Proton Decay in Product Group Unification

TL;DR

This paper analyzes proton decay in a product group unification model, showing minimal models are excluded by current data, but extended models predict observable proton decay and potential dark matter candidates.

Contribution

It demonstrates that minimal SU(5)×U(2)_H models are ruled out by proton decay constraints and proposes an extended model with testable predictions for upcoming experiments.

Findings

Minimal model excluded by dimension-6 proton decay

Extended model predicts proton lifetime within experimental reach

Dark matter may include Wino LSP and axion

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.