We study axion effective field theories (EFTs), with a focus on axion couplings to massive chiral gauge fields. We investigate the EFT operators that couple an axion with two gauge bosons, and we show that, when massive chiral gauge fields are present, such interactions do not entirely originate from the usual anomalous EFT terms. The lack of relation between couplings and anomalies is caused by the presence of chiral fermions in the UV. For the case of an axion interacting with the Standard Model (SM) W and Z bosons, we show how anomaly-based sum rules in the IR one can detect whether the axion couplings are given or not by anomalies. Furthermore, the violation of those sum rules becomes a signal of heavy chiral matter. As an illustration, we study a UV-complete chiral extension of the SM, containing an axion arising from an extended Higgs sector and heavy fermionic matter that obtains most of its mass by coupling to the Higgs doublets. We assess the viability of such a SM extension through electroweak precision tests, bounds on Higgs rates and direct searches for heavy charged matter. We show that at energies below the
mass of the new chiral fermions, the model matches onto an EFT where the electroweak gauge symmetry is non-linearly realised.