order $n_f\\,\\alpha_s^2$ and substituting the dependence on the number of flavours by the first coefficient of the $\\beta$-function. Both for vector and axial vector currents, we find moderate two-loop corrections below 1\\% in magnitude. 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