Nucleon decay in a realistic SO(10) SUSY GUT

In this paper, we calculate neutron and proton decay rates and branching ratios in a predictive SO(10) SUSY GUT which agrees well with low energy data. We show that the nucleon lifetimes are consistent with the experimental bounds. The nucleon decay rates are calculated using all one-loop chargino and gluino-dressed diagrams regardless of their chiral structure. We show that the four-fermion operator $C_{\mathrm{jk}}{(u}_R{d}_{\mathrm{jR}}{\left)\right(d}_{\mathrm{kL}}{\nu }_{\tau L}),$ commonly neglected in previous nucleon decay calculations, not only contributes significantly to nucleon decay, but, for many values of the initial GUT parameters and for large $\tan \beta ,$ actually dominates the decay rate. As a consequence, we find that ${\tau }_p/{\tau }_n$ is often substantially larger than the prediction obtained in small $\tan \beta$ models. We also find that gluino-dressed diagrams, often neglected in nucleon decay calculations, contribute significantly to nucleon decay. In addition we find that the branching ratios obtained from this realistic SO(10) SUSY GUT differ significantly from the predictions obtained from “generic” SU(5) SUSY GUT’s. Thus, nucleon decay branching ratios, when observed, can be used to test theories of fermion masses.