Horizontal permutation symmetry, fermion masses, and pseudo-Goldstone bosons inSU(2)L×U(1)

Abstract

We perform a systematic study of all possible $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ models with ${\mathrm{S}}_{3}$ as a horizontal symmetry in an attempt to find a realistic fermion mass matrix for six quarks. The appearance of accidental symmetries in the Higgs potential leads to ambiguities in the tree-level vacuum expectation values and the minimalization of the effective potential is therefore carried out including one-loop corrections. A way of eliminating undesired effects of almost-zero-mass pseudo-Goldstone boson without explicit ${\mathrm{S}}_{3}$ breaking is presented. We suggest a specific $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}_{3}$ model with four Higgs isodoublets. Taking the experimental value of ${sin\ensuremath{\theta}}_{c}$ as an input, the other weak mixing angles are predicted. We find that ${sin\ensuremath{\theta}}_{2}\ensuremath{\simeq}0.14$, ${sin\ensuremath{\theta}}_{3}\ensuremath{\simeq}{10}^{\ensuremath{-}4}$, and $\ensuremath{\delta}=0$. The $B$-meson lifetime is found to be 4.7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ sec and is essentially independent of the $t$-quark mass. $\mathrm{CP}$ violation occurs only by spontaneous breaking. Other topics, such as flavor-changing neutral currents and the Higgs-boson masses, are discussed.