Gauge coupling unification and doublet-triplet splitting via GUT dynamical breaking

TL;DR

This paper explores how non-renormalizable operators and fermion condensates in specific representations can achieve gauge coupling unification and address the doublet-triplet splitting problem within GUT frameworks.

Contribution

It demonstrates that dynamical breaking patterns with fermion condensates in 10 and 24 representations can unify gauge couplings and solve the doublet-triplet splitting issue.

Findings

Fermion condensates in the 5 representation are incompatible with proton decay constraints.

Condensates in the 10 and 24 representations lead to viable unification models.

Non-renormalizable operators influence gauge kinetic terms and unification prospects.

Abstract

An interesting framework to achieve gauge coupling unification consists in adding to the Standard Model Lagrangian non-renormalizable operators of $d \geq 5$, which affect the kinetic term of gauge fields. We first review the phenomenology related to this framework in the context of $SU(5)$, identifying which are the most interesting representations for the sake of achieving coupling unification. Secondly, we point out that in the case of a dynamical breaking pattern, it is possible to relate gauge coupling unification with the doublet-triplet splitting problem. We show that condensates of fermions in the $5$ representation do not lead to viable models because of proton decay constraints. At difference, we point out that successful models can be obtained by considering condensates of fermions in the $10$, as well as in the $24$ representations.