Inverse Hierarchy Approach to Fermion Masses

Abstract

The first fermion family might play a special role in understanding the physics of flavour. This possibility is suggested by the observation that the up-down splitting within quark families increases with the family number: $m_u\sim m_d$, $m_c>m_s$, $m_t\gg m_b$. We construct a model that realizes this feature of the spectrum in a natural way. The inter-family hierarchy is first generated by radiative phenomena in a sector of heavy isosinglet fermions and then transferred to quarks by means of a universal seesaw. A crucial role is played by left-right parity and up-down isotopic symmetry. No family symmetry is introduced. The model implies $m_u/m_d>$ 0.5 and the Cabibbo angle is forced to be $\sim \sqrt{m_d/m_s}$. The top quark is naturally in the 100 GeV range, but not too heavy: $m_t<$ 150 GeV. Inspired by the mass matrices obtained in the model for quarks, we suggest an ansatz also including charged leptons. The differences between $u$-, $d$- and $e$-type fermions are simply parametrized by three complex coefficients $\text{eps}u$, $\text{eps}d$ and $\text{eps}e$. Additional consistent predictions are obtained: $m_s$=100-150 MeV and $m_u/m_d<$ 0.75.

Comments: 19 pages (standard TeX) + 1 table (cut out and LaTeX separately) + 1 figure (cut out and postscript separately); 2 additional figures available by fax upon request, LBL-32889, LMU-13/92