A Lattice Chiral Gauge Theory with Multifermion Couplings

Analyzing an $S{U}_L(2)$-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 ${\psi }_L^i$ can be defined. This is not in agreement with the general belief of the failure of theories so constructed .