# A Lattice Chiral Gauge Theory with Multifermion Couplings

## TL;DR

This paper explores a lattice chiral gauge theory with multifermion couplings, identifying a potential scaling region where doublers decouple and a chiral continuum theory can be formulated, challenging previous beliefs.

## Contribution

It demonstrates a possible way to define a chiral continuum theory on the lattice with multifermion couplings, contrary to prior assumptions.

## Key findings

- Doublers acquire chiral-invariant masses and decouple.
- The $ ext{psi}_R$ mode remains free due to shift-symmetry.
- A consistent chiral continuum theory can be constructed.

## Abstract

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 .