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

Understand

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.