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A Lattice Chiral Theory with Multifermion Couplings

Analyzing an $SU_L(2)\otimes U_R(1)$ chiral theory with multifermion couplings on a lattice, we find a possible region in the phase space of multifermion couplings, where no spontaneous symmetry breaking occurs, doublers are decoupled as massive Dirac fermions consistently with the $SU_L(2)\otimes U_R(1)$ chiral symmetry, the ``spectator'' fermion $ψ_R(x)$ is free mode, whereas the normal mode of $ψ^i_L(x)$ 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.