Seesaw Scale, Unification, and Proton Decay

Abstract

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.

Comments: new plot and appendix, minor corrections, version to appear in Physical Review D