On the electromagnetic hadron current derived from the gauged Wess-Zumino-Witten action

TL;DR

This paper critiques a recent study on the electromagnetic properties of hadrons derived from the gauged Wess-Zumino-Witten action, highlighting issues with current conservation that affect conclusions about neutron charge in magnetic fields.

Contribution

It identifies a fundamental problem in the gauged Wess-Zumino-Witten action related to non-conservation of the source current, impacting previous results on hadron electromagnetic properties.

Findings

The gauged Wess-Zumino-Witten action leads to non-conservation of the source current.

This non-conservation affects the validity of the Gell-Mann-Nishijima relation in electromagnetic fields.

Previous conclusions about neutron charge in magnetic fields are called into question.

Abstract

In a recent paper, based on the Skyrme model with the Wess-Zumino-Witten term including electromagnetism, Eto et al. pointed out an intriguing possibility that the Gell-Mann-Nishijima relation is corrected under the presence of back-ground electromagnetic fields, thereby being led to the conclusion that even a neutron acquires non-zero net charge in external magnetic fields. We point out that this remarkable conclusion is inseparably connected with an unwelcome feature of the gauged Wess-Zumino-Witten action, i.e. the non-conservation of source current of Maxwell equation.