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Effects of non-zero charm-quark mass in the bottomonium masses are incorporated up to next-to-next-to-leading order. We obtain $\\overline m_c=1246\\pm 2 (d_3) \\pm 4 (\\alpha_s) \\pm 23 (\\text{h.o.} )~{\\rm MeV} $ and $\\overline m_b=4197\\pm 2 (d_3) \\pm 6 (\\alpha_s) \\pm 20 (\\text{h.o.} )\\p"},"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":"1510.07072","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-10-23T21:32:12Z","cross_cats_sorted":[],"title_canon_sha256":"14ff67c1151c87f2bf5e3b4fd980665d59615ca00c0b28a13ca5484bd908fc19","abstract_canon_sha256":"ee1b42ae6501841b91f0ead1dd9859438ec3de388e815c0baae54d0ed5e94f55"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:10.035514Z","signature_b64":"vHeCMF70GSSjqVvwiibhZZbfOORRUWjz9BdobTGR8zAwIfATA+EH0XpJP9B0ASRZt3rJVTi2/M3zm8U4saJ9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04e6ecf8eba80138372e0e56da545cfc35f92f951c9fa4ba66443645243ef031","last_reissued_at":"2026-05-18T00:48:10.034929Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:10.034929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Determination of $m_c$ and $m_b$ from quarkonium 1S energy levels in perturbative QCD","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Go Mishima, Yuichiro Kiyo, Yukinari Sumino","submitted_at":"2015-10-23T21:32:12Z","abstract_excerpt":"We update determination of the $\\overline{\\rm MS}$ masses of the charm and bottom quarks, from comparisons of the masses of the charmonium and bottomonium $1S$ states with their perturbative predictions up to next-to-next-to-next-to-leading order in $\\varepsilon$ expansion and using the $\\overline{\\rm MS}$ masses. Effects of non-zero charm-quark mass in the bottomonium masses are incorporated up to next-to-next-to-leading order. We obtain $\\overline m_c=1246\\pm 2 (d_3) \\pm 4 (\\alpha_s) \\pm 23 (\\text{h.o.} )~{\\rm MeV} $ and $\\overline m_b=4197\\pm 2 (d_3) \\pm 6 (\\alpha_s) \\pm 20 (\\text{h.o.} )\\p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07072","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.07072","created_at":"2026-05-18T00:48:10.035031+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.07072v2","created_at":"2026-05-18T00:48:10.035031+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07072","created_at":"2026-05-18T00:48:10.035031+00:00"},{"alias_kind":"pith_short_12","alias_value":"ATTOZ6HLVAAT","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"ATTOZ6HLVAATQNZO","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"ATTOZ6HL","created_at":"2026-05-18T12:29:10.953037+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.02862","citing_title":"New high-precision $b$, $c$, and $s$ masses from pseudoscalar-pseudoscalar correlators in $n_f=4$ lattice QCD","ref_index":61,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ATTOZ6HLVAATQNZOBZLNUVC47Q","json":"https://pith.science/pith/ATTOZ6HLVAATQNZOBZLNUVC47Q.json","graph_json":"https://pith.science/api/pith-number/ATTOZ6HLVAATQNZOBZLNUVC47Q/graph.json","events_json":"https://pith.science/api/pith-number/ATTOZ6HLVAATQNZOBZLNUVC47Q/events.json","paper":"https://pith.science/paper/ATTOZ6HL"},"agent_actions":{"view_html":"https://pith.science/pith/ATTOZ6HLVAATQNZOBZLNUVC47Q","download_json":"https://pith.science/pith/ATTOZ6HLVAATQNZOBZLNUVC47Q.json","view_paper":"https://pith.science/paper/ATTOZ6HL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.07072&json=true","fetch_graph":"https://pith.science/api/pith-number/ATTOZ6HLVAATQNZOBZLNUVC47Q/graph.json","fetch_events":"https://pith.science/api/pith-number/ATTOZ6HLVAATQNZOBZLNUVC47Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ATTOZ6HLVAATQNZOBZLNUVC47Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ATTOZ6HLVAATQNZOBZLNUVC47Q/action/storage_attestation","attest_author":"https://pith.science/pith/ATTOZ6HLVAATQNZOBZLNUVC47Q/action/author_attestation","sign_citation":"https://pith.science/pith/ATTOZ6HLVAATQNZOBZLNUVC47Q/action/citation_signature","submit_replication":"https://pith.science/pith/ATTOZ6HLVAATQNZOBZLNUVC47Q/action/replication_record"}},"created_at":"2026-05-18T00:48:10.035031+00:00","updated_at":"2026-05-18T00:48:10.035031+00:00"}