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

Abstract

This work presents a complete analysis of fermion fitting and proton

decay in a supersymmetric $SO(10)$ model previously suggested by

Dutta, Mimura, and Mohapatra.

A key question in any grand unified theory is whether it satisfies the

stringent experimental lower limits on the partial lifetimes of the

proton. In more 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 minor ${\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

largely sub-dominant to gauge boson decay channels.