Question of Peccei-Quinn symmetry and quark masses in the economical 3-3-1 model

TL;DR

The paper investigates the Peccei-Quinn symmetry in the minimal 3-3-1 model, showing all such symmetries are broken and that some quarks gain mass at one-loop, with axions being gauged away.

Contribution

It demonstrates the complete breaking of U(1) symmetries like Peccei-Quinn in the minimal 3-3-1 model and analyzes the implications for quark masses and axions.

Findings

All U(1) symmetries are broken by scalars.

Some quarks are massless at tree-level but gain mass at one-loop.

Axions are gauged away as Goldstone bosons.

Abstract

We show that there is an infinite number of U(1) symmetries like Peccei-Quinn symmetry in the 3-3-1 model with minimal scalar sector---two scalar triplets. Moreover, all of them are completely broken due to the model's scalars by themselves (notice that these scalars as known have been often used to break the gauge symmetry and generating the masses for the model's particles). There is no any residual Peccei-Quinn symmetry. Because of the minimal scalar content there are some quarks that are massless at tree-level, but they can get consistent mass contributions at one-loop due to this fact. Interestingly, axions as associated with the mentioned U(1)s breaking (including Majoron due to lepton-charge breaking) are all gauged away because they are also the Goldstone bosons responsible for the gauge symmetry breaking as usual.