Abstract
A minimal renormalizable SUSY SO(10) model with B–L symmetry broken by 126 Higgs field has recently been shown to predict all neutrino mixings and the ratio Δm2⊙/Δm2A in agreement with observations. Unlike models where B–L is broken by 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 τ(n→π0ν̄)=2τ(p→π+ν̄)⩽(5.7−13)×1032 yrs and τ(n→K0ν̄)⩽2.97×1033 yrs for the average squark mass of a TeV and wino mass of 200 GeV, when the parameters satisfy the present lower limits on τ(p→K+ν̄) mode. These results can be used to test the model.
Highlights
Grand unified theories [1] provide an attractive framework for understanding the origin of the diverse strengths of the various forces observed in Nature
A concrete realization of this hypothesis is provided within the framework of supersymmetric models where the unification scale is MU ≃ 2 × 1016 GeV, provided one assumes that there are no intermediate scales below MU and the scale of supersymmetry breaking is at the weak scale [2]
For a specific choice of these parameters, which is commonly used in literature, we find that the partial lifetime for the mode p → ν + π+ has an upper limit of 2.2 × 1032 years
Summary
Grand unified theories [1] provide an attractive framework for understanding the origin of the diverse strengths of the various forces observed in Nature. The main observation in the papers [12,13,14] is that if B-L symmetry is broken by a 126 dimensional representation of SO(10), the coupling of 126 to fermions unifies the flavor structure of the quarks and charged leptons with those of the neutrinos This makes the model remarkably predictive in the neutrino sector and the predictions obtained in [14] are in full accord with all known data for neutrino mixings. We give the partial lifetimes for other charged lepton modes For this choice of supersymmetry breaking parameters, we find that breaking GUT symmetry by only a 210 Higgs multiplet is incompatible with present proton decay limits. What is important for our considerations is that the matrix f that determines the flavor structure of the neutrinos is related to the quark and lepton masses
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