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We present a further study of the dynamics of high-dimension fermion operators attributed to the theoretical inconsistency of the fundamental cutoff (quantum gravity) and the parity-violating gauge symmetry of the standard model. Studying the phase transition from a symmetry-breaking phase to a strong-coupling symmetric phase and the β-function behavior in terms of four-fermion coupling strength, we discuss the critical transition point as a ultraviolet-stable fixed point where a quantum field theory preserving the standard model gauge symmetry with composite particles can be realized. The form-factors and masses of composite particles at TeV scales are estimated by extrapolating the solution of renormalization-group equations from the infrared-stable fixed point where the quantum field theory of standard model is realized and its phenomenology including Higgs mass has been experimentally determined. We discuss the probability of composite-particle formation and decay that could be experimentally verified in the LHC by measuring the invariant mass of relevant final states and their peculiar kinetic distributions.