{"paper":{"title":"Hierarchies of quark masses and the mixing matrix in the standard theory","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"B. Machet, S.T. Petcov","submitted_at":"2001-03-30T12:25:59Z","abstract_excerpt":"We study the general dependence of mixing angles on heavy fermion masses when mass hierarchies exist among the fermions. For two generations and small Cabibbo angle, this angle is directly shown to scale like $\\mu_1/m_s \\pm \\mu_2/m_c$, where $|\\mu_1| \\ll m_s, |\\mu_2| \\ll m_c$ are independent mass scales. For $n=3$ generations, we extend to the Yukawa matrices of $u$- and $d$-type quarks the property that the $2\\times 2$ upper-left sub-matrix of the Cabibbo-Kobayashi-Maskawa matrix $K$ is a good approximation to the Cabibbo matrix $C$. Then, without any additional Ansatz concerning the existenc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0103334","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"}