Hierarchy spectrum of SM fermions: from top quark to electron neutrino

A bstract In the SM gauge symmetries and fermion content of neutrinos, charged leptons and quarks, we study the effective four-fermion operators of Einstein-Cartan type and their contributions to the Schwinger-Dyson equations of fermion self-energy functions. The study is motivated by the speculation that these four-fermion operators are probably originated due to the quantum gravity, which provides the natural regularization for chiral-symmetric gauge field theories. In the chiral-gauge symmetry breaking phase, as to achieve the energetically favorable ground state, only the top-quark mass is generated via the spontaneous symmetry breaking, and other fermion masses are generated via the explicit symmetry breaking induced by the top-quark mass, four-fermion interactions and fermion-flavor mixing matrices. A phase transition from the symmetry breaking phase to the chiral-gauge symmetric phase at TeV scale occurs and the drastically fine-tuning problem can be resolved. In the infrared fixed-point domain of the four-fermion coupling for the SM at low energies, we qualitatively obtain the hierarchy patterns of the SM fermion Dirac masses, Yukawa couplings and family-flavor mixing matrices with three additional right-handed neutrinos ν R f . Large Majorana masses and lepton-number symmetry breaking are originated by the four-fermion interactions among ν R f and their left-handed conjugated fields ν R fc . Light masses of gauged Majorana neutrinos in the normal hierarchy (10 −5 − 10 −2 eV) are obtained consistently with neutrino oscillations. We present some discussions on the composite Higgs phenomenology and forward-backward asymmetry of t t ¯ -production, as well as remarks on the candidates of light and heavy dark matter particles (fermions, scalar and pseudoscalar bosons).