A possible scaling region of chiral fermions on a lattice

Abstract

We present the details of analyzing an $S{U}_L(2)\otimes U_R(1)$ chiral theory with multifermion couplings on a lattice. An existence of a possible scaling region in the phase space of multifermion couplings for defining the continuum limit of chiral fermions is advocated. In this scaling region, no spontaneous symmetry breaking occurs; the ``spectator'' fermion ${\psi }_R(x)$ is a free mode and decoupled; doublers are decoupled as massive Dirac fermions consistently with the $S{U}_L(2)\otimes U_R(1)$ chiral symmetry, whereas the normal mode of ${\psi }_L^i(x)$ 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.

Comments: 32 pages, Latex and 5 figures, to appear in Nucl. Phys. B