A possible scaling region of chiral fermions on a lattice

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We present the details of analyzing an SUₗ(2)⊗ Uᵣ(1) chiral theory with multifermion couplings on a lattice. An existence of a possible scaling region in the phase space of multifermion couplings for defining the continuum limit of chiral fermions is advocated. In this scaling region, no spontaneous symmetry breaking occurs; the ``spectator'' fermion ψᵣ(x) is a free mode and decoupled; doublers are decoupled as massive Dirac fermions consistently with the SUₗ(2)⊗ Uᵣ(1) chiral symmetry, whereas the normal mode of ψₗⁱ(x) is plausibly speculated to be chiral in the continuum limit. This is not in agreement with the general belief of the definite failure of theories so constructed.