Accidental symmetries and massless quarks in the economical 3-3-1 model

TL;DR

This paper investigates the economical 3-3-1 model's ability to generate realistic quark masses, revealing an accidental symmetry that prevents some quarks from acquiring mass, thus challenging the model's viability.

Contribution

It identifies an accidental axial symmetry in the minimal scalar sector of the economical 3-3-1 model that inhibits certain quarks from gaining mass, and assesses non-perturbative effects on this issue.

Findings

Some quarks remain massless at all orders in perturbation theory.

Non-perturbative effects are insufficient to generate realistic quark masses.

The model requires modifications to be a viable description of electroweak interactions.

Abstract

In the framework of a 3-3-1 model with a minimal scalar sector, known as the economical 3-3-1 model, we study its capabilities of generating realistic quark masses. After a detailed study of the symmetries of the model, before and after the spontaneous symmetry breaking, we find a remaining axial symmetry that prevents some quarks to gain mass at all orders in perturbation theory. Since this accidental symmetry is anomalous, we also consider briefly the possibility to generate their masses for non-perturbative effects. However, we find that non-perturbative effects are not enough to generate the measured masses for that three massless quarks. Hence, these results imply that the economical 3-3-1 model is not a realistic description of the electroweak interaction and it has to be modified.