Non-supersymmetric SO(10) models with Gauge and Yukawa coupling unification

TL;DR

This paper explores a non-supersymmetric SO(10) Grand Unified Theory with high-scale symmetry breaking, focusing on gauge and Yukawa coupling unification, and analyzes the resulting phenomenological constraints and proton decay implications.

Contribution

It presents a detailed analysis of gauge and Yukawa unification in non-supersymmetric SO(10) models with specific intermediate symmetry breaking patterns and includes two-loop level calculations and phenomenological constraints.

Findings

Gauge coupling unification conditions derived at two-loop level.

Yukawa unification imposes relations between fermion couplings and scalar representations.

Constraints on model parameters, including $ aneta$, from phenomenology and proton decay.

Abstract

We study a non-supersymmetric SO(10) Grand Unification Theory with a very high energy intermediate symmetry breaking scale in which not only gauge but also Yukawa coupling unification are enforced via suitable threshold corrections and matching conditions. For gauge unification, we focus on a few symmetry breaking patterns with the intermediate gauge groups ${\rm SU(4)_C \times SU(2)_L \times SU(2)_R}$ (Pati-Salam) and ${\rm SU(3)_C \times SU(2)_L \times SU(2)_R\times U(1)_{B-L}}$ (minimal left-right symmetry) assuming an additional global U(1) Peccei--Quinn symmetry, and having the Standard Model supplemented by a second Higgs doublet field at the electroweak scale. We derive the conditions as well as the approximate analytical solutions for the unification of the gauge coupling constants at the two-loop level and discuss the constraints from proton decay on the resulting high scale. Specializing to the case of the Pati-Salam intermediate breaking pattern, we then impose also the unification of the Yukawa couplings of third generation fermions at the high scale, again at the two-loop level. In the considered context, Yukawa unification implies a relation between the fermion couplings to the 10- and 126-dimensional scalar representations of the SO(10) group. We consider one such possible relation which is obtainable in an ${\rm E_6}$ model where the previous two scalar fields are part of a single multiplet. Taking into account some phenomenological features such as the absence of flavor changing neutral currents at tree-level, we derive constraints on the parameters of the low energy model, in particular on the ratio of the two Higgs doublets vacuum expectation values $\tan\beta$.