  In this paper, we discuss the construction of Effective Field Theories (EFTs)
in which a chiral fermion, charged under both gauge and global symmetries, is
integrated out. Inspired by typical axion models, these symmetries can be
spontaneously broken, and the global ones might also be anomalous. In this
context, particular emphasis is laid on the derivative couplings of the
Goldstone bosons to the fermions, as these lead to severe divergences and
ambiguities when building the EFT. We show how to precisely solve these
difficulties within the path integral formalism, by adapting the anomalous Ward
identities to the EFT context. Our results are very generic, and when applied
to axion models, they reproduce the non-intuitive couplings between the massive
SM gauge fields and the axion. Altogether, this provides an efficient
formalism, paving the way for a systematic and consistent methodology to build
entire EFTs involving anomalous symmetries, as required for axion or ALP
searches.
