2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147813Analyzing 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 $ψ_R$ is free mode owing to the $ψ_R$-shift-symmetry, the chiral continuum theory of $ψ^i_L$ can be defined. This is not in agreement with the general belief of the failure of theories so constructed .9 pages, latex and three figures upon request. eqs. (10) and (11) have been changed into correct propagators instead of inverse propagatorsHigh Energy Physics - LatticeHigh Energy Physics - PhenomenologyHigh Energy Physics - Theorytext