We propose a non-universal U(1) X gauge extension to the standard model (SM) and an additional Peccei–Quinn (PQ) global symmetry to study the mass hierarchy and strong CP problem. The scheme allows us to distinguish among fermion families and to generate the fermionic mass spectrum of particles of the SM. The symmetry breaking is performed by two scalar Higgs doublets and two scalar Higgs singlets, where one of these has the axion which turns out to be a candidate for cold dark matter. The exotic sector is composed by one up-like T and two down-like J 1,2 heavy quarks, two heavy charged leptons , one additional right-handed neutrino per family , and an invisible axion a. In addition, the large energy scale associated to the breaking of the PQ-symmetry gives masses to the right-handed neutrinos in such a way that the active neutrinos acquire eV-mass values due to the see-saw mechanism. On the other hand, from the non-linear effective Lagrangian, the flavour changing of the down quarks and charged leptons with the axion are considered.

We present a non-universal U (1) X gauge extension and an additional global Peccei-Quinn (PQ) symmetry to the Standard Model (SM). The scheme proposed allows us to distinguish among fermion families and to generate the correct ansatz of mass matrices to obtain the fermionic mass spectrum in SM. The symmetry breakdown is performed by two scalar Higgs doublets and two scalar singlets, where one of these has the excitation associated with the axion which turns out to be a candidate for dark matter. The exotic sector is composed of an invisible axion a, one up-type T and two down-type J 1,2 heavy quarks, two heavy charged leptons E, E and one additional right-handed ν e,µ,τ R neutrino per family. In addition, the large energy scale associated with the spontaneously breaking of the PQ-symmetry provides a solution to the strong CP-problem, also giving masses to the right-handed neutrinos in such manner that the active neutrinos acquire eV -mass values due to the see-saw mechanism.

We propose a non-universal U (1) X extension to the Standard Model with three families and an additional global anomala Peccei-Quinn (PQ) symmetry. The breaking of the former allows us to give masses to the exotic fermionic sector and the later generates the necessary zeros in the mass matrices to explain the fermionic mass hierarchy. In addition, the large energy scale associated with the spontaneously breaking (SSB) of the PQ symmetry provides a solution to the strong CP-problem and an axion that could be a possible dark matter candidate. Also, the SSB allows to generate right-handed neutrino masses, so the active neutrinos acquire eV -mass values due to the see-saw mechanism implementation.