Discrete symmetries in the six-quark SU(2) × U(1) model

Abstract

If a discrete symmetry $D$ is imposed upon the six-quark-six-lepton SU(2) \ifmmode\times\else\texttimes\fi{} U(1) model such that all SU(2) \ifmmode\times\else\texttimes\fi{} U(1)-equivalent fermions are unified in one irreducible representation of $D$, then it is argued that $D$ is quite uniquely determined. A model is constructed in which all the mixing angles are functions of mass ratios. Cabibbo universality is well satisfied with ${\ensuremath{\theta}}_{C}\ensuremath{\approx}{(\frac{{m}_{d}}{{m}_{s}})}^{\frac{1}{2}}$. The lifetime of $b$ is found to be 4 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}9}$ sec; the ratio $\frac{\ensuremath{\Gamma}(b\ensuremath{\rightarrow}c+\mathrm{leptons})}{\ensuremath{\Gamma}(b\ensuremath{\rightarrow}u+\mathrm{leptons})}$ is 2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}3}$. The mass of the $t$ quark is predicted to lie between 12 and 21 GeV; $\mathrm{CP}$ violation arises in the gauge sector as well as in the Yukawa interactions. Some results pertaining to the breaking of discrete symmetries are also given.