Neutrino Sector and Proton Lifetime in a Realistic SUSY SO(10) Model

In this work I present a full analysis of proton decay in an $SO(10)$ model previously proposed by Dutta, Mimura, and Mohapatra. The $\mathbf{10}$, $\overline{\mathbf{126}}$, and $\mathbf{120}$ Yukawa couplings contributing to fermion masses in this model have well-motivated restrictions on their textures intended to give favorable results for proton lifetime as well as a realistic fermion sector without the need for fine-tuning and for either type-I or type-II dominance in the neutrino mass matrix. 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 satisfied for nearly every pertinent decay mode, even for nearly arbitrary values of the triplet Higgs mixing parameters, with only the $K^{+}\bar{\nu }$ mode requiring a minor $\mathcal{O}({10}^{-1})$ cancellation in order to satisfy the experimental limit. I also find a maximum lifetime for that mode of $\tau (K^{+}\bar{\nu })\sim {10}^{36}$ years, which should be tested by eventual experiments. For the type-I seesaw case, I find that all six pertinent decay modes of interest are satisfied for values of the triplet mixing parameters giving no major enhancement, with modes other than $K^{+}\bar{\nu }$ easily satisfied for arbitrary mixing values, and with a maximum lifetime for $K^{+}\bar{\nu }$ of nearly ${10}^{38}$ years.