A bstract We present a complete Lagrangian describing axion interactions with pseudoscalar and (axial-)vector mesons within the three light-flavor quark framework. This formulation incorporates both the standard chiral Lagrangian and the full Wess-Zumino-Witten (WZW) term. By including instanton effects associated with the anomalous U(1) A symmetry, we demonstrate that physical observables remain invariant under arbitrary chiral phase rotations of the quark fields. This comprehensive Lagrangian provides a robust and consistent framework for exploring axion phenomenology through its interactions with mesons and gauge bosons. As a demonstration, we compute the decay widths of GeV-scale axions into various mesonic final states for several benchmark axion models.
Bai et al. (Tue,) studied this question.