Slavnov-Taylor parameterization of Yang-Mills theory with massive fermions in the presence of singlet axial-vector currents

TL;DR

This paper investigates the all-order restoration of Slavnov-Taylor identities in Yang-Mills theory with massive fermions and axial-vector currents, providing explicit formulas and a systematic normalization approach.

Contribution

It introduces a Slavnov-Taylor parameterization method that simplifies higher-order identities and derives explicit formulas for the symmetric vertex functional.

Findings

Explicit all-order formulas for the symmetric vertex functional.

A set of normalization conditions simplifying ST identities.

Reduction of algebraic complexity in higher-order calculations.

Abstract

We study the all-order restoration of the Slavnov-Taylor (ST) identities for Yang-Mills theory with massive fermions in the presence of singlet axial-vector currents. By making use of the ST parameterization of the symmetric quantum effective action a natural set of normalization conditions is derived allowing to reduce the algebraic complexity of higher orders ST identities up to a homogeneous linear problem. Explicit formulas for the action-like part of the symmetric vertex functional are given to all orders in the loop expansion.