  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.
