Light-Heavy Symmetry: Geometric Mass Hierarchy for Three Families

Abstract

The Universal Seesaw pattern coupled with a Light$\leftrightarrow$Heavy symmetry principle leads to the Diophantine equation $N=\sum _{i=1}^N{n}_i$, where $n_i\ge 0$ and distinct. Its unique non-trivial solution $(3=0+1+2)$ gives rise to the geometric mass hierarchy $m_W$, $m_Wϵ$, $m_W{ϵ}^2$ for $N=3$ fermion families. This is realized in a model where the hybrid (yet Up$\leftrightarrow$Down symmetric) quark mass relations $m_d{m}_t\approx m_c^2\leftrightarrow m_u{m}_b\approx m_s^2$ play a crucial role in expressing the CKM mixings in terms of simple mass ratios, notably $\sin {\theta }_C\approx \frac{m_c}{m_b}$.

Comments: 12 pages, no figures, Revtex file