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 $p\to K^{+}\overline{\nu }$ and $p\to {\pi }^{+}\overline{\nu }$, i.e., $\tau (p\to K^{+}\overline{\nu })\lesssim 3.4\times {10}^{35}$ and $\tau (p\to {\pi }^{+}\overline{\nu })\lesssim 1.7\times {10}^{34}\mathrm{years}$, 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.

• Received 15 May 2018

DOI:https://doi.org/10.1103/PhysRevD.98.035032

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Published by the American Physical Society