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

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.

Axion dark matter in a 3−3−1 model

“…In particular, in Ref. [20] a gravitationally stable PQ mechanism for the model considered here is successfully implemented. We are going to review its main results for completeness.…”

“…However, it is a visible axion because the Uð1Þ PQ symmetry is actually broken by v ρ 0 2 , which is upper bounded by the value of v SM ≃ 246 GeV, as shown in Refs. [20,37]. Hence, this scenario is ruled out [42].…”

“…In general, the implementation of the PQ mechanism in the 3 − 3 − 1 models is relatively straightforward [20,28]. In particular, in Ref.…”

“…Thus, a mechanism to stabilize the axion solution has to be introduced. As usual, the entire Lagrangian is considered to be invariant under a Z D discrete gauge symmetry (anomaly free) [20,28,[45][46][47][48] and, in addition, this symmetry is supposed to induce the Uð1Þ PQ symmetry. For Z D≥10 it is found that all effective operators of the form…”

“…The PecceiQuinn symmetry, usually introduced to solve the strong CP problem, can be introduced in a natural way [20]. In this work we consider a version of a 3 − 3 − 1 model where a gravity stable PQ mechanism can be implemented.…”