An SO(10) Solution to the Puzzle of Quark and Lepton Masses

Abstract

It is shown that almost all features of the quark and lepton masses can be satisfactorily and simply explained without family symmetry, including the threefold mass hierarchy among the generations, and the relations ${m}_{\ensuremath{\tau}}^{0}\ensuremath{\cong}{m}_{b}^{0}$, ${m}_{\ensuremath{\mu}}^{0}\ensuremath{\cong}{3m}_{s}^{0}$, ${m}_{e}^{0}\ensuremath{\cong}\frac{1}{3}{m}_{d}^{0}$, ${m}_{u}^{0}/{m}_{t}^{0}\ensuremath{\ll}{m}_{d}^{0}/{m}_{b}^{0}$, $\mathrm{tan}{\ensuremath{\theta}}_{c}\ensuremath{\cong}\sqrt{{m}_{d}^{0}{m}_{s}^{0}}$, ${V}_{\mathrm{cb}}\ensuremath{\ll}\sqrt{{m}_{s}^{0}/{m}_{b}^{0}}$, and ${V}_{\mathrm{ub}}\ensuremath{\sim}{V}_{\mathrm{cb}}{V}_{\mathrm{us}}$. Various aspects of the group theory of $\mathrm{SO}(10)$ play an essential role in explaining these relations. There are distinctive and testable predictions for $\mathrm{tan}\ensuremath{\beta}$ and the neutrino mixing angles.