The trouble with the minimal renormalizable SO(10) GUT

We scrutinize the physical viability of the minimal non-supersymmetric $\mathrm{S}\mathrm{O}(10)$ GUT with the scalar sector $\mathbf{45}\oplus \mathbf{126}\oplus {\mathbf{10}}_{\mathbb{C}}$, in which the unified symmetry is broken by the former two representations, and a realistic Yukawa sector is supported by the last two. Alongside the known issue of a relatively low GUT scale (and thus overly fast proton decay) encountered in minimally fine-tuned scenarios, we identify a very general problem of the model: the inability to properly accommodate a Standard-Model-like low-energy Higgs doublet in the perturbative regime.