Cabibbo angle in a six-quark gauge model

Abstract

General structures of the mass matrices resulting from a quark-Higgs-boson Yukawa interaction are discussed. We assume that there are two sets of Higgs bosons in a six-quark $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_R\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ gauge model and require that the interaction be invariant under a general discrete symmetry. We find three physically acceptable mass matrices including those of Fritzsch and Hagiwara et al. Special attention is paid to the phase of the vacuum expectation value of the Higgs boson, which is related to $\mathrm{CP}$ violation. A mass relation among six quarks, $m_t=m_b{\left(\frac{m_u{m}_c}{m_d{m}_s}\right)}^{\frac{1}{2}}$, is obtained for the latter models. No new mass matrices are found when there are three sets of Higgs bosons.