  We present a consistent derivation of the complete Wess-Zumino-Witten
interactions of axions, including the counter-term necessary to guarantee the
gauge invariance of the Standard Model. By treating the derivative of the axion
field as a background gauge field and incorporating auxiliary chiral rotation
phases, we ensure consistency in the axion-interaction Lagrangian. This
approach allows us to derive basis-independent physical interactions of axions
with gauge bosons and vector mesons. As an example, we explore the interaction
of $a$-$\omega$-$\gamma$ to illustrate the potential for searching for
axion-like particles at colliders.
