Predictive SUSY SO(10) model with very low $\tan\beta$

Abstract

The first fermion family might play a key role in understanding the structure of flavour: a role of the mass unification point. The GUT scale running masses $\bar{m}_{e,u,d}$ are rather close, which may indicate an approximate symmetry limit. Following this observation, we present a new predictive approach based on the SUSY $SO(10)$ theory with $\tan\beta\sim 1$. The inter-family hierarchy is first generated in a sector of hypothetical superheavy fermions and then transfered inversely to ordinary quarks and leptons by means of the universal seesaw mechanism. The Yukawa matrices are simply parametrized by the small complex coefficients $\eps_{u,d,e}$ which are related by the $SO(10)$ symmetry properties. Their values are determined by the ratio of the GUT scale $M_X\simeq 10^{16}$ GeV to a higher (possibly string) scale $M\simeq 10^{17}-10^{18}$ GeV. The suggested ansatz correctly reproduces the fermion mass and mixing pattern. By taking as input the masses of leptons and $c$ and $b$ quarks, the ratio $m_s/m_d$ and the value of the Cabibbo angle, we compute the $u,d,s$ quark masses, top mass and $\tan\beta$. The top quark is naturally in the 100 GeV range, but with upper limit $M_t<165$ GeV, while the lower bound $M_t>160$ GeV implies $m_s/m_d>22$. $\tan\beta$ can vary from 1.4 to 1.7. The proton decaying $d=5$ operators $qqql$ are naturally suppressed.