Possible origin of fermion generations

In the model with the spontaneous breaking of chiral gauge symmetry, the vacuum structure for the pair of Higgs fields can cause the appearance of two generations of fermions. Two generations of fermions, say, electron and muon, have identical properties with respect to a gauge interaction and differ by the mass values yet. In the Standard Model [1] the masses are caused by the spontaneous breaking of gauge symmetry [2], so that the difference between the masses corresponds to the variation of Yukawa constants for the interaction between the fermions and Higgs fields. The values of those constants and the origin for the copying of generations are the problems, which are studied beyond the Standard Model. Consider the chiral interaction of dirac spinor with the abelian gauge field Aμ and Higgs field h L = ψ̄Rpμγ ψR + ψ̄L(pμ − eAμ)γψL + gψ̄RψLh+ gψ̄LψRh + LGF + L0(h,A), (1) where LGF is the lagrangian of free gauge field (with a possible introduction of term fixing the gauge and the corresponding lagrangian for the Faddeev–Popov ghosts), L0 is the lagrangian of Higgs field with a self-action and the gauge interaction, g is the Yukawa constant. At the spontaneous breaking of symmetry, the vacuum expectation of Higgs field is not equal to zero 〈0|h|0〉 = ηe. (2) In the unitary gauge φ = 0, the fermion becomes massive, so m = gη Lm = gη(ψ̄RψL + ψ̄LψR). (3) In the arbitrary gauge, it is convenient to use the method of auxiliary fields, so that, for example, fL = 1 √ 2 (