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However, the Altarelli-Parisi evolution of the $\\bar b$-quark fragmentation functions $D_{\\bar b \\to B_c}(z)$ and $D_{\\bar b \\to B_c^*}(z)$ from the heavy quark mass scales up to the collider energy scale $Q$ can induce the gluon fragmentation functions $D_{g \\to B_c}(z)$ and $D_{g \\to B_c^*}(z)$, respectively, through the gluon splitting $g\\to \\bar b$ at the order $\\alpha_s^3 \\, {\\rm log} (Q/m_{b,c})$. We will determine these induced gluon fragmentation functions. The $B_c$ meson productions due to the induced gluo"},"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/9312302","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"1993-12-17T23:06:00Z","cross_cats_sorted":[],"title_canon_sha256":"542e89244036dd05e84c76c1801d95de2ce5c216356ead278e9671d734ab8d63","abstract_canon_sha256":"845c1f4a108c13bc32dcd1278703fca9b19220915755030b0ada43a0cd6ad332"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:19.224768Z","signature_b64":"BTOgg4oj+NwquW4MtjxhpLB6wqyHMYb6wAmkR38tpqN5BjnKKFlhWqEX3XHUVadselrAQWq/0NIK6GKUmbBZAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b644b9fb4e4f09de016ed49990a214f8ae932b17fab4ec31e37172f124b68c6f","last_reissued_at":"2026-05-18T02:37:19.224342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:19.224342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$B_c$ Meson Productions Via Induced Gluon Fragmentation","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"kingman Cheung, Tzu Chiang Yuan","submitted_at":"1993-12-17T23:06:00Z","abstract_excerpt":"Gluons cannot directly fragment into $B_c$ mesons until at order $\\alpha_s^3$. 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