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# Mass Relations, Unification, and Proton Decay in the Mirror GUT Model

Dec 2022

We propose an SU(5)$\times$U(1)$_\text{X}\times$U(1)$_\text{PQ}$ modelwithout SUSY because the SUSY particles have not been observed yet. The$\mathrm{U(1)_{X}}$ gauge symmetry is the generalization of the$\mathrm{U(1)_{B-L}}$ gauge symmetry and $\mathrm{U(1)_{PQ}}$ symmetry is theglobal Peccei-Quinn symmetry. We introduce three mirror families in order tounify the SM gauge couplings and avoid the restriction of proton lifetime. Inorder to obtain the difference of the masses for the down-type quarks andcharged leptons, we also introduce the $\mathbf{45}$ representation Higgs inaddition to the $\mathbf{5}$ representation one. In this paper, we discuss themass relations between the SM and mirror particles and identify the mass scalesof the mirror particles. Since the new particles exist in the intermediateenergy scale and contribute to the renormalization group equation, the SM gaugecouplings unify successfully at high energy. Our model can be tested by thefuture proton decay search, e.g., the Hyper-Kamiokande experiment expected as$\tau_p(p\to\pi^0{e^+})<1.0\times10^{35}$ years. Also, by using the massrelations between the active and mirror neutrinos, we estimate the lower boundof the heavy neutrino masses.

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