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The amplitudes are extracted directly on the lattice for $N_c = 3-7$ (with preliminar results for $N_c = 8$ and $17$) using twisted mass QCD. It is shown that the (sub-leading) $1/N_c$ corrections to $\\hat B_K$ are small and that the naive $N_c \\to \\infty$ limit, $\\hat B_K = 3/4$, seems to be recovered. On the other hand, the ${\\cal O}\\, (1/N_c)$ corrections in $K \\to \\pi \\pi$ amplitudes (derived from $K \\to \\pi$ matrix elements) a"},"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":"1711.10248","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2017-11-28T12:25:04Z","cross_cats_sorted":[],"title_canon_sha256":"e701fbccb6ca26ea62a5c6bbef0f2b3860d35f1248cdff9cf46d892d6fbd22d6","abstract_canon_sha256":"cb458c46b0688dc35136b88e5b2e44f3d515527713d7a7d593a972a668c713e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:14.920058Z","signature_b64":"FlchBYcRGrio5p9ZIQShRKUrnJbcNC+d+rJjvfOwEzYenXQ+DRbtL8otJ5UbtPLp7w0y3KkkLuWchElI5/DPDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac8af3a2f4502aac45952d5a3ee1be58e1c78e259e1f947d5daffed0a99ad92e","last_reissued_at":"2026-05-18T00:18:14.919536Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:14.919536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-leptonic kaon decays at large $N_c$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-lat","authors_text":"Andrea Donini, Carlos Pena, Fernando Romero-Lopez, Pilar Hernandez","submitted_at":"2017-11-28T12:25:04Z","abstract_excerpt":"We study the scaling with the number of colors $N_c$ of the weak amplitudes mediating kaon mixing and decay, in the limit of light charm masses ($m_u=m_d=m_s=m_c$). 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