Quantum nature of the minimal potentially realistic SO(10) Higgs model

We study several aspects of the quantum structure minimal potentially realistic renormalizable $\mathrm{SO}(10)$ Higgs model in which $\mathbf{45}\oplus \mathbf{126}$ scalars spontaneously break symmetry down to Standard Model group $\mathrm{SU}(3)_{c}\times \mathrm{SU}(2)_{L}\times \mathrm{U}(1)_{Y}$. With a complete information about one-loop corrections masses all theory and beta functions governing running dimensionless scalar self-couplings, domains parameter space where can be treated perturbatively are established, along with improved bounds from requirements SM vacuum stability gauge coupling unification. demonstrate that is fully consistent only very narrow regions corresponding breaking chains well pronounced $\mathrm{SU}(4)_{C}\times \mathrm{SU}(2)_L\times \mathrm{U}(1)_R$ \mathrm{SU}(2)_R\times \mathrm{U}(1)_{B-L}$ intermediate symmetries, clear preference for former case. Barring accidental fine-tunings sector, this makes it possible provide sharp prediction position unification scale value associated coupling, implications phenomenology grand unified models based on structure.