Pattern of quark mass matrices and the mixing-angle hierarchy

Abstract

By expressing the quark masses, as well as the quark-mixing angles, in powers of the Cabibbo angle (λ) we show that the up- and down-quark mass matrices are proportional to each other up to terms of order ${\lambda }^2$. This implies that the mass ratio of these two types of quarks should be roughly the same in each generation except for the lightest quarks. We then demonstrate that this is the key ingredient that enables the Fritzsch ansatz for quark mass matrices to reproduce the observed pattern of Kobayashi-Maskawa (KM) mixings and predict that the KM angle ${\mathrm{theta}}_3$=O(${\lambda }^3$). Some of the phenomelogical implications, including that for the kaon CP-violation parameter ε, are worked out.