Natural PQ symmetry in the 3-3-1 model with a minimal scalar sector

TL;DR

This paper explores implementing the Peccei-Quinn symmetry in a minimal 3-3-1 model to address the strong CP problem, proposing extensions with scalar singlets and discrete symmetries to produce a viable invisible axion.

Contribution

It demonstrates how adding a scalar singlet and discrete gauge symmetry can realize an invisible axion in the 3-3-1 model, ensuring anomaly cancellation and quantum gravitational protection.

Findings

Original model has a PQ-like symmetry but no axion due to unbroken subgroup.

Adding a third scalar triplet removes massless quarks but yields a visible axion.

Extension with scalar singlet and Z_N symmetry produces a realistic, invisible axion.

Abstract

In the framework of a 3-3-1 model with a minimal scalar sector we make a detailed study concerning the implementation of the PQ symmetry in order to solve the strong CP problem. For the original version of the model, with only two scalar triplets, we show that the entire Lagrangian is invariant under a PQ-like symmetry but no axion is produced since an U(1) subgroup remains unbroken. Although in this case the strong CP problem can still be solved, the solution is largely disfavored since three quark states are left massless to all orders in perturbation theory. The addition of a third scalar triplet removes the massless quark states but the resulting axion is visible. In order to become realistic the model must be extended to account for massive quarks and invisible axion. We show that the addition of a scalar singlet together with a Z_N discrete gauge symmetry can successfully accomplish these tasks and protect the axion field against quantum gravitational effects. To make sure that the protecting discrete gauge symmetry is anomaly free we use a discrete version of the Green-Schwarz mechanism.