The Missing Doublet Model Revamped

Abstract

We revisit the Missing Doublet Model (MDM) as a means to address the apparent difficulties of the minimal $SU(5)$ supergravity model in dealing with the doublet-triplet splitting problem, the prediction of $α_3(M_Z)$, and the proton lifetime. We revamp the original MDM by extending its observable sector to include fields and interactions that naturally suppress the dimension-five proton decay operators and that allow see-saw neutrino masses. We also endow the model with a hidden sector which (via gaugino condensation) triggers supersymmetry breaking of the desired magnitude, and (via hidden matter condensation) yields a new dynamical intermediate scale for the right-handed neutrino masses ($\sim10^{10}\GeV$), and provides an effective Higgs mixing parameter $μ$. The model is consistent with gauge coupling unification for experimentally acceptable values of $α_3(M_Z)$, and with proton decay limits even for large values of $\tanβ$. The right-handed neutrinos can be produced subsequent to inflation, and their out-of-equilibrium decays induce a lepton asymmetry which is later reprocessed (via sphaleron interactions) into a baryon asymmetry at the electroweak scale. The resulting see-saw neutrino masses provide a candidate for the hot dark matter component of the Universe ($m_{ν_τ}\sim{\cal O}(10\eV)$) and are consistent with the MSW solution to the solar neutrino problem. We finally compare the features of this traditional GUT model with that of the readily string-derivable $SU(5)\times U(1)$ model, and discuss the prospects of deriving the revamped MDM from string theory.