Neutrino Mass and Proton Decay in a Realistic Supersymmetric SO(10) Model

This work presents a complete analysis of fermion fitting and proton decay in a SUSY $SO(10)$ model previously suggested by Dutta, Mimura, and Mohapatra. A key question in any grand unified theory is whether it satisfies the experimental lower limits on proton partial lifetimes. In generic models, substantial fine-tuning is required among GUT-scale parameters to satisfy the limits. In the proposed model, the ${\bf 10}$, $\overline{\bf{126}}$, and ${\bf 120}$ Yukawa couplings contributing to fermion masses have restricted textures intended to give favorable results for proton lifetime, while still giving rise to a realistic fermion sector, without the need for fine-tuning, even for large $\tan\beta$, and for either type-I or type-II dominance in the neutrino mass matrix. In this thesis, I investigate the above hypothesis at a strict numerical level of scrutiny; I obtain a valid fit for the entire fermion sector for both types of seesaw dominance, including $\theta_{13}$ in good agreement with the most recent data. For the case with type-II seesaw, I find that, using the Yukawa couplings fixed by the successful fermion sector fit, proton partial lifetime limits are readily satisfied for all but one of the pertinent decay modes for nearly arbitrary values of the triplet-Higgs mixing parameters, with the $K^+ \bar\nu$ mode requiring a ${\cal O}(10^{-1})$ cancellation in order to satisfy its limit. I also find a maximum partial lifetime for that mode of $\tau(K^+ \bar\nu) \sim 10^{36}\,$years. For the type-I seesaw case, I find that $K^+ \bar\nu$ decay mode is satisfied for any values of the triplet mixing parameters giving no major enhancement, and all other modes are easily satisfied for arbitrary mixing values; I also find a maximum partial lifetime for $K^+ \bar\nu$ of nearly $10^{38}\,$years, which is sub-dominant to gauge boson decay channels.