Abstract
Product group unification is an attractive alternative to simple grand unification. It solves the infamous doublet-triplet splitting problem and the dimension-5 proton decay problems without introducing any fine-tuning. Furthermore, the matter multiplets are still embedded into unified SU(5) representations. In this paper, we discuss proton decay of the simplest product group unification model based on SU(5)XU(2)_H . We find that the minimal setup of the model has already been excluded by dimension-6 proton decay. We also show that a simple extension of the model, with naturally generated SU(5) incomplete multiplets, can rectify this problem. We find that the proton lifetime will be in reach of coming experiments like DUNE and Hyper-K, when the mass of the incomplete multiplet is associated with the Peccei-Quinn symmetry breaking. In this case, the dark matter may be an admixture of the Wino LSP and the axion.
Highlights
One of the challenges of supersymmetric (SUSY) grand unified theories (GUT), is the doublet-triplet splitting
By requiring the model be perturbative up to the cutoff scale, we find that the effective GUT scale is considerably smaller than the conventional GUT scale, which roughly corresponds to the scale the minimal supersymmetric standard model (MSSM) gauge coupling constants unify
We find that the minimal setup of the SU(5)×U(2)H model has been excluded by the proton decay experiments
Summary
One of the challenges of supersymmetric (SUSY) grand unified theories (GUT), is the doublet-triplet splitting. The presence of a triplet Higgs boson, at the energy scale of the minimal supersymmetric standard model (MSSM), ruins the precise coupling unification at the GUT scale. In addition to this complication, the predicted lifetime for the proton through the exchange of this very light triplet Higgs boson would be in conflict with experimental constraints. This product group unification model is characterized by having an R-symmetry which forbids the Higgs bilinear term 5 ̄5 and the dimension-five proton decay operators simultaneously3 For this model, the doublet-triplet splitting is accomplished without any unnaturally small couplings.
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