Fermion Mass Hierarchy in the Nu MSGUT I : The Real Core

Abstract

The recent failure of the scenario which uses only $\mathbf{10,\oot}$ Higgs multiplets to yield large enough neutrino masses in the $\mathbf{SO(10) }$ \textbf{MSGUT} motivates an alternative scenario\cite{blmdoom} where the $\mathbf{120}$ -plet collaborates with the $ \mathbf{10}$ -plet to fit the dominant charged fermion masses. The small $\mathbf{\oot} $ -plet couplings give appreciable contributions only to light charged fermion masses {\textit{and}} enhance the Type I seesaw masses to viable values. We analyze the 2-3 generation core of the complete hierarchical fermion mass system in the CP conserving approximation. \emph{Ansatz} consistency \emph{requires} ${\mathbf{m_b-m_s = m_{\tau}-m_{\mu}}} $ at the GUT scale $M_X$ and predicts near maximal (PMNS) mixing in the leptonic sector for central values of charged fermion parameters and for wide ranges of the other relevant parameters : righthanded neutrino masses and relative strength of contributions of the two doublet pairs from the $\mathbf{120}$-plet to the effective MSSM Higgs pair. These features are preserved in the CP preserving 3 generation system whose results are previewed : an additional consistency requirement $\mathbf{\theta_{13}^c =\theta_{12}^c \theta_{23}^c }$ on the CKM angles at $M_X$ arises for 3 generations. Right handed neutrino masses in such scenarios are all less than about $10^{12} GeV$.