${1\over m_b}$ and ${1\over m_t}$ Expansion of the Weak Mixing Matrix

Abstract

We perform a $1/m_b$ and $1/m_t$ expansion of the Cabibbo-Kobayashi- Maskawa mixing matrix. Data suggest that the dominant parts of the Yukawa couplings are factorizable into sets of numbers $\vert r>$, $\vert s>$, and $\vert s'>$, associated, respectively, with the left-handed doublets, the right-handed up singlets, and the right- handed down singlets. The first order expansion is consistent with Wolfenstein parameterization, which is an expansion in $sin \theta _c$ to third order. The mixing matrix elements in the present approach are partitioned into factors determined by the relative orientations of $\vert r>$, $\vert s>$, and $\vert s'>$ and the dynamics provided by the subdominant mass matrices. A short discussion is given of some experimental support and a generalized Fritzsch model is used to contrast our approach.