# A possible scaling region of chiral fermions on a lattice

## TL;DR

This paper explores a lattice approach to chiral fermions, proposing a scaling region where continuum limits can be achieved without symmetry breaking, decoupling doublers, and maintaining chiral symmetry, challenging previous beliefs.

## Contribution

It introduces a potential scaling region in lattice chiral theories where fermions behave correctly in the continuum, contrary to prior assumptions.

## Key findings

- A scaling region exists with decoupled doublers and free spectator fermions.
- No spontaneous symmetry breaking occurs in this region.
- Normal mode of $ ext{psi}_L^i(x)$ is plausibly chiral in the continuum.

## Abstract

We present the details of analyzing an $SU_L(2)\otimes U_R(1)$ 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 $SU_L(2)\otimes U_R(1)$ 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.