Do anomalies break the momentum routing invariance?

TL;DR

This paper demonstrates that under gauge invariance, chiral and scale anomalies are independent of momentum routing choices, challenging the common association of anomalies with routing invariance breaking, and applies this to Lorentz-violating QED.

Contribution

It shows that anomalies can be momentum routing invariant if gauge invariance is assumed, providing a new perspective on the relationship between anomalies and routing invariance.

Findings

Anomalies are independent of momentum routing when gauge invariance is maintained.

Chiral and scale anomalies do not necessarily break momentum routing invariance.

Application to Lorentz-violating QED reveals symmetry breaking in Ward identities.

Abstract

The diagrammatic computation of anomalies is usually associated with the breaking of the momentum routing invariance. This is because the momentum routing is usually chosen to fulfill the desired Ward identity. In the case of the chiral anomaly, the momentum routing is chosen in order to fulfill the gauge Ward identity and break the chiral Ward identity. Although the chiral anomaly is physical because it is associated with the pion decay into two photons, this does not necessarily mean that the momentum routing invariance is broken because the momentum routing was chosen in the computation of the anomaly. The reciprocal is not true, {\it i. e.} anomalies do not imply in momentum routing invariance breaking. In this work, we show that if gauge invariance is assumed, the chiral and the scale anomalies are independent of the momentum routing chosen and as a result they are momentum routing invariant. This idea is applied to a QED with non-minimal CPT and Lorentz violation, where momentum routing invariance is used to find out what symmetry is broken in the Ward identities.