Four-generation model based on an S4 permutation symmetry.

Abstract

We consider an ${\mathrm{S}}_{4}$ family-symmetry model with four generations of leptons and quarks. A mass relation of the form $\frac{{m}_{L}}{{m}_{\ensuremath{\tau}}}=\frac{{m}_{v}}{{m}_{b}}=\frac{{m}_{a}}{{m}_{t}}$ is obtained. The predicted values of individual 4\ifmmode\times\else\texttimes\fi{}4 Kobayashi-Maskawa matrix elements are within recent experimental data. If the charged-lepton mass of the fourth generation is at 30 GeV and the $t$-quark mass is at 35 GeV, the masses of the $d$- and $u$-type quarks of the fourth generation are predicted to be 73\ifmmode\pm\else\textpm\fi{}2 GeV and 523\ifmmode\pm\else\textpm\fi{}3 GeV, respectively, taking account of the renormalization-group effect.