A Lattice Chiral Gauge Theory with Multifermion Couplings

Analyzing an $SU_L(2)$-chiral gauge theory with external multifermion couplings, we find a possible scaling region where doublers decouple by acquiring chiral-invariant masses and $\psi_R$ is free mode owing to the $\psi_R$-shift-symmetry, the chiral continuum theory of $\psi^i_L$ can be defined. This is not in agreement with the general belief of the failure of theories so constructed .