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.

我们提出了标准模型 (SM)的非通用 U(1) _X规范扩展和额外的 Peccei-Quinn (PQ) 全局对称性，以研究质量等级和强 CP 问题。该方案使我们能够区分费米子家族并生成 SM 粒子的费米子质谱。对称性破缺由两个标量希格斯双峰和两个标量希格斯单峰执行，其中一个具有轴子，结果证明是冷暗物质的候选者。奇异扇区由一个类似向上的T和两个类似向下的J ^1,2重夸克、两个重带电轻子、每个家族一个额外的右手中微子和一个不可见的轴子a 组成。 . 此外，与 PQ 对称性破坏相关的大能量标度赋予右手中微子质量，使得活动中微子由于跷跷板机制而获得 eV 质量值。另一方面，从非线性有效拉格朗日算子，考虑下夸克和带电轻子随轴子的风味变化。