The trouble with the minimal renormalizable SO(10) GUT

TL;DR

This paper critically examines the minimal non-supersymmetric SO(10) GUT, revealing fundamental issues with accommodating a Standard-Model-like Higgs doublet, which challenges its physical viability.

Contribution

It identifies a general problem in the minimal SO(10) GUT model related to Higgs doublet accommodation, beyond known proton decay issues.

Findings

Low GUT scale leads to rapid proton decay

Model cannot properly host a Standard-Model-like Higgs doublet

Perturbative regime limitations hinder model viability

Abstract

We scrutinize the physical viability of the minimal non-supersymmetric $\mathrm{SO}(10)$ 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.