  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 that
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 $\nu^f_R$. Large Majorana masses and lepton-symmetry
breaking are originated by the four-fermion interactions among $\nu^f_R$ and
their left-handed conjugated fields $\nu^{fc}_R$. 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 $t\bar
t$-production, as well as remarks on the candidates of light and heavy dark
matter particles (fermions, scalar and pseudoscalar bosons).
