The anomalous case of axion EFTs and massive chiral gauge fields

A bstract We study axion effective field theories (EFTs), with a focus on couplings to massive chiral gauge fields. investigate the EFT interactions that participate in processes an and two bosons, we show that, when fields are present, such do not entirely originate from usual anomalous terms. illustrate this both at level by matching UV-complete theories. In order assess consistency of Peccei-Quinn (PQ) anomaly matching, it is useful introduce auxiliary, non-dynamical associated PQ symmetry. When applied case Standard Model (SM) electroweak sector, our results imply anomaly-based sum rules between violated matter integrated out, which constitutes smoking gun latter. As illustration, extension SM, containing arising extended Higgs sector heavy fermionic obtains most its mass coupling doublets. viability SM through precision tests, bounds rates direct searches for charged matter. At energies below new fermions, model matches onto where symmetry non-linearly realised.