Minimal $SU(5)$ GUTs with vectorlike fermions

TL;DR

This paper identifies the minimal renormalizable SU(5) GUT model with vectorlike fermions and specific Higgs representations that can explain fermion masses, neutrino masses, and matter-antimatter asymmetry, and discusses its testability.

Contribution

It proposes a minimal SU(5) GUT model with vectorlike fermions and Higgs fields that is highly predictive and experimentally testable.

Findings

Model accommodates correct fermion and neutrino masses.

Model can address matter-antimatter asymmetry.

Proton decay experiments will test the model's predictions.

Abstract

In this work, we attempt to answer the question, "What is the minimal viable renormalizable $SU(5)$ GUT with representations no higher than adjoints?". We find that an $SU(5)$ model with a pair of vectorlike fermions $5_F+\overline{5}_F$, as well as two copies of $15_H$ Higgs fields, is the minimal candidate that accommodates for correct charged fermion and neutrino masses and can also address the matter-antimatter asymmetry of the universe. Our results show that the presented model is highly predictive and will be fully tested by a combination of upcoming proton decay experiments, collider searches, and low-energy experiments in search of flavor violations. Moreover, we also entertain the possibility of adding a pair of vectorlike fermions $10_F+\overline{10}_F$ or $15_F+\overline{15}_F$ (instead of a $5_F+\overline{5}_F$). Our study reveals that the entire parameter space of these two models, even with minimal particle content, cannot be fully probed due to possible longer proton lifetime beyond the reach of Hyper-Kamiokande.