  In the fermion content and gauge symmetry of the standard model (SM), we
study the four-fermion operators in the torsion-free Einstein-Cartan theory.
The collider signatures of irrelevant operators are suppressed by the
high-energy cutoff (torsion-field mass) $\Lambda$, and cannot be experimentally
accessible at TeV scales. Whereas the dynamics of relevant operators accounts
for (i) the SM symmetry-breaking in the domain of infrared-stable fixed point
with the energy scale $v\approx 239.5$ GeV and (ii) composite Dirac particles
restoring the SM symmetry in the domain of ultraviolet-stable fixed point with
the energy scale ${\mathcal E}\gtrsim 5$ TeV. To search for the resonant
phenomena of composite Dirac particles with peculiar kinematic distributions in
final states, we discuss possible high-energy processes: multi-jets and
dilepton Drell-Yan process in LHC $p\,p$ collisions, the resonant cross-section
in $e^-e^+$ collisions annihilating to hadrons and deep inelastic lepton-hadron
$e^-\,p$ scatterings. To search for the nonresonant phenomena due to the
form-factor of Higgs boson, we calculate the variation of Higgs-boson
production and decay rate with the CM energy in LHC. We also present the
discussions on four-fermion operators in the lepton sector and the mass-squared
differences for neutrino oscillations in short baseline experiments.
