New Predictive Framework for Fermion Masses in SUSY SO(10)

Abstract

We present a new predictive approach based on SUSY $SO(10)$ theory. The inter-family hierarchy is first generated in the sector of hypothetical superheavy fermions and then transfered inversely to ordinary quarks and leptons by means of the universal seesaw mechanism. The obtained mass matrices are simply parametrized by two small complex coefficients $\eps_u$ and $\eps_d$, which can be given by the ratio of the GUT scale $M_G\simeq 10^{16}$ GeV and some higher scale $M\simeq 10^{17}-10^{18}$ GeV (presumably superstring scale). The model provides a possibility for doublet-triplet splitting without fine tuning and the Higgsino mediated $d=5$ operators for the proton decay are naturally suppressed. Our ansatz provides the correct {\em qualitative} picture of fermion mass hierarchy and mixing pattern, provided that $\eps_d/\eps_u\sim 10$. The running masses of the first family fermions: electron, u-quark and d-quark obey an approximate $SO(10)$ symmetry limit. At GUT scale we have: $u\sim d\simeq 3e$, $(\frac{\eps_u}{\eps_d})c\sim s\simeq \frac{1}{3}μ$ and $(\frac{\eps_u}{\eps_d})^2t\sim b\simeq τ$. The Cabibbo angle is large: $s_{12}\simeq \sqrt{m_d/m_s}$ while other mixing angles have their natural size: $s_{23}\sim m_s/m_b$ and $s_{13}\sim m_d/m_b$. We have many strong {\em quantitative} predictions though no special `zero' texture is utilized (in contrast to the known predictive frameworks). Namely, taking as input the lepton, c-quark and b-quark masses, $m_s/m_d$ mass ratio and Cabibbo angle, we can obtain the light (u,d,s) quark masses, top mass and $\tanβ$. The top quark is naturally in the 100 GeV range, but not too heavy: $m_t<165$ GeV. The lower bound $M_t>150$ GeV (160 GeV)