Wess-Zumino-Witten Interactions of Axions: Three-Flavor

Abstract

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.

25 pages, 4 figures, 1 table, typo corrected, accompanying Mathematica notebook is available on https://github.com/nun3366/Axion-WZW-3