One-loop pseudo-Goldstone masses in the minimal $SO(10)$ Higgs model

TL;DR

This paper computes one-loop corrections to the scalar spectrum in a minimal non-supersymmetric $SO(10)$ Higgs model, revealing stable vacuum regions and comparing computational methods.

Contribution

It provides a detailed analysis of pseudo-Goldstone boson masses at one-loop in the minimal $SO(10)$ Higgs model with a focus on stability and computational approaches.

Findings

Extended parameter space with stable SM-like vacua identified.

One-loop pseudo-Goldstone masses are explicitly calculated.

Comparison made between different computational methods for effective potential.

Abstract

We calculate the prominent perturbative contributions shaping the one-loop scalar spectrum of the minimal non-supersymmetric renormalizable $SO(10)$ Higgs model whose unified gauge symmetry is spontaneously broken by an adjoint scalar. Focusing on its potentially realistic $45\oplus 126$ variant in which the rank is reduced by a VEV of the 5-index self-dual antisymmetric tensor, we provide a thorough analysis of the corresponding one-loop Coleman-Weinberg potential, paying particular attention to the masses of the potentially tachyonic pseudo-Goldstone bosons (PGBs) transforming as $(8,1,0)$ and $(1,3,0)$ under the Standard Model gauge group. The results confirm the assumed existence of extended regions in the parameter space supporting a locally stable SM-like quantum vacuum inaccessible at the tree-level. The effective potential (EP) tedium is compared to that encountered in the previously studied $45\oplus 16$ $SO(10)$ Higgs model where the polynomial corrections to the relevant pseudo-Goldstone masses turn out to be easily calculable within a very simplified purely diagrammatic approach.