Axions and Anomaly-Mediated Interactions: The Green-Schwarz and Wess-Zumino Vertices at Higher Orders and g-2 of the muon

TL;DR

This paper explores anomaly cancellation mechanisms in quantum field theory, focusing on the Green-Schwarz approach and its implications for muon g-2 and muonium hyperfine splitting, including potential effects of anomalous Z' and axion-like particles.

Contribution

It demonstrates the realization of the Green-Schwarz anomaly cancellation at the field theory level using transverse invariant amplitudes and analyzes its impact on muon g-2 and related processes.

Findings

Green-Schwarz mechanism restores Ward identities at higher orders.

Analysis of the role of GS and Wess-Zumino vertices in muon g-2.

Potential contributions of anomalous Z' and axion-like particles to observables.

Abstract

We present a study of the mechanism of anomaly cancellation using only transverse invariant amplitudes on anomaly diagrams at higher perturbative orders. The method is the realization of the Green-Schwarz (GS) mechanism at field theory level, which restores the Ward identities by a subtraction of the anomaly pole. Some of the properties of the GS vertex are analyzed both in the context of unitarity and of the organization of the related perturbative expansion. We investigate the role played by the GS and the Wess-Zumino vertices in the anomalous magnetic moment of the muon and in the hyperfine splitting of muonium, which are processes that can be accompanied by the exchange of a virtual anomalous extra Z-prime and an axion-like particle.