Viable quark-lepton Yukawa ratios and nucleon decay predictions in $SU(5)$ GUTs with type-II seesaw

TL;DR

This paper explores predictive quark-lepton Yukawa ratios and nucleon decay in non-supersymmetric SU(5) GUTs with type II seesaw, identifying only two viable Yukawa ratio sets and analyzing their phenomenological implications.

Contribution

It demonstrates that only two specific Yukawa ratio predictions are viable in these GUT models with type II seesaw and extends the analysis to include first-family fermions and nucleon decay predictions.

Findings

Only two Yukawa ratio sets are viable: 3/2 and 9/2, or 2 and 6.

Predicted nucleon decay rates and relic masses within collider reach.

Extended models include first-family fermions for comprehensive phenomenology.

Abstract

We investigate the viability of predictive schemes for quark-lepton Yukawa ratios and nucleon decay in non-supersymmetric SU(5) Grand Unified Theories (GUTs) where neutrino masses are generated by a type II seesaw mechanism. The scalar sector of the considered scenario contains 5-, 24- and 45-dimensional representations plus a 15-dimensional representation for realising the type II seesaw. Predictions for the ratios of the quark and lepton Yukawa couplings 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"). Focusing on the 2nd and 3rd family and hierarchical Yukawa matrices, we show that only two sets of predictions, $\frac{y_\tau}{y_b}=\frac{3}{2}$, $\frac{y_\mu}{y_s}=\frac{9}{2}$ and $\frac{y_\tau}{y_b}=2$, $\frac{y_\mu}{y_s}=6$ are viable. To further investigate both options, we extend the minimal scenarios to two "toy models", including the 1st family of charged fermions, and calculate the models' predictions, e.g. for the nucleon decay rates and for the masses of the light relics that are potentially within reach of colliders.