Abstract

The axion couplings to SM gauge bosons are derived in various models, and shown to always arise entirely from non-anomalous fermion loops. They are thus independent of the anomaly structure of the model. This fact is without consequence for vector gauge interactions like QCD and QED, but has a major impact for chiral gauge theories. For example, in the DFSZ axion model, the couplings of axions to electroweak gauge bosons do not follow the pattern expected from chiral anomalies, as we prove by an explicit calculation. The reason for this mismatch is traced back to triangle Feynman diagrams sensitive to the anomalous breaking of the vector Ward identity, and is ultimately related to the conservation of baryon and lepton numbers. Though our analyses are entirely done for true axion models, this observation could have important consequences for axion-like particle searches.

Highlights

  • Axions have been around for more than 40 years, and even if the simplest models have been ruled out, they still remain probably the best solution for the strong C P problem of the Standard Model

  • We turn to the Peccei-Quinn axion model in Sect. 4, derive the correct axion couplings to gauge bosons, and identify precisely where the naive procedure leading to Eq (2) fails

  • We started from a simplified toy model, and extended the discussions to the KSVZ axion [13,14], the original PQ axion [1,2], and the DFSZ axion [26,27]

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Summary

Introduction

Axions have been around for more than 40 years, and even if the simplest models have been ruled out, they still remain probably the best solution for the strong C P problem of the Standard Model. The true processes driving these decays are not anomalous and their relative strengths do not follow the pattern expected from Eq (2) The reason for this mismatch between the anomalous couplings and the true axion couplings will be traced to the existence of additional anomalies, occurring only for chiral theories. It is necessary to go beyond simple regularization procedures to be able to locate the anomaly of the AV V triangle in one of the vector Ward identities or to break explicitly the Bose symmetry of the A A A triangle Equipped with these results, we turn to the Peccei-Quinn axion model, derive the correct axion couplings to gauge bosons, and identify precisely where the naive procedure leading to Eq (2) fails.

An axionic toy model
Linear representation
Polar representation
On the consistent use of anomalies
The Peccei-Quinn axion and its couplings
Matching the polar and linear representations
Impact of heavy neutrinos
Application to the DFSZ axion model
Anomaly cancellation in generic axion models
Conclusion and perspective
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