Implications of the SO(12) gauge symmetry for grand unification

Abstract

Arguments following from analyzing constraints on the currently available neutral-current data are reviewed that allow for the possible existence of a neutral boson "lighter" than the one encountered in the standard $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{L+R}$ electroweak theory. An attractive possibility of accommodating this idea of a light boson in grand unified theories is to extend the popular SO(10) gauge symmetry to SO(12) gauge symmetry. It is explicitly shown that the 32-dimensional irreducible spinor representation of the SO(12) grand unified theory accommodates the electron family, which leads to the usual left-handed currents with strength ${G}_{F}$, and a "twin" electron family which leads to right-handed currents also with strength ${G}_{F}$, leaving no room for the muon ($\ensuremath{\tau}$) family.