The absence of the 4$\psi$ divergence in noncommutative chiral models

TL;DR

This paper demonstrates that in noncommutative chiral gauge theories, the 4-fermion vertices are finite, contrasting with previous models where such vertices were divergent and nonrenormalizable, indicating improved theoretical consistency.

Contribution

It shows that noncommutative chiral gauge theories have finite 4-fermion vertices, providing a significant advancement over prior models with divergent vertices.

Findings

4-fermion vertices are finite in noncommutative chiral models

Previous Dirac fermion models had divergent 4-fermion vertices

Finite vertices suggest better renormalizability in these theories

Abstract

In this paper we show that in the noncommutative chiral gauge theories the 4-fermion vertices are finite. The $4\psi$-vertices appear in linear order in quantization of the $\theta$-expanded noncommutative gauge theories; in all previously considered models, based on Dirac fermions, the $4\psi$-vertices were divergent and nonrenormalizable.