PerturbativeSO(10)grand unification

Abstract

We consider a phenomenologically viable $SO(10)$ grand unification model of the unification scale ${M}_{G}$ around ${10}^{16}\text{ }\text{ }\mathrm{GeV}$ which reproduces the minimal supersymmetric standard model at low energy and allows perturbative calculations up to the Planck scale ${M}_{P}$ or the string scale ${M}_{st}$. Both requirements strongly restrict a choice of Higgs representations in a model. We propose a simple $SO(10)$ model with a set of Higgs representations ${2\ifmmode\times\else\texttimes\fi{}\mathbf{10}+\overline{\mathbf{16}}+\mathbf{16}+\mathbf{45}}$ and show its phenomenological viability. This model can indeed reproduce the low-energy experimental data relating the charged fermion masses and mixings. Neutrino oscillation data can be consistently incorporated in the model, leading to the right-handed neutrino mass scale ${M}_{R}\ensuremath{\simeq}{M}_{G}^{2}/{M}_{P}$. Furthermore, there exists a parameter region which results the proton lifetime consistent with the experimental results.