Proton Decay in a Minimal SUSY SO(10) Model for Neutrino Mixings

A minimal renormalizable SUSY SO(10) model with B-L symmetry broken by {\bf 126} Higgs field has recently been shown to predict all neutrino mixings and the ratio $\Delta m^2_{\odot}/\Delta m^2_A$ in agreement with observations. Unlike models where B-L is broken by {\bf 16} Higgs, this model guarantees automatic R-parity conservation and hence a stable dark matter as well as the absence of dim=4 baryon violating operator without any additional symmetry assumptions. In this paper, we discuss the predictions of the model for proton decay induced at the GUT scale. We scan over the parameter space of the model allowed by neutrino data and find upper bounds on the partial lifetime for the modes $\tau(n\to \pi^0\bar{\nu})=~2\tau(p\to \pi^+\bar{\nu})\leq (5.7-13)\times 10^{32}$ yrs and $\tau(n\to K^0\bar{\nu})\leq 2.97\times 10^{33}$ yrs for the average squark mass of a TeV and wino mass of 200 GeV, when the parameters satisfy the present lower limits on $\tau(p\to K^+\bar{\nu})$ mode. These results can be used to test the model.