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

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 $m_{\tau }^0\cong m_b^0$, $m_{\mu }^0\cong {3m}_s^0$, $m_e^0\cong \frac{1}{3}{m}_d^0$, $m_u^0/m_t^0\ll m_d^0/m_b^0$, $\tan {\theta }_c\cong \sqrt{m_d^0{m}_s^0}$, $V_{\mathrm{cb}}\ll \sqrt{m_s^0/m_b^0}$, and $V_{\mathrm{ub}}\sim V_{\mathrm{cb}}{V}_{\mathrm{us}}$. Various aspects of the group theory of $\mathrm{SO}\left(10\right)$ play an essential role in explaining these relations. There are distinctive and testable predictions for $\tan \beta$ and the neutrino mixing angles.