In a general three-family Hermitian quark mass matrix model ($M_u,M_d$), if we take a quark basis on which $M_u$ takes a diagonal form $D_u$, the structure of $M_d\equiv M$ is almost determined by three down-quark masses ($m_d,m_s,m_b$) and three Kobayashi-Maskawa matrix parameters ($\left|V_{\mathrm{us}}\mathrm{}\right|,\left|\mathrm{}{V}_{\mathrm{cb}}\mathrm{}\right|,\left|\mathrm{}{V}_{\mathrm{ub}}\right|$), except for phases of the matrix elements ${\hat{M}}_{\mathrm{ij}}$. By using the experimental facts $\left|V_{\mathrm{us}}\right|\sim \lambda , \left|V_{\mathrm{cb}}\right|\sim {\lambda }^2$, $\left|V_{\mathrm{ub}}\right|\sim {\lambda }^3$, and $\frac{m_d}{m_s}\sim \frac{m_s}{m_b}\sim {\lambda }^2$, the mass matrices ($D_u,\hat{M}$) are presented in terms of a power series in $\lambda$.

• Received 21 August 1992

DOI:https://doi.org/10.1103/PhysRevD.46.R4813