Nucleon Decay in Non-Minimal Supersymmetric SO(10)

Evaluation of nucleon decay modes and branching ratios in a non-minimal supersymmetric SO(10) grand unified theory is presented. The non-minimal GUT considered is the supersymmetrised version of the `realistic' SO(10) model originally proposed by Harvey, Reiss, and Ramond, which is realistic in that it gives acceptable charged fermion and neutrino masses within the context of a phenomenological fit to the low energy standard model inputs. Despite a complicated Higgs sector, the SO(10) $\underline{10}$ Higgs superfield mass insertion is found to be the sole contribution to the tree level F-term governing nucleon decay. The resulting dimension 5 operators that mediate nucleon decay give branching ratio predictions parameterised by a single parameter, the ratio of the Yukawa couplings of the $\underline{10}$ to the fermion generations. For parameter values corresponding to a lack of dominance of the third family self coupling, the dominant nucleon decay modes are $p \rightarrow K^{+} + \bar{\nu}_{\mu}$ and $n \rightarrow K^{0} + \bar{\nu}_{\mu}$, as expected. Further, the charged muon decay modes are enhanced by two orders of magnitude over the standard minimal SUSY SU(5) predictions, thus predicting a distinct spectrum of `visible' modes. These charged muon decay modes, along with $p \rightarrow \pi^{+} + \bar{\nu}_{\mu}$ and $n \rightarrow \pi^{0} + \bar{\nu}_{\mu}$, which are moderately enhanced over the SUSY SU(5) prediction, suggest a distinguishing fingerprint of this particular GUT model, and if nucleon decay is observed at Super-KAMIOKANDE the predicted branching ratio spectrum can be used to determine the validity of this `realistic' SO(10) SUSY GUT model.