Axial Vector Coupling and Chiral Anomaly in the Spectral Quark Model

TL;DR

This paper investigates the axial vector coupling and chiral anomaly within the Spectral Quark Model, deriving a non-local axial vertex form that ensures anomaly consistency and finiteness in a finite chiral quark framework.

Contribution

It introduces a non-local axial vertex form in the Spectral Quark Model that maintains anomaly properties and finiteness, advancing understanding of chiral symmetry breaking.

Findings

Derived the non-local axial vertex compatible with a non-zero axial coupling.

Computed the triangle anomaly within the model.

Showed the spectral mass dependence is essential for anomaly consistency.

Abstract

We studied the Adler-Bardeen-Bell-Jackiw anomaly in the context of a finite chiral quark model known as the Spectral Quark Model. Within this model, we obtain the general non-local form of the axial vertex compatible with a non vanishing axial coupling, in the chiral limit. The triangle anomaly is computed and we show that the obtained dependence of the axial vertex with the spectral mass is necessary to ensure both finiteness and the correct violation of the chiral Ward-Takahashi identity.