The Standard Model and its Generalizations in Epstein-Glaser Approach to Renormalization Theory II: the Fermion Sector and the Axial Anomaly

TL;DR

This paper extends the Epstein-Glaser approach to non-Abelian gauge theories with fermions, analyzing consistency conditions up to third order and deriving anomaly cancellation criteria.

Contribution

It provides a detailed third-order perturbative analysis of the fermion sector and axial anomaly cancellation within Epstein-Glaser renormalization.

Findings

Group theoretical relations in second order

Representation property of interaction coefficients

Condition for axial anomaly cancellation

Abstract

We complete our study of non-Abelian gauge theories in the framework of Epstein-Glaser approach to renormalization theory including in the model an arbitrary number of Dirac Fermions. We consider the consistency of the model up to the third order of the perturbation theory. In the second order we obtain pure group theoretical relations expressing a representation property of the numerical coefficients appearing in the left and right handed components of the interaction Lagrangian. In the third order of the perturbation theory we obtain the the condition of cancellation of the axial anomaly.