Quark-lepton Yukawa ratios and nucleon decay in SU(5) GUTs with type-III seesaw

TL;DR

This paper explores an extended SU(5) GUT model with additional scalar and fermionic fields, analyzing Yukawa ratio predictions, nucleon decay rates, and collider-testable relic states within a unified framework.

Contribution

It introduces a novel SU(5) GUT extension with combined type I and III seesaw mechanisms, deriving specific Yukawa ratio predictions and examining their implications for nucleon decay and collider phenomenology.

Findings

Three viable Yukawa ratio combinations identified.

Predictions for nucleon decay rates in extended models.

Constraints on relic particle masses from gauge unification.

Abstract

We consider an extension of the Georgi-Glashow SU(5) GUT model by a 45-dimensional scalar and a 24-dimensional fermionic representation, where the latter leads to the generation of the observed light neutrino masses via a combination of a type I and a type III seesaw mechanism. Within this scenario, we investigate the viability of predictions for the ratios between the charged lepton and down-type quark Yukawa couplings, focusing on the second and third family. Such predictions can emerge when the relevant entries of the Yukawa matrices are generated from single joint GUT operators (i.e. under the condition of single operator dominance). We show that three combinations are viable, (i) $y_\tau/y_b=3/2$, $y_\mu/y_s=9/2$, (ii) $y_\tau/y_b=2$, $y_\mu/y_s=9/2$, and (iii) $y_\tau/y_b=2$, $y_\mu/y_s=6$. We extend these possibilities to three toy models, accounting also for the first family masses, and calculate their predictions for various nucleon decay rates. We also analyse how the requirement of gauge coupling unification constrains the masses of potentially light relic states testable at colliders.