Perspective on Quark Mass and Mixing Relations

Abstract

Recent data indicate that $V_{ub}\cong {\lambda }^4\cong (0.22{)}^4$, while $m_t$ seems to be $174$ GeV. The relations $m_d/m_s\sim m_s/m_b\sim \delta \sim {\lambda }^2\simeq |V_{cb}|$ and $m_u/m_c\sim m_c/m_t\sim {\delta }^2\sim {\lambda }^4\sim |V_{ub}|$ suggest that %a plausible clean separation of the %origin of the quark mixing matrix: the down type sector is responsible for $|V_{us}|$ and $|V_{cb}|$, while $V_{ub}$ comes from the up type sector. Five to six parameters might suffice to account for the ten quark mass and mixing parameters, resulting in specific power series representations for the mass matrices. In this picture, $\delta$ seems to be the more sensible expansion parameter, while $\lambda \cong \sqrt{m_d/m_s}\sim \sqrt{\delta }$ is tied empirically to $(M_d{)}_{11}=0$.

Comments: 10 pages, ReVtex, no figures