"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 $m_τ^0 = m_b^0$, $m_μ^0 = 3 m_s^0$, $m_e^0 = \frac{1}{3} m_d^0$, $m_u^0/m_t^0 << m_d^0/m_b^0$, $\tan θ_c = \sqrt{m_d^0/m_s^0}$, $V_{cb} << \sqrt{m_s^0/m_b^0}$, and $V_{ub} \sim V_{cb}V_{us}$. Various aspects of the group theory of $SO(10)$ play an essential role in explaining these relations. The form of the mass matrices, rather than being imposed arbitrarily, emerges naturally from a simple structure at the unification scale. This structure involves only vector, spinor and adjoint representations. There are distinctive and testable predictions for $\tan β$ and the neutrino mixing angles.