How to treat $\gamma_5$

TL;DR

The paper introduces a method for renormalized perturbation calculations in gauge theories with chiral fermions, emphasizing Ward-Takahashi identities over dimensional regularization, and demonstrates it by showing the vanishing of the triangular anomaly.

Contribution

It proposes a novel approach focusing on Ward-Takahashi identities for handling $ ext{γ}_5$ in chiral gauge theories, avoiding traditional regularization complications.

Findings

Anomaly amplitude calculated without regularization vanishes.

Method successfully handles fermion amplitudes involving $ ext{γ}_5$.

Demonstrated on Abelian-Higgs theory with chiral fermions.

Abstract

We present a method to perform renormalized perturbation calculation in gauge theories with chiral fermions. We find it proper to focus directly on the Ward-Takahashi identities, relegating dimensional regularization into a supplementary and secondary role. We show with the example of the Abelian-Higgs theory how to handle amplitudes involving fermions, particularly how to handle the matrix $\gamma_5$. As a demonstration of our method of renormalization, we evaluate the radiative corrections of the triangular anomaly in the Abelian-Higgs theory with appropriate number of chiral fermions. This anomaly amplitude is calculated without any regularization and is found to vanish.