SU(8) theory of multigenerational grand unification

Abstract

As a concrete example of $\mathrm{SU}(N)$ theory of grand unification, an SU(8) model which contains three generations of light fermions and three new generations of heavy fermions (one of which lacks a toplike quark) are presented. The model consists of ${\overline{8}}_{L}$, ${\stackrel{-}{28}}_{L}$, and ${56}_{L}$ representations of fermions, and it requires 63 gauge bosons with new generation vector bosons and an extra boson ${Z}^{{0}^{\ensuremath{'}}}$ in addition to the $\ensuremath{\gamma}$, $W$, ${Z}^{0}$, $X$, and $Y$ bosons in the standard SU(5) model. It satisfactorily embeds all features of the SU(5) model extended to three generations of light fermions, and predicts new interactions such as quantum generation dynamics, which changes generation. This interaction can cause various mixing angles among fermions. The complete gauge interactions and the masses of gauge bosons as well as fermions are derived. The masses of neutral vector bosons ${Z}^{0}$ and ${Z}^{{0}^{\ensuremath{'}}}$ are predicted to be, by crude estimates, $92.3\ensuremath{\ge}{M}_{Z}\ensuremath{\ge}91.5$ GeV and > 200 GeV, respectively. The mass of ${Z}^{0}$ is practically the same as, but slightly less than, that predicted by the standard SU(2)\ifmmode\times\else\texttimes\fi{}U(1) model.