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

Abdelhak Djouadi; Renato Fonseca; Ruiwen Ouyang; Martti Raidal

doi:10.1140/epjc/s10052-023-11696-4

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 529
https://doi.org/10.1140/epjc/s10052-023-11696-4

Regular Article - Theoretical Physics

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

Abdelhak Djouadi¹^,2, Renato Fonseca¹, Ruiwen Ouyang²^c and Martti Raidal²

¹ Centro Andaluz de Fisica de Particulas Elementales (CAFPE) and Depto. de Física Teórica y del Cosmos, Universidad de Granada, 18071, Granada, Spain
² Laboratory of High Energy and Computational Physics, NICPB, Rävala pst. 10, 10143, Tallinn, Estonia

^c ruiwen.ouyang@gmail.com

Received: 27 February 2023
Accepted: 7 June 2023
Published online: 24 June 2023

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 $SU {(4)}_{C} \times SU {(2)}_{L} \times SU {(2)}_{R}$ $\text {SU}(4)_{\textrm{C}} \times \text {SU}(2)_{\textrm{L}} \times \text {SU}(2)_{\textrm{R}}$ (Pati–Salam) and $SU {(3)}_{C} \times SU {(2)}_{L} \times SU {(2)}_{R} \times U {(1)}_{B - L}$ $\text {SU}(3)_{\textrm{C}} \times \text {SU}(2)_{\textrm{L}} \times \text {SU}(2)_{\textrm{R}}\times \text {U}(1)_{{\textrm{B}}-{\textrm{L}}}$ (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 $E_{6}$ $\text {E}_6$ 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 $tan β$ $\tan \beta$ .

© The Author(s) 2023

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