Implications of the Quark Mass Hierarchy on Flavor Mixings

Abstract

We stress that the observed pattern of flavor mixings can be partly interpreted by the quark mass hierarchy without the assumption of specific quark mass matrices. The quantitatively proper relations between the Kobayashi-Maskawa matrix elements and quark mass ratios, such as $$|V_{cb}| \approx |V_{ts}| \approx \sqrt{2} (\frac{m_s}{m_b} -\frac{m_c}{m_t}) [1 + 3 (\frac{m_s}{m_b} + \frac{m_c}{m_t} ) ],$$ are obtainable from a simple {\it Ansatz} of flavor permutation symmetry breaking at the weak scale. We prescribe the same {\it Ansatz} at the supersymmetric grand unified theory scale, and find that its all low-energy consequences on flavor mixings and $CP$ violation are in good agreement with current experimental data.