ON THE HIGHER-LOOP CONTRIBUTIONS TO THE AXIAL ANOMALY

TL;DR

This paper investigates how higher-loop calculations affect the axial anomaly, revealing that the results depend on the calculation order and method used, with implications for nonperturbative and perturbative approaches.

Contribution

It introduces a new method to reexamine higher-loop contributions to the axial anomaly and highlights the dependence of results on calculation order and approach.

Findings

Nonperturbative Fujikawa method yields nonzero contributions when calculated first.

Perturbative Feynman diagram method results depend on calculation order, leading to uncertainty.

Calculation order influences whether the axial anomaly receives a nonzero correction.

Abstract

The problem of the higher-loop contributions to the axial anomaly is reexamined by a new method. We demonstrate that these contributions depend on the order of the calculations. If the divergence of the axial current by nonperturbative Fujikawa method is calculated first and then average it over the photon field in the presence of an external photon source, a nonzero contribution is obtained. However perturbative Feynman diagram method has an uncertainty. Depending on the order of the calculations above mentioned or zero results are obtained.