Perspectives on Quark Mass and Mixing Relations

Abstract

Two down-up perspectives on quark mass-mixing relations are reviewed. The modified Fritzsch path relates $V_{cb}$ and $V_{ub}$ to $M_u$, but has trouble with the low $V_{cb}\simeq 0.04$ value. The modified Wolfenstein path focuses on the change in $V_{ub}$ from ${\lambda }^3(ca.1983)⇝{\lambda }^4(ca.1994)$. The relations $m_d/m_s\sim m_s/m_b\sim \delta \sim {\lambda }^2\simeq |V_{cb}|\simeq |V_{us}{|}^2$ and $m_u/m_c\sim m_c/m_t\sim {\delta }^2\sim {\lambda }^4\sim |V_{ub}|$ suggest a clean separation of the origin of $V_{KM}$: $|V_{us}|\equiv \lambda$ and $|V_{cb}|\equiv \delta$ arise from $M_d$ while $V_{ub}\equiv B{\lambda }^4{e}^{-i\varphi }$ comes from $M_u$. Five to six parameters might suffice for ten mass-mixing parameters, with $\delta$ seemingly the more sensible expansion parameter, while $\lambda \simeq \sqrt{m_d/m_s}$ is tied empirically to $(M_d{)}_{11}=0$. The approximate relations suggest a near weak scale origin of flavor.

Comments: 16 pages, latex, two eps figures (included). [NOTE ADDED: Talk presented at the Workshop on Masses and Mixings of Quarks and Leptons, University of Shizuoka, Japan, March 19 - 21, 1997]