Do Anomalies Break Momentum Routing Invariance?

TL;DR

This paper demonstrates that the chiral anomaly is actually invariant under momentum routing, clarifying its theoretical nature and implications for symmetry breaking in CPT and Lorentz-violating quantum electrodynamics.

Contribution

It proves the momentum-routing invariance of the chiral anomaly, impacting the understanding of symmetry breaking in theories without experimental routing guidance.

Findings

Chiral anomaly is momentum-routing invariant.

Implications for symmetry breaking in CPT and Lorentz-violating theories.

Clarifies the theoretical basis of anomaly calculations.

Abstract

The diagrammatic computation of the chiral anomaly is associated with momentum-routing invariance breaking. This happens because the momentum routing in the internal lines of a loop diagram is chosen such that the gauge Ward identities hold and the chiral Ward identity is broken by the finite term measured in the pion decay into two photons. Since the latter is observable, it seems that there is a preferred momentum routing set by experiments. However, it is shown in this work that the chiral anomaly is momentum-routing invariant. This idea is specially important for situations in which there are no experiments yet to decide on the momentum routing, like in supersymmetric theories and in frameworks with CPT and Lorentz violation. Therefore, we resort to momentum-routing invariance to find out what symmetry is broken in a nonminimal CPT- and Lorentz-violating version of quantum electrodynamics.