MSGUT : From Bloom to Doom

Abstract

By a systematic survey of the parameter space we confirm our surmise\cite{gmblm} that the Minimal Supersymmetric GUT(MSGUT) based on the ${\bf{210\oplus 126\oplus {\bar {126}}\oplus 10}}$ Higgs system is incompatible with the generic Type I and Type II seesaw mechanisms. The incompatibility of the Type II seesaw mechanism with this MSGUT is due to its generic extreme sub-dominance with respect to the Type I contribution. The Type I mechanism although dominant over Type II is itself unable to provide Neutrino masses larger than $ \sim 10^{-3}$ eV anywhere in the parameter space. Our Renormalization Group based analysis shows the origin of these difficulties to lie in a conflict between baryon stability and neutrino oscillation. The MSGUT completed with a {\bf{120}}-plet Higgs is the natural next to minimal candidate. We propose a scenario where the {\bf{120}}-plet collaborates with the {\bf{10}}-plet to fit the charged fermion masses. The freed {\bf{126}}-plet couplings can then give sub-dominant contributions to charged fermion masses {\textit{and}} enhance the Type I seesaw masses sufficiently to provide a viable seesaw mechanism. We give formulae required to verify this scenario.