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Proton decay and $μ\to e+γ$ Connection in a Renormalizable SO(10) GUT for Neutrinos

Supersymmetric SO(10) grand unified models with renormalizable Yukawa couplings involving {\bf 10}, {\bf 126} and {\bf 120} Higgs fields have been shown to give a very economical theory for understanding quark-lepton flavor in a unified framework. In previous papers, we showed how nucleon decay can be suppressed in these models without invoking cancellation, by choice of Yukawa flavor texture within a type II seesaw framework for neutrinos that explains all mixings and masses including the recently observed "large" $θ_{13}$. In this follow-up paper, we extend our earlier work to the case of type I seesaw and show that the recently measured "large" $θ_{13}$ can be accommodated in this case while suppressing proton decay. We then point out that the two cases (type I and II) lead to different testable predictions for $B(μ\to e+γ)$ and $B(τ\to μ(e) +γ)$ as well as different flavor final states in nucleon decay. In particular, we find that for the type I seesaw case, $B(τ\to μ+γ)$ can be observable while at the same time suppressing $B(μ\to e+γ)$, whereas in the type II seesaw case, $B(τ\to μ+γ)$ is always suppressed whereas $B(μ\to e+γ)$ is observable.