Cabibbo angle in theSU(2)L×U(1)gauge theories

Abstract

If a gauge group without left-right symmetry is supplemented by a finite group $D$ of discrete transformations in order to get a relation between the Cabibbo angle and the masses I show that quarks and Higgs fields cannot be only in one-dimensional representations of $D$ and that at least three Higgs multiplets, either in a triplet or in a doublet and a singlet of $D$, are needed. Then I give an $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ model in which ${\theta }_C\approx \frac{m_d}{m_s}$ and $m_c$, $m_d$, $m_s$, and $m_u$ are free parameters.