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 without any additional symmetry assumptions. In this paper, we discuss the predictions of the model for proton decay. We scan over the parameter space of the model allowed by neutrino data to obtain the maximum values for the partial lifetimes for proton decay to various modes. We find that the partial lifetime for the mode $\tau(p\to \pi^+\bar{\nu})$ has an upper bound of $ 2.2\times 10^{32}$ yrs for average squark mass of 500 GeV and wino mass of 200 GeV, when we require the parameters to satisfy the present $\tau(p\to K^+\bar{\nu})$ and $\tau (p\to K^0+\mu^+)$ lower limits. All other decay modes have lifetimes longer than the present lower limits