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 \psi_R(x) is free mode, whereas the normal mode of \psi^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