Seesaw Scale, Unification, and Proton Decay

We investigate a simple realistic grand unified theory based on the $SU(5)$ gauge symmetry which predicts an upper bound on the proton decay lifetime for the channels $p\to K^{+}\bar{\nu }$ and $p\to {\pi }^{+}\bar{\nu }$, i.e. $\tau (p \to K^+ \bar{\nu}) \lesssim 3.4 \times 10^{35}$and$\tau (p \to \pi^+ \bar{\nu}) \lesssim 1.7 \times 10^{34}$ years, respectively. In this context, the neutrino masses are generated through the type I and type III seesaw mechanisms, and one predicts that the field responsible for type III seesaw must be light with a mass below 500 TeV. We discuss the testability of this theory at current and future proton decay experiments.