On axion properties in the 3-3-1 model with $U(1)_{B-L}$ and Peccei-Quinn symmetries

Abstract

The Peccei-Quinn ($PQ$) mechanism is applied to the $\mathrm{SU(3)_c \otimes SU(3)_L \otimes U(1)_X}$ model with $U(1)_{B-L}$ symmetry. The structures in the $PQ$ charges of all fermions and scalar fields in the model are investigated by applying the invariant condition under the symmetry group transformations on all Yukawa interaction terms. All defined $PQ$ charges depend just on the $PQ$ charge of the complex singlet scalar field which causes the $U(1)_{PQ}$ spontaneous symmetry breaking in the model. The mixing and mass hierarchy in the scalar sector of the model are studied in detail. The constraints on the $PQ$ charges and imaginary parts of scalars are derived. It is shown that only neutral scalar fields carry $PQ$ charges while charged ones do not. As the result, the physical state of axion which obeys the invariance under $\mathrm{SU(3)_L \otimes U(1)_X}$ and $PQ$ transformations, is a linear combination of all imaginary parts associated with the $X$ charges of scalar triplets. The anomaly axion-fermion interactions are presented. Explicit expressions for axion and light Standard Model (SM) like Higgs boson are shown. Mass of the axion and its coupling to photon are derived. The decays of the SM-like Higgs boson into a pair of either charged leptons or bottom quarks are presented and constrained. The triple-coupling axion-photon-photon arisen from kinetic terms of scalar fields is derived. Hence, the decay of axion into a pair of photons consists of two parts: the first is related to the anomaly coupling and the second is come from kinetic terms of scalar fields. The result shows that the new contribution can be helpful for searching axion with mass at hundred keV.